Miracle-dz/UniFAR-FTUs huggingface dataset:
A unified approach to mass transference principle and large intersection property

The mass transference principle, discovered by Beresnevich and Velani [Ann Math (2), 2006], is a landmark result in Diophantine approximation that allows us to obtain the Hausdorff measure theory of $\limsup$ set. Another important tool is the notion of large intersection property, introduced and systematically studied by Falconer [J. Lond. Math. Soc. (2), 1994]. The former mainly focuses on passing between full (Lebesgue) measure and full Hausdorff measure statements, while the latter transfers full Hausdorff content statement to Hausdorff dimension. From this perspective, the proofs of the two results are quite similar but often treated in different ways. In this paper, we establish a general mass transference principle from the viewpoint of Hausdorff content, aiming to provide a unified proof for the aforementioned results. More precisely, this principle allows us to transfer the Hausdorff content bounds of a sequence of open sets $E_n$ to the full Hausdorff measure statement and large intersection property for $\limsup E_n$. One of the advantages of our approach is that the verification of the Hausdorff content bound does not require the construction of Cantor-like subset, resulting in a much simpler proof. As an application, we provide simpler proofs for several mass transference principles.
EXMOS: Explanatory Model Steering Through Multifaceted Explanations and Data Configurations

Explanations in interactive machine-learning systems facilitate debugging and improving prediction models. However, the effectiveness of various global model-centric and data-centric explanations in aiding domain experts to detect and resolve potential data issues for model improvement remains unexplored. This research investigates the influence of data-centric and model-centric global explanations in systems that support healthcare experts in optimising models through automated and manual data configurations. We conducted quantitative (n=70) and qualitative (n=30) studies with healthcare experts to explore the impact of different explanations on trust, understandability and model improvement. Our results reveal the insufficiency of global model-centric explanations for guiding users during data configuration. Although data-centric explanations enhanced understanding of post-configuration system changes, a hybrid fusion of both explanation types demonstrated the highest effectiveness. Based on our study results, we also present design implications for effective explanation-driven interactive machine-learning systems.
Genetic-based Constraint Programming for Resource Constrained Job Scheduling

Resource constrained job scheduling is a hard combinatorial optimisation problem that originates in the mining industry. Off-the-shelf solvers cannot solve this problem satisfactorily in reasonable timeframes, while other solution methods such as many evolutionary computation methods and matheuristics cannot guarantee optimality and require low-level customisation and specialised heuristics to be effective. This paper addresses this gap by proposing a genetic programming algorithm to discover efficient search strategies of constraint programming for resource-constrained job scheduling. In the proposed algorithm, evolved programs represent variable selectors to be used in the search process of constraint programming, and their fitness is determined by the quality of solutions obtained for training instances. The novelties of this algorithm are (1) a new representation of variable selectors, (2) a new fitness evaluation scheme, and (3) a pre-selection mechanism. Tests with a large set of random and benchmark instances, the evolved variable selectors can significantly improve the efficiency of constraining programming. Compared to highly customised metaheuristics and hybrid algorithms, evolved variable selectors can help constraint programming identify quality solutions faster and proving optimality is possible if sufficiently large run-times are allowed. The evolved variable selectors are especially helpful when solving instances with large numbers of machines.
Comparing Spectral Bias and Robustness For Two-Layer Neural Networks: SGD vs Adaptive Random Fourier Features

We present experimental results highlighting two key differences resulting from the choice of training algorithm for two-layer neural networks. The spectral bias of neural networks is well known, while the spectral bias dependence on the choice of training algorithm is less studied. Our experiments demonstrate that an adaptive random Fourier features algorithm (ARFF) can yield a spectral bias closer to zero compared to the stochastic gradient descent optimizer (SGD). Additionally, we train two identically structured classifiers, employing SGD and ARFF, to the same accuracy levels and empirically assess their robustness against adversarial noise attacks.
Deep Room Impulse Response Completion

Rendering immersive spatial audio in virtual reality (VR) and video games demands a fast and accurate generation of room impulse responses (RIRs) to recreate auditory environments plausibly. However, the conventional methods for simulating or measuring long RIRs are either computationally intensive or challenged by low signal-to-noise ratios. This study is propelled by the insight that direct sound and early reflections encapsulate sufficient information about room geometry and absorption characteristics. Building upon this premise, we propose a novel task termed"RIR completion,"aimed at synthesizing the late reverberation given only the early portion (50 ms) of the response. To this end, we introduce DECOR, Deep Exponential Completion Of Room impulse responses, a deep neural network structured as an autoencoder designed to predict multi-exponential decay envelopes of filtered noise sequences. The interpretability of DECOR's output facilitates its integration with diverse rendering techniques. The proposed method is compared against an adapted state-of-the-art network, and comparable performance shows promising results supporting the feasibility of the RIR completion task. The RIR completion can be widely adapted to enhance RIR generation tasks where fast late reverberation approximation is required.
Migration of amphibians and their mortality on the road of Knyszyn Forest Landscape Park

