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This report describes the current version of the Why System, a script-based Socratic tutor which uses tutoring strategies formulated as production rules. The current system is capable of carrying on a dialogue about the factors influencing rainfall by presenting different cases to the student, asking for predictions, probing for relevant factors, entrapping the student when he has not identified all necessary factors, and presenting counterexamples. This system is incomplete because it lacks a goal structure to guide the tutorial sessions. The report outlines a more complete theory of the goal structure of Socratic tutors based on analysis of human tutorial dialogues. The main goals are to refine the student's causal model and predictive abilities. Sub-goals include the diagnosis of deficiencies in the student's knowledge and the correction of these deficiencies. (Author)

We extend graphic statics to describe the forces and moments in 3D rigid-jointed frame structures. Graphic statics relates the form diagram (the geometrical layout of structural bars) to a reciprocal force diagram representing the forces in those bars. For 3D structures, Rankine reciprocals represent bar forces by areas of polygons perpendicular to bars. Unfortunately, that description is incomplete. Here, Rankine reciprocals are generalised to provide a complete description. Not only can any state of axial self-stress be described, but so can any state of self-stress involving axial and shear forces coexistent with bending and torsional moments. This is achieved using a discrete version of Maxwell's Diagram of Stress which maps the body space containing the structure into the stress space containing the force diagram. This mapping is a Legendre transform, defined via a stress function and its gradients. The description resulting here is applicable to any state of self-stress in any 3D bar structure whose joints may have any degree of fixity. Using homology theory, a structural frame is decomposed into a set of loops, with states of self-stress being represented by dual loops in the stress space. Loops need not be plane. At any point on the structure the six components of stress resultant (axial and two shear force components, with torsional and two bending moment components) are represented by the oriented areas of the dual loops projected onto the six basis bivector planes in the 4D stress space. This description is complete: any self-stress of any frame can be represented. Finally, this paper describes an object whose projections encode internal moments. It is a hybrid of form and force: it plots the original stress function at the dual coordinates. This allows internal bending and torsional moments to be separated from the moments about the origin associated with the forces., Comment: 14 pages, 8 figures

This paper investigates the transparency in the creation of benchmarks and the use of leaderboards for measuring progress in NLP, with a focus on the relation extraction (RE) task. Existing RE benchmarks often suffer from insufficient documentation, lacking crucial details such as data sources, inter-annotator agreement, the algorithms used for the selection of instances for datasets, and information on potential biases like dataset imbalance. Progress in RE is frequently measured by leaderboards that rank systems based on evaluation methods, typically limited to aggregate metrics like F1-score. However, the absence of detailed performance analysis beyond these metrics can obscure the true generalisation capabilities of models. Our analysis reveals that widely used RE benchmarks, such as TACRED and NYT, tend to be highly imbalanced and contain noisy labels. Moreover, the lack of class-based performance metrics fails to accurately reflect model performance across datasets with a large number of relation types. These limitations should be carefully considered when reporting progress in RE. While our discussion centers on the transparency of RE benchmarks and leaderboards, the observations we discuss are broadly applicable to other NLP tasks as well. Rather than undermining the significance and value of existing RE benchmarks and the development of new models, this paper advocates for improved documentation and more rigorous evaluation to advance the field., Comment: This paper was accepted at the GenBench workshop at EMNLP2024

We study a generalisation of Vizing's theorem, where the goal is to simultaneously colour the edges of graphs $G_1,\dots,G_k$ with few colours. We obtain asymptotically optimal bounds for the required number of colours in terms of the maximum degree $\Delta$, for small values of $k$ and for an infinite sequence of values of $k$. This asymptotically settles a conjecture of Cabello for $k=2$. Moreover, we show that $\sqrt k \Delta + o(\Delta)$ colours always suffice, which tends to the optimal value as $k$ grows. We also show that $\ell \Delta + o(\Delta)$ colours are enough when every edge appears in at most $\ell$ of the graphs, which asymptotically confirms a conjecture of Cambie. Finally, our results extend to the list setting. We also find a close connection to a conjecture of F\"uredi, Kahn, and Seymour from the 1990s and an old problem about fractional matchings., Comment: 14 pages

Achieving a provable exponential quantum speedup for an important machine learning task has been a central research goal since the seminal HHL quantum algorithm for solving linear systems and the subsequent quantum recommender systems algorithm by Kerenidis and Prakash. These algorithms were initially believed to be strong candidates for exponential speedups, but a lower bound ruling out similar classical improvements remained absent. In breakthrough work by Tang, it was demonstrated that this lack of progress in classical lower bounds was for good reasons. Concretely, she gave a classical counterpart of the quantum recommender systems algorithm, reducing the quantum advantage to a mere polynomial. Her approach is quite general and was named quantum-inspired classical algorithms. Since then, almost all the initially exponential quantum machine learning speedups have been reduced to polynomial via new quantum-inspired classical algorithms. From the current state-of-affairs, it is unclear whether we can hope for exponential quantum speedups for any natural machine learning task. In this work, we present the first such provable exponential separation between quantum and quantum-inspired classical algorithms. We prove the separation for the basic problem of solving a linear system when the input matrix is well-conditioned and has sparse rows and columns.

