Miracle-dz/UniFAR-FTUs huggingface dataset:
Whitney Twins, Whitney Duals, and Operadic Partition Posets

We say that a pair of nonnegative integer sequences $(\{a_k\}_{k\geq 0},\{b_k\}_{k\geq 0})$ is Whitney-realizable if there exists a poset $P$ for which (the absolute values) of the Whitney numbers of the first and second kind are given by the numbers $a_k$ and $b_k$ respectively. The pair is said to be Whitney-dualizable if, in addition, there exists another poset $Q$ for which their Whitney numbers of the first and second kind are instead given by $b_k$ and $a_k$ respectively. In this case, we say that $P$ and $Q$ are Whitney duals. We use results on Whitney duality, recently developed by the first two authors, to exhibit a family of sequences which allows for multiple realizations and Whitney-dual realizations. More precisely, we study edge labelings for the families of posets of pointed partitions $\Pi_n^{\bullet}$ and weighted partitions $\Pi_n^{w}$ which are associated to the operads $\mathcal{P}erm$ and $\mathcal{C}om^2$ respectively. The first author and Wachs proved that these two families of posets share the same pair of Whitney numbers. We find EW-labelings for $\Pi_n^{\bullet}$ and $\Pi_n^{w}$ and