Spring migration and mortality of two common amphibian species on the road in one of the landscape parks in north-eastern Poland (Knyszyn Forest Landscpae Park) were studied in the years 2013–2015. During three years of the study, total number of 2745 individuals classified to 7 different species and one amphibian group were transfered through the road. The most popular species caught into the traps were: common toad, smooth newt and the common frog. Mortality of two studied amphibian species (Bufo bufo and rana temporaria) dropped over three years of the study. There were positive significant correlation between temperature and the number of migrating amphibians on the road.
Comparing Template-based and Template-free Language Model Probing

The differences between cloze-task language model (LM) probing with 1) expert-made templates and 2) naturally-occurring text have often been overlooked. Here, we evaluate 16 different LMs on 10 probing English datasets – 4 template-based and 6 template-free – in general and biomedical domains to answer the following research questions: (RQ1) Do model rankings differ between the two approaches? (RQ2) Do models’ absolute scores differ between the two approaches? (RQ3) Do the answers to RQ1 and RQ2 differ between general and domain-specific models? Our findings are: 1) Template-free and template-based approaches often rank models differently, except for the top domain- specific models. 2) Scores decrease by up to 42% Acc@1 when comparing parallel template-free and template-based prompts. 3) Perplexity is negatively correlated with accuracy in the template-free approach, but, counter-intuitively, they are positively correlated for template-based probing. 4) Models tend to predict the same answers frequently across prompts for template-based probing, which is less common when employing template-free techniques.
Simulations of poloidal flow stabilization of ballooning modes in a classical l=2 stellarator using JOREK

Magnetohydrodynamics (MHD), combining fluid dynamics and Maxwell's equations, provides a useful means of analysing the dynamic evolution of plasmas and plasma instabilities. JOREK is a non-linear MHD code which solves these equations in the context of magnetic confinement fusion. Originally developed for tokamaks, JOREK has been extended to model stellarators. In this project, ExB poloidal flows are implemented in a classical l=2 stellarator configuration, by imposing a simple radial electric potential profile via initial conditions. The influence of this sheared background flow velocity on pressure-driven modes is interrogated, demonstrating a stabilizing effect when the shearing rate is comparable to the growth rate. This effect is observed for multiple toroidal modes and at different viscosities, demonstrating that the stabilization occurs as a result of shear decorrelation. Oscillations of the linear growth rate are observed in cases with higher flow speeds; this phenomenon is hypothesized to be due to phase misalignment between the poloidally coupled modes contributing to the ballooning mode. Some indicators are provided to support this, however analysis of this phenomenon is ongoing.
Bias in Opinion Summarisation from Pre-training to Adaptation: A Case Study in Political Bias

Opinion summarisation aims to summarise the salient information and opinions presented in documents such as product reviews, discussion forums, and social media texts into short summaries that enable users to effectively understand the opinions therein.Generating biased summaries has the risk of potentially swaying public opinion. Previous studies focused on studying bias in opinion summarisation using extractive models, but limited research has paid attention to abstractive summarisation models. In this study, using political bias as a case study, we first establish a methodology to quantify bias in abstractive models, then trace it from the pre-trained models to the task of summarising social media opinions using different models and adaptation methods. We find that most models exhibit intrinsic bias. Using a social media text summarisation dataset and contrasting various adaptation methods, we find that tuning a smaller number of parameters is less biased compared to standard fine-tuning; however, the diversity of topics in training data used for fine-tuning is critical.
Modeling of heat conduction through rate equations

Starting from a classical thermodynamic approach, we derive rate-type equations to describe the behavior of heat flow in deformable media. Constitutive equations are defined in the material (Lagrangian) description where the standard time derivative satisfies the principle of objectivity. The statement of the Second Law is formulated in the classical form and the thermodynamic restrictions are then developed following the Coleman-Noll procedure. However, instead of the Clausius Duhem inequality we consider the corresponding equality where the entropy production rate is prescribed by a non-negative constitutive function. Both the free energy and the entropy production are assumed to depend on a common set of independent variables involving, in addition to temperature, both temperature gradient and heat-flux vector together with their time derivatives. This approach results in rate-type constitutive equations for the heat-flux vector that are intrinsically consistent with the Second Law and easily amenable to analysis. In addition to obtaining already known models (e.g. Cattaneo-Maxwell's, Jeffreys-like and Green-Naghdi's heat conductors), this scheme allows us to build new and more complex models of heat transport that may have applications in describing the thermal behavior in nanosystems. Indeed, when higher order time derivatives of the heat flux vector are involved, many different relaxation times occur within the rate equation.
Evaluating Large Language Models for Generalization and Robustness via Data Compression