Numerical simulations have shown that the strength of planetary magnetic fields depends on the convective energy flux emerging from planetary interiors. Here we model the interior structure of gas giant planets using \texttt{MESA}, to determine the convective energy flux that can drive the generation of magnetic field. This flux is then incorporated in the Christensen et al. dynamo formalism to estimate the maximum dipolar magnetic field $B^\mathrm{(max)}_\mathrm{dip}$ of our simulated planets. First, we explore how the surface field of intensely irradiated hot Jupiters ($\sim 300 M_\oplus$) and hot Neptunes ($\sim 20 M_\oplus$) evolve as they age. Assuming an orbital separation of 0.1 au, for the hot Jupiters, we find that $B^\mathrm{(max)}_\mathrm{dip}$ evolves from 240 G at 500 Myr to 120 G at 5~Gyr. For hot Neptunes, the magnetic field evolves from 11 G at young ages and dies out at $\gtrsim$ 2 Gyr. Furthermore, we also investigate the effects of atmospheric mass fraction, atmospheric evaporation, orbital separations $\alpha$ and additional planetary masses on the derived $B^\mathrm{(max)}_\mathrm{dip}$. We found that $B^\mathrm{(max)}_\mathrm{dip}$ increases with $\alpha$ for very close-in planets and plateaus out after that. Higher atmospheric mass fractions lead in general to stronger surface fields, because they allow for more extensive dynamo regions and stronger convection., Comment: 10 pages, 8 figures

GPT-4o is an autoregressive omni model that accepts as input any combination of text, audio, image, and video, and generates any combination of text, audio, and image outputs. It's trained end-to-end across text, vision, and audio, meaning all inputs and outputs are processed by the same neural network. GPT-4o can respond to audio inputs in as little as 232 milliseconds, with an average of 320 milliseconds, which is similar to human response time in conversation. It matches GPT-4 Turbo performance on text in English and code, with significant improvement on text in non-English languages, while also being much faster and 50\% cheaper in the API. GPT-4o is especially better at vision and audio understanding compared to existing models. In line with our commitment to building AI safely and consistent with our voluntary commitments to the White House, we are sharing the GPT-4o System Card, which includes our Preparedness Framework evaluations. In this System Card, we provide a detailed look at GPT-4o's capabilities, limitations, and safety evaluations across multiple categories, focusing on speech-to-speech while also evaluating text and image capabilities, and measures we've implemented to ensure the model is safe and aligned. We also include third-party assessments on dangerous capabilities, as well as discussion of potential societal impacts of GPT-4o's text and vision capabilities.

Preclinical diffusion MRI (dMRI) has proven value in methods development and validation, characterizing the biological basis of diffusion phenomena, and comparative anatomy. While dMRI enables in vivo non-invasive characterization of tissue, ex vivo dMRI is increasingly being used to probe tissue microstructure and brain connectivity. Ex vivo dMRI has several experimental advantages that facilitate high spatial resolution and high signal-to-noise ratio (SNR) images, cutting-edge diffusion contrasts, and direct comparison with histological data as a methodological validation. However, there are a number of considerations that must be made when performing ex vivo experiments. The steps from tissue preparation, image acquisition and processing, and interpretation of results are complex, with many decisions that not only differ dramatically from in vivo imaging of small animals, but ultimately affect what questions can be answered using the data. This work concludes a 3-part series of recommendations and considerations for preclinical dMRI. Herein, we describe best practices for dMRI of ex vivo tissue, with a focus on image pre-processing, data processing and model fitting, and tractography. In each section, we attempt to provide guidelines and recommendations, but also highlight areas for which no guidelines exist (and why), and where future work should lie. We end by providing guidelines on code sharing and data sharing, and point towards open-source software and databases specific to small animal and ex vivo imaging., Comment: Part 3 of 3 in "Considerations and recommendations for preclinical diffusion MRI"

Transformer networks, especially those with performance on par with GPT models, are renowned for their powerful feature extraction capabilities. However, the nature and correlation of these features with human-engineered ones remain unclear. In this study, we delve into the mechanistic workings of state-of-the-art, fine-tuning-based passage-reranking transformer networks. Our approach involves a probing-based, layer-by-layer analysis of neurons within ranking LLMs to identify individual or groups of known human-engineered and semantic features within the network's activations. We explore a wide range of features, including lexical, document structure, query-document interaction, advanced semantic, interaction-based, and LLM-specific features, to gain a deeper understanding of the underlying mechanisms that drive ranking decisions in LLMs. Our results reveal a set of features that are prominently represented in LLM activations, as well as others that are notably absent. Additionally, we observe distinct behaviors of LLMs when processing low versus high relevance queries and when encountering out-of-distribution query and document sets. By examining these features within activations, we aim to enhance the interpretability and performance of LLMs in ranking tasks. Our findings provide valuable insights for the development of more effective and transparent ranking models, with significant implications for the broader information retrieval community. All scripts and code necessary to replicate our findings are made available., Comment: 9 pages