Existing methods for evaluating large language models face challenges such as data contamination, sensitivity to prompts, and the high cost of benchmark creation. To address this, we propose a lossless data compression based evaluation approach that tests how models' predictive abilities generalize after their training cutoff. Specifically, we collect comprehensive test data spanning 83 months from 2017 to 2023 and split the data into training and testing periods according to models' training data cutoff. We measure: 1) the compression performance on the testing period as a measure of generalization on unseen data; and 2) the performance gap between the training and testing period as a measure of robustness. Our experiments test 14 representative large language models with various sizes on sources including Wikipedia, news articles, code, arXiv papers, and multi-modal data. We find that the compression rate of many models reduces significantly after their cutoff date, but models such as Mistral and Llama-2 demonstrate a good balance between performance and robustness. Results also suggest that models struggle to generalize on news and code data, but work especially well on arXiv papers. We also find the context size and tokenization implementation have a big impact of on the overall compression performance.
Water storage dynamics in a till hillslope: the foundation for modeling flows and turnover times

Studies on hydrology, biogeochemistry, or mineral weathering often rely on assumptions about flow paths, water storage dynamics, and transit times. Testing these assumptions requires detailed hydrometric data that are usually unavailable at the catchment scale. Hillslope studies provide an alternative for obtaining a better understanding, but even on such well‐defined and delimited scales, it is rare to have a comprehensive set of hydrometric observations from the water divide down to the stream that can constrain efforts to quantify water storage, movement, and turnover time. Here, we quantified water storage with daily resolution in a hillslope during the course of almost an entire year using hydrological measurements at the study site and an extended version of the vertical equilibrium model. We used an exponential function to simulate the relationship between hillslope discharge and water table; this was used to derive transmissivity profiles along the hillslope and map mean pore water velocities in the saturated zone. Based on the transmissivity profiles, the soil layer transmitting 99% of lateral flow to the stream had a depth that ranged from 8.9 m at the water divide to under 1 m closer to the stream. During the study period, the total storage of this layer varied from 1189 to 1485 mm, resulting in a turnover time of 2172 days. From the pore water velocities, we mapped the time it would take a water particle situated at any point of the saturated zone anywhere along the hillslope to exit as runoff. Our calculations point to the strengths as well as limitations of simple hydrometric data for inferring hydrological properties and water travel times in the subsurface.
Ultrahigh Thermal Conductivity of Cubic Boron Arsenide with an Unexpectedly Strong Temperature Dependence

Materials with high thermal conductivity are needed to conduct heat away from hot spots in power electronics and optoelectronic devices. Cubic boron arsenide (c-BAs) has a high thermal conductivity due to its special phonon dispersion relation. Previous experimental studies of c-BAs report a room-temperature thermal conductivity between 1000 and 1300 watts per meter-kelvin. We synthesized high purity c-BAs single crystals with room-temperature thermal conductivity of 1500 watts per meter-kelvin. We observed its thermal conductivity to be proportional to the inverse square of temperature between 300 and 600 kelvin, a stronger dependence than predicted by state-of-the-art theory.
Quantum tunneling from excited states: Recovering imaginary-time instantons from a real-time analysis

We revisit the path integral description of quantum tunneling and show how it can be generalized to excited states. For clarity, we focus on the simple toy model of a point particle in a double-well potential, for which we perform all steps explicitly. Instead of performing the familiar Wick rotation from physical to imaginary time - which is inconsistent with the requisite boundary conditions when treating tunneling from excited states - we regularize the path integral by adding an infinitesimal complex contribution to the Hamiltonian, while keeping time strictly real. We find that this gives rise to a complex stationary-phase solution, in agreement with recent insights from Picard-Lefshitz theory. We then show that there exists a class of analytic solutions for the corresponding equations of motion, which can be made to match the appropriate boundary conditions in the physically relevant limits of a vanishing regulator and an infinite physical time. We provide a detailed discussion of this non-trivial limit. We find that, for systems without an explicit time-dependence, our approach reproduces the picture of an instanton-like solution defined on a finite Euclidean-time interval. Lastly, we discuss the generalization of our approach to broader classes of systems, for which it serves as a reliable framework for high-precision calculations.
Dynamic Texture Transfer using PatchMatch and Transformers