Effective control of magnetic phases in two-dimensional magnets would constitute crucial progress in spintronics, holding great potential for future computing technologies. Here, we report a new approach of leveraging tunneling current as a tool for controlling spin states in CrI3. We reveal that a tunneling current can deterministically switch between spin-parallel and spin-antiparallel states in few-layer CrI3, depending on the polarity and amplitude of the current. We propose a mechanism involving nonequilibrium spin accumulation in the graphene electrodes in contact with the CrI3 layers. We further demonstrate tunneling current-tunable stochastic switching between multiple spin states of the CrI3 tunnel devices, which goes beyond conventional bi-stable stochastic magnetic tunnel junctions and has not been documented in two-dimensional magnets. Our findings not only address the existing knowledge gap concerning the influence of tunneling currents in controlling the magnetism in two-dimensional magnets, but also unlock possibilities for energy-efficient probabilistic and neuromorphic computing., Comment: 23 pages, 4 figures

The present paper reports on wind tunnel tests and analyses carried out to investigate the effect of the static angle of attack on the aerodynamic stability of a twin-box bridge deck section. It is found that the critical wind speed for onset of flutter increases with increasing positive static angles (nose-up) and that this effect relates mainly to a decrease in the loss of aerodynamic stiffness. A simplified flutter analysis, linking the slope of the static moment coefficient to the increase of flutter stability for increasing positive angles of attack. It is concluded that it is desirable to design twin-box bridge deck sections to have a positive moment coefficient at zero angle of attack and a positive, decreasing moment slope for increasing nose-up angles. With these requirements fulfilled, the present study show that the critical wind speeds for onset of flutter increase with increasing angles, and ensures that the elastically supported deck will always meet the wind at ever increasing angles for increasing wind speeds., Comment: 12 pages, 6 figures, submitted to proceedings of the 16th International Conference on Wind Engineering (ICWE16) 2023, Florence, Italy

The family of mappings of the plane possessing a biquadratic invariant, which is known collectively as QRT maps, is composed of two involutions, one preserving a vertical shift and the other preserving a horizontal shift in the plane. In this paper, we extend the map by replacing each shift by the group operation on each of two families of elliptic curves, whose product forms a bielliptic surface., Comment: 17 pages; typos corrected

The composition of pretraining data is a key determinant of foundation models' performance, but there is no standard guideline for allocating a limited computational budget across different data sources. Most current approaches either rely on extensive experiments with smaller models or dynamic data adjustments that also require proxy models, both of which significantly increase the workflow complexity and computational overhead. In this paper, we introduce Adaptive Data Optimization (ADO), an algorithm that optimizes data distributions in an online fashion, concurrent with model training. Unlike existing techniques, ADO does not require external knowledge, proxy models, or modifications to the model update. Instead, ADO uses per-domain scaling laws to estimate the learning potential of each domain during training and adjusts the data mixture accordingly, making it more scalable and easier to integrate. Experiments demonstrate that ADO can achieve comparable or better performance than prior methods while maintaining computational efficiency across different computation scales, offering a practical solution for dynamically adjusting data distribution without sacrificing flexibility or increasing costs. Beyond its practical benefits, ADO also provides a new perspective on data collection strategies via scaling laws., Comment: 21 pages, 10 figures

Mapping the conformational dynamics of proteins is crucial for elucidating their functional mechanisms. While Molecular Dynamics (MD) simulation enables detailed time evolution of protein motion, its computational toll hinders its use in practice. To address this challenge, multiple deep learning models for reproducing and accelerating MD have been proposed drawing on transport-based generative methods. However, existing work focuses on generation through transport of samples from prior distributions, that can often be distant from the data manifold. The recently proposed framework of stochastic interpolants, instead, enables transport between arbitrary distribution endpoints. Building upon this work, we introduce EquiJump, a transferable SO(3)-equivariant model that bridges all-atom protein dynamics simulation time steps directly. Our approach unifies diverse sampling methods and is benchmarked against existing models on trajectory data of fast folding proteins. EquiJump achieves state-of-the-art results on dynamics simulation with a transferable model on all of the fast folding proteins.

Most efforts in interpreting neural relevance models have focused on local explanations, which explain the relevance of a document to a query but are not useful in predicting the model's behavior on unseen query-document pairs. We propose a novel method to globally explain neural relevance models by constructing a "relevance thesaurus" containing semantically relevant query and document term pairs. This thesaurus is used to augment lexical matching models such as BM25 to approximate the neural model's predictions. Our method involves training a neural relevance model to score the relevance of partial query and document segments, which is then used to identify relevant terms across the vocabulary space. We evaluate the obtained thesaurus explanation based on ranking effectiveness and fidelity to the target neural ranking model. Notably, our thesaurus reveals the existence of brand name bias in ranking models, demonstrating one advantage of our explanation method.

M-type stars are the most common stars in the universe. They are ideal hosts for the search of exoplanets in the habitable zone (HZ), as their small size and low temperature make the HZ much closer in than their solar twins. Harboring very deep convective layers, they also usually exhibit very intense magnetic fields. Understanding their environment, in particular their coronal and wind properties, is thus very important, as they might be very different from what is observed in the solar system. The mass loss rate of M-type stars is poorly known observationally, and recent attempts to estimate it for some of them (TRAPPIST-1, Proxima Cen) can vary by an order of magnitude. In this work, we revisit the stellar wind properties of M-dwarfs in the light of the latest estimates of $\dot{M}$ through Lyman-$\alpha$ absorption at the astropause and slingshot prominences. We outline a modeling strategy to estimate the mass loss rate, radiative loss and wind speed, with uncertainties, based on an Alfv\'en wave driven stellar wind model. We find that it is very likely that several TRAPPIST-1 planets lie within the Alfv\'en surface, which imply that these planets experience star-planet magnetic interactions (SPMI). We also find that SPMI between Proxima Cen b and its host star could be the reason of recently observed radio emissions., Comment: 15 pages, 9 figures, accepted for publication in ApJ

Objectives: To identify a head acceleration event (HAE) severity measure associated with HIA1 removals in elite level rugby union. Methods: HAEs were recorded from 215 men and 325 women with 30 and 28 HIA1 removals from men and women, respectively. Logistical regression were calculated to identify if peak power, maximum principal strain (MPS) and or Head Acceleration Response Metric (HARM) were associated with HIA1 events compared to non-cases. Optimal threshold values were determined using the Youden Index. Area under the curve (AUC) were compared using a paired sample approach. Significant differences were set at p<0.05. Results: All three severity measures were associated with HIA1 removals in both the mens and womens game. Power performed greatest for HIA1 removals in both the mens and womens games, based on overall AUC, sensitivity, and specificity values. HARM and MPS were found to perform lower than PLA in the womens game based on AUC comparisons (p=0.006 and 0.001, respectively), with MPS performing lower than PAA (p=0.001). Conclusion: The findings progress our understanding of HAE measures associated with HIA1 removals. Peak power, a measure based on fundamental mechanics and commonly used in sports performance, may be a suitable HAE severity measure., Comment: 4 Tables, 2 Figures

Mediation analysis aims to identify and estimate the effect of an exposure on an outcome that is mediated through one or more intermediate variables. In the presence of multiple intermediate variables, two pertinent methodological questions arise: estimating mediated effects when mediators are correlated, and performing high-dimensional mediation analysis when the number of mediators exceeds the sample size. This paper presents a two-step procedure for high-dimensional mediation analysis. The first step selects a reduced number of candidate mediators using an ad-hoc lasso penalty. The second step applies a procedure we previously developed to estimate the mediated and direct effects, accounting for the correlation structure among the retained candidate mediators. We compare the performance of the proposed two-step procedure with state-of-the-art methods using simulated data. Additionally, we demonstrate its practical application by estimating the causal role of DNA methylation in the pathway between smoking and rheumatoid arthritis using real data.

We investigate the failure process of fiber bundles with structural disorder represented by the random misalignment of fibers. The strength of fibers is assumed to be constant so that misalignment is the only source of disorder, which results in a heterogeneous load distribution over fibers. We show by analytical calculations and computer simulations that increasing the amount of structural disorder a transition occurs from a perfectly brittle behaviour with abrupt global failure to a quasi-brittle phase where failure is preceded by breaking avalanches. The size distribution of avalanches follows a power law functional form with a complex dependence of the exponent on the amount of disorder. In the vicinity of the critical point the avalanche exponent is 3/2, however, with increasing disorder a crossover emerges to a higher exponent 5/2. We show analytically that the mechanical behaviour of the bundle of misaligned fiber with no strength disorder can be mapped to an equal load sharing fiber bundle of perfectly aligned fibers with properly selected strength disorder., Comment: 11 pages, 11 figures