How to automatically transfer the dynamic texture of a given video to the target still image is a challenging and ongoing problem. In this paper, we propose to handle this task via a simple yet effective model that utilizes both PatchMatch and Transformers. The key idea is to decompose the task of dynamic texture transfer into two stages, where the start frame of the target video with the desired dynamic texture is synthesized in the first stage via a distance map guided texture transfer module based on the PatchMatch algorithm. Then, in the second stage, the synthesized image is decomposed into structure-agnostic patches, according to which their corresponding subsequent patches can be predicted by exploiting the powerful capability of Transformers equipped with VQ-VAE for processing long discrete sequences. After getting all those patches, we apply a Gaussian weighted average merging strategy to smoothly assemble them into each frame of the target stylized video. Experimental results demonstrate the effectiveness and superiority of the proposed method in dynamic texture transfer compared to the state of the art.
Comparative Analysis of LLaMA and ChatGPT Embeddings for Molecule Embedding

Purpose: Large Language Models (LLMs) like ChatGPT and LLaMA are increasingly recognized for their potential in the field of cheminformatics, particularly in interpreting Simplified Molecular Input Line Entry System (SMILES), a standard method for representing chemical structures. These LLMs can decode SMILES strings into vector representations, providing a novel approach to understanding chemical graphs. Methods: We investigate the performance of ChatGPT and LLaMA in embedding SMILES strings. Our evaluation focuses on two key applications: molecular property (MP) prediction and drug-drug interaction (DDI) prediction, both essential in drug development and healthcare. Results: We find that SMILES embeddings generated using LLaMA outperform those from ChatGPT in both MP and DDI prediction tasks. Notably, LLaMA-based SMILES embeddings show results comparable to existing methods in both prediction tasks. Conclusion: The application of LLMs in cheminformatics, particularly in utilizing SMILES embeddings, shows significant promise for advancing drug development. This includes improving the prediction of chemical properties and facilitating the drug discovery process. GitHub: https://github.com/sshaghayeghs/LLaMA-VS-ChatGPT
Instruction Makes a Difference

We introduce Instruction Document Visual Question Answering (iDocVQA) dataset and Large Language Document (LLaDoc) model, for training Language-Vision (LV) models for document analysis and predictions on document images, respectively. Usually, deep neural networks for the DocVQA task are trained on datasets lacking instructions. We show that using instruction-following datasets improves performance. We compare performance across document-related datasets using the recent state-of-the-art (SotA) Large Language and Vision Assistant (LLaVA)1.5 as the base model. We also evaluate the performance of the derived models for object hallucination using the Polling-based Object Probing Evaluation (POPE) dataset. The results show that instruction-tuning performance ranges from 11X to 32X of zero-shot performance and from 0.1% to 4.2% over non-instruction (traditional task) finetuning. Despite the gains, these still fall short of human performance (94.36%), implying there's much room for improvement.
The development of the concept of exchange forces in the 1930s: close encounters between Europe and Japan and the birth of nuclear theory

The onset and the development of the concept of exchange force in quantum physics are historically reconstructed, starting from Heisenberg's seminal contributions in 1926 and going through the great developments in nuclear physics, which allowed the emergence of the idea of force mediating virtual quanta. Although most of such work was performed in Europe, the last and decisive effort in this long path was carried out by Japanese scientists in the 1930s. This is the main focus of the present work, which retraces the achievements of Yukawa and Tomonaga, whose results and mutual interactions are carefully analyzed and related to those of European physicists.
Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Loss

Constructing the architecture of a neural network is a challenging pursuit for the machine learning community, and the dilemma of whether to go deeper or wider remains a persistent question. This paper explores a comparison between deeper neural networks (DeNNs) with a flexible number of layers and wider neural networks (WeNNs) with limited hidden layers, focusing on their optimal generalization error in Sobolev losses. Analytical investigations reveal that the architecture of a neural network can be significantly influenced by various factors, including the number of sample points, parameters within the neural networks, and the regularity of the loss function. Specifically, a higher number of parameters tends to favor WeNNs, while an increased number of sample points and greater regularity in the loss function lean towards the adoption of DeNNs. We ultimately apply this theory to address partial differential equations using deep Ritz and physics-informed neural network (PINN) methods, guiding the design of neural networks.