The pseudogap stands out in the phase diagram of the cuprate high-temperature superconductors because its origin and relationship to superconductivity remain elusive. The origin of the pseudogap has been debated, with competing hypotheses attributing it to preformed electron pairs or local order, such as charge density waves. Here, we present unambiguous evidence supporting the pairing scenario, using local shot-noise spectroscopy measurements in Bi2Sr2CaCu2O8+{\delta}. Our data demonstrates that the pseudogap energy coincides with the onset of electron pairing, and is spatially heterogeneous with values reaching up to 70 meV. Our results exclude a pure local order origin of the pseudogap, link the pseudogap to Cooper pair formation, and show that the limiting factor for higher Tc in cuprates is phase coherence., Comment: 5 pages, 4 figures and Supplementary Materials

We present a new multi-dimensional, robust, and cell-centered finite-volume scheme for the ideal MHD equations. This scheme relies on relaxation and splitting techniques and can be easily used at high order. A fully conservative version is not entropy satisfying but is observed experimentally to be more robust than standard constrained transport schemes at low plasma beta. At very low plasma beta and high Alfv\'en number, we have designed an entropy-satisfying version that is not conservative for the magnetic field but preserves admissible states and we switch locally a-priori between the two versions depending on the regime of plasma beta and Alfv\'en number. This strategy is robust in a wide range of standard MHD test cases, all performed at second order with a classic MUSCL-Hancock scheme., Comment: accepted in JCP

Inertial microfluidics have been limited to dilute particle concentrations due to defocusing at high particle concentrations. However, we observed a counterintuitive shift of focusing to the outer wall at high concentrations, which contradicts the existing particle focusing theory based on Navier-Stokes equation. We developed a multiphase model incorporating lift forces and particle-particle interactions to explain this behaviour. Numerical simulations validated by experimental data reveal the shift is governed by the ratio of the lift force strength to that of particle interaction frequencies.

Tunneling spectroscopy is an important tool for the study of both real-space and momentum-space electronic structure of correlated electron systems. However, such measurements often yield noisy data. Machine learning provides techniques to reduce the noise in post-processing, but traditionally requires noiseless examples which are unavailable for scientific experiments. In this work we adapt the unsupervised Noise2Noise and self-supervised Noise2Self algorithms, which allow for denoising without clean examples, to denoise quasiparticle interference data. We first apply the techniques on simulated data, and demonstrate that we are able to reduce the noise while preserving finer details, all while outperforming more traditional denoising techniques. We then apply the Noise2Self technique to experimental data from an overdoped cuprate ((Pb,Bi)$_2$Sr$_2$CuO$_{6+\delta}$) sample. Denoising enhances the clarity of quasiparticle interference patterns, and helps to obtain a precise extraction of electronic structure parameters. Self-supervised denoising is a promising tool for denoising quasiparticle interference data, facilitating deeper insights into the physics of complex materials., Comment: 7 pages, 5 figures, plus 4 pages and 5 figures appendix

Control barrier functions (CBFs) offer an efficient framework for designing real-time safe controllers. However, CBF-based controllers can be short-sighted, resulting in poor performance, a behaviour which is aggravated in uncertain conditions. This motivated research on safety filters based on model predictive control (MPC) and its stochastic variant. MPC deals with safety constraints in a direct manner, however, its computational demands grow with the prediction horizon length. We propose a safety formulation that solves a finite horizon optimization problem at each time instance like MPC, but rather than explicitly imposing constraints along the prediction horizon, we enforce probabilistic safety constraints by means of CBFs only at the first step of the horizon. The probabilistic CBF constraints are transformed in a finite number of deterministic CBF constraints via the scenario based methodology. Capitalizing on results on scenario based MPC, we provide distribution-free, \emph{a priori} guarantees on the system's closed loop expected safety violation frequency. We demonstrate our results through a case study on unmanned aerial vehicle collision-free position swapping, and provide a numerical comparison with recent stochastic CBF formulations., Comment: To be published in: The 63rd IEEE Conference on Decision and Control (CDC-2024 Milano, Italy)

3D scene reconstruction from stereo endoscopic video data is crucial for advancing surgical interventions. In this work, we present an online framework for online, dense 3D scene reconstruction and tracking, aimed at enhancing surgical scene understanding and assisting interventions. Our method dynamically extends a canonical scene representation using Gaussian splatting, while modeling tissue deformations through a sparse set of control points. We introduce an efficient online fitting algorithm that optimizes the scene parameters, enabling consistent tracking and accurate reconstruction. Through experiments on the StereoMIS dataset, we demonstrate the effectiveness of our approach, outperforming state-of-the-art tracking methods and achieving comparable performance to offline reconstruction techniques. Our work enables various downstream applications thus contributing to advancing the capabilities of surgical assistance systems.

Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman's graduate statistical mechanics course at Berkeley from the 1972-1973 academic year. Part 1 addresses equilibrium statistical mechanics with topics: fundamentals, classical fluids and other systems, chemical equilibrium, and long-range interactions. Part 2 addresses non-equilibrium statistical mechanics with topics: fundamentals, Brownian motion, Liouville and Klimontovich equations, Landau equation, Markov processes and Fokker-Planck equation, linear response and transport theory, and an introduction to non-equilibrium quantum statistical mechanics., Comment: 156 pages, lecture notes, a dozen or less figures

Sensitive information detection is crucial in content moderation to maintain safe online communities. Assisting in this traditionally manual process could relieve human moderators from overwhelming and tedious tasks, allowing them to focus solely on flagged content that may pose potential risks. Rapidly advancing large language models (LLMs) are known for their capability to understand and process natural language and so present a potential solution to support this process. This study explores the capabilities of five LLMs for detecting sensitive messages in the mental well-being domain within two online datasets and assesses their performance in terms of accuracy, precision, recall, F1 scores, and consistency. Our findings indicate that LLMs have the potential to be integrated into the moderation workflow as a convenient and precise detection tool. The best-performing model, GPT-4o, achieved an average accuracy of 99.5\% and an F1-score of 0.99. We discuss the advantages and potential challenges of using LLMs in the moderation workflow and suggest that future research should address the ethical considerations of utilising this technology., Comment: 2024 Oz CHI conference

Let $K_n^{(k)}$ be the complete $k$-graph on $n$ vertices. A $k$-uniform tight cycle is a $k$-graph with its vertices cyclically ordered so that every $k$ consecutive vertices form an edge and any two consecutive edges share exactly $k-1$ vertices. A result of Bustamante, Corsten, Frankl, Pokrovskiy and Skokan shows that all $r$-edge coloured $K_{n}^{(k)}$ can be partitioned into $c_{r,k}$ vertex disjoint monochromatic tight cycles. However, the constant $c_{r,k}$ is of tower-type. In this work, we show that $c_{r, k}$ is a polynomial in $r$., Comment: 36 pages

The iron-based superconductor FeTe$_{0.55}$Se$_{0.45}$ is a peculiar material: it hosts a surface state with a Dirac dispersion, is a putative topological superconductor hosting Majorana modes in vortices, and has an unusually low Fermi energy. The superconducting state is generally thought to be characterized by three gaps in different bands, with the usual homogenous, spatially extended Bogoliubov excitations -- in this work, we uncover evidence that it is instead of a very different nature. Our scanning tunneling spectroscopy data shows several peaks in the density of states above a full gap, and by analyzing the spatial and junction-resistance dependence of the peaks, we conclude that the peaks above the first one are not coherence peaks from different bands. Instead, comparisons with our simulations indicate that they originate from generalized Shiba states that are spatially overlapping. This can lead to an amorphous state of Bogoliubov quasiparticles, reminiscent of impurity bands in semiconductors. We discuss the origin and implications of this new state., Comment: 6 pages, 4 figures

To enhance the field of continuous motor health monitoring, we present FAN-COIL-I, an extensive vibration sensor dataset derived from a Fan Coil motor. This dataset is uniquely positioned to facilitate the detection and prediction of motor health issues, enabling a more efficient maintenance scheduling process that can potentially obviate the need for regular checks. Unlike existing datasets, often created under controlled conditions or through simulations, FAN-COIL-I is compiled from real-world operational data, providing an invaluable resource for authentic motor diagnosis and predictive maintenance research. Gathered using a high-resolution 32KHz sampling rate, the dataset encompasses comprehensive vibration readings from both the forward and rear sides of the Fan Coil motor over a continuous two-week period, offering a rare glimpse into the dynamic operational patterns of these systems in a corporate setting. FAN-COIL-I stands out not only for its real-world applicability but also for its potential to serve as a reliable benchmark for researchers and practitioners seeking to validate their models against genuine engine conditions.

Direct imaging of exoplanets relies on complex wavefront sensing and control architectures. In addition to fast adaptive optics systems, most of the future high-contrast imaging instruments will soon be equipped with focal plane wavefront sensing algorithms. These techniques use the science detector to estimate the static and quasi-static aberrations induced by optical manufacturing defects and system thermal variations. Pair-wise probing (PWP) has been the most widely used, especially for space-based application and will be tested at contrast levels of ~1e-9 on-sky along with the future coronagraph instrument onboarding the Roman Space Telescope. This algorithm leans on phase diversities applied on the deformable mirror that are recorded in pairs. A minimum of two pairs of probes are required per bandwidth. An additional unprobed image is also recorded to verify the convergence rate of the correction. Before PWP, Borde & Traub proposed a similar algorithm that takes advantage of the unprobed image in the estimation process to get rid of the pair diversity requirement. In this work, we theoretically show that this latter technique should be more efficient than PWP when the convergence time is not limited by photon noise. We then present its performance and practical limitations on coronagraphic testbeds at JPL and exhibit a first on-sky control of non-common path aberrations with such method on VLT/SPHERE., Comment: Proceedings of SPIE Astronomical Telescopes + Instrumentation, Tokyo (2024)

A classical result of Corr\'adi and Hajnal states that every graph $G$ on $n$ vertices with $n\in 3\mathbb{N}$ and $\delta(G) \ge 2n/3$ contains a perfect triangle-tiling, i.e.,\ a spanning set of vertex-disjoint triangles. We explore a generalisation of this result to edge-coloured graphs. Let $G$ be an edge-coloured graph on $n$ vertices. The minimum colour degree $\delta^c(G)$ of $G$ is the largest integer $k$ such that, for every vertex $v \in V(G)$, there are at least $k$ distinct colours on edges incident to $v$. We show that if $\delta^c(G) \ge (5/6 + \varepsilon) n$, then $G$ has a spanning set of vertex-disjoint rainbow triangles. On the other hand, we find an example showing the bound should be at least $5n/7$. We also discuss a related tiling problems on digraphs, which may be of independent interest.

INTRODUCTION: Mild cognitive impairment (MCI) is characterized by a decline in cognitive functions beyond typical age and education-related expectations. Since, MCI has been linked to reduced social interactions and increased aimless movements, we aimed to automate the capture of these behaviors to enhance longitudinal monitoring. METHODS: Using a privacy-preserving distributed camera network, we collected movement and social interaction data from groups of individuals with MCI undergoing therapy within a 1700$m^2$ space. We developed movement and social interaction features, which were then used to train a series of machine learning algorithms to distinguish between higher and lower cognitive functioning MCI groups. RESULTS: A Wilcoxon rank-sum test revealed statistically significant differences between high and low-functioning cohorts in features such as linear path length, walking speed, change in direction while walking, entropy of velocity and direction change, and number of group formations in the indoor space. Despite lacking individual identifiers to associate with specific levels of MCI, a machine learning approach using the most significant features provided a 71% accuracy. DISCUSSION: We provide evidence to show that a privacy-preserving low-cost camera network using edge computing framework has the potential to distinguish between different levels of cognitive impairment from the movements and social interactions captured during group activities.

Nucleic acids such as mRNA have emerged as a promising therapeutic modality with the capability of addressing a wide range of diseases. Lipid nanoparticles (LNPs) as a delivery platform for nucleic acids were used in the COVID-19 vaccines and have received much attention. While modern manufacturing processes which involve rapidly mixing an organic stream containing the lipids with an aqueous stream containing the nucleic acids are conceptually straightforward, detailed understanding of LNP formation and structure is still limited and scale-up can be challenging. Mathematical and computational methods are a promising avenue for deepening scientific understanding of the LNP formation process and facilitating improved process development and control. This article describes strategies for the mechanistic modeling of LNP formation, starting with strategies to estimate and predict important physicochemical properties of the various species such as diffusivities and solubilities. Subsequently, a framework is outlined for constructing mechanistic models of reactor- and particle-scale processes. Insights gained from the various models are mapped back to product quality attributes and process insights. Lastly, the use of the models to guide development of advanced process control and optimization strategies is discussed., Comment: 67 pages, 10 figures

Motivated by an inclination for symmetry and possible extension of the General Theory of Relativity within the framework of Scalar Theory, we investigate the Bekenstein's disformal transformation of the Einstein-Hilbert action. Owing to the complicated combinations of second order metric derivatives encoded in the Ricci scalar of the action, such a transformation yields an unwieldy expression. To `tame' the transformed action, we exploit the conformal-disformal (KG) constraint previously discovered in the study of the invariance of the massless Klein-Gordon equation under disformal transformation. The result upon its application is a surprisingly much more concise and simple action in four spacetime dimensions containing three out of four sub-Lagrangians found in the Horndeski action, and three beyond-Horndeski terms. The latter group of terms may be attributed to the kinetic dependence of the conformal and disformal factors in the Bekenstein's disformal transformation. This is consistent with a related study on the special disformal transformation of the Einstein-Hilbert action where no such beyond-Horndeski terms are found to exist. Going down to three dimensions, we find a relatively simpler resulting action but the signature of three three `extraneous' terms remains. Remarkably, we find in two dimensions the Einstein-Hilbert action to be invariant under the KG-constrained Bekenstein's disformal transformation., Comment: 12 pages

We present a new version of the stochastic sewing lemma, capable of handling multiple discontinuous control functions. This is then used to develop a theory of rough stochastic analysis in a c\`adl\`ag setting. In particular, we define rough stochastic integration and establish solutions to rough stochastic differential equations with jump discontinuities in both sources of noise, along with an It\^o formula for stochastic controlled paths with jumps., Comment: 55 pages

Although with great successes in explaining phenomena and natural behaviour involving the Universe or a part thereof, the General Theory of Relativity is far from a complete theory. Focusing on its extension within the framework of scalar tensor theory, we investigate the transformation of the Einstein-Hilbert action under the general disformal transformation coupled with a set of triple KG constraints. The idea is that the general disformal transformation leads to an extremely complicated action necessitating a set of constraints to tame the resulting form. Motivated by previous studies on the invertibility and invariance of the massless Klein-Gordon equation under the general disformal transformation, we identify three constraints that significantly simplifies the transformed Einstein-Hilbert action. In four spacetime dimensions, we find that the transformed action is a sum of the original action and a disformal contribution involving a six-term Lagrangian that includes the Ricci tensor coupled to a sum of derivatives of scalar fields and kinetic terms. In three spacetime dimensions, the disformal contribution becomes a five-term Lagrangian. Lastly, in two spacetime dimensions, the Einstein-Hilbert action is invariant under the constrained disformal transformation., Comment: 17 pages, version 3: added references; revised paper for greater clarity

We develop a surface for the electric dipole moment of three interacting helium atoms and use it, together with state-of-the-art potential and polarizability surfaces, to compute the third dielectric virial coefficient, $C_\varepsilon$, for both $^4$He and $^3$He isotopes. Our results agree with previously published data computed using an approximated form for the three-body polarizability, and are extended to the low-temperature regime by including exchange effects. Additionally, the uncertainty of $C_\varepsilon$ is rigorously determined for the first time by propagating the uncertainties of the potential and polarizability surfaces; this uncertainty is much larger than the contribution from the dipole-moment surface to $C_\varepsilon$. Our results compare reasonably well with the limited experimental data. The first-principles values of $C_\epsilon$ computed in this work will enhance the accuracy of primary temperature and pressure metrology based on measurements of the dielectric constant of helium., Comment: 18 pages, 7 figures

In the problem of online unweighted interval selection, the objective is to maximize the number of non-conflicting intervals accepted by the algorithm. In the conventional online model of irrevocable decisions, there is an Omega(n) lower bound on the competitive ratio, even for randomized algorithms [Bachmann et al. 2013]. In a line of work that allows for revocable acceptances, [Faigle and Nawijn 1995] gave a greedy 1-competitive (i.e. optimal) algorithm in the real-time model, where intervals arrive in order of non-decreasing starting times. The natural extension of their algorithm in the adversarial (any-order) model is 2k-competitive [Borodin and Karavasilis 2023], when there are at most k different interval lengths, and that is optimal for all deterministic, and memoryless randomized algorithms. We study this problem in the random-order model, where the adversary chooses the instance, but the online sequence is a uniformly random permutation of the items. We consider the same algorithm that is optimal in the cases of the real-time and any-order models, and give an upper bound of 2.5 on the competitive ratio under random-order arrivals. We also show how to utilize random-order arrivals to extract a random bit with a worst case bias of 2/3, when there are at least two distinct item types. We use this bit to derandomize the barely random algorithm of [Fung et al. 2014] and get a deterministic 3-competitive algorithm for single-length interval selection with arbitrary weights., Comment: 18 pages, 7 figures

Claim verification can be a challenging task. In this paper, we present a method to enhance the robustness and reasoning capabilities of automated claim verification through the extraction of short facts from evidence. Our novel approach, FactDetect, leverages Large Language Models (LLMs) to generate concise factual statements from evidence and label these facts based on their semantic relevance to the claim and evidence. The generated facts are then combined with the claim and evidence. To train a lightweight supervised model, we incorporate a fact-detection task into the claim verification process as a multitasking approach to improve both performance and explainability. We also show that augmenting FactDetect in the claim verification prompt enhances performance in zero-shot claim verification using LLMs. Our method demonstrates competitive results in the supervised claim verification model by 15% on the F1 score when evaluated for challenging scientific claim verification datasets. We also demonstrate that FactDetect can be augmented with claim and evidence for zero-shot prompting (AugFactDetect) in LLMs for verdict prediction. We show that AugFactDetect outperforms the baseline with statistical significance on three challenging scientific claim verification datasets with an average of 17.3% performance gain compared to the best performing baselines.

Transport of dense core vesicles (DCVs) in neurons is crucial for distributing molecules like neuropeptides and growth factors. We studied the experimental trajectories of dynein-driven directed movement of DCVs in the ALA neuron C. elegans over a duration of up to 6 seconds. We analysed the DCV movement in three strains of C. elegans: 1) with normal kinesin-1 function, 2) with reduced function in kinesin light chain 2 (KLC-2), and 3) a null mutation in kinesin light chain 1 (KLC-1). We find that DCVs move superdiffusively with displacement variance $var(x) \sim t^2$ in all three strains with low reversal rates and frequent immobilization of DCVs. The distribution of DCV displacements fits a beta-binomial distribution with the mean and the variance following linear and quadratic growth patterns, respectively. We propose a simple heterogeneous random walk model to explain the observed superdiffusive retrograde transport behaviour of DCV movement. This model involves a random probability with the beta density for a DCV to resume its movement or remain in the same position., Comment: 9 pages, 5 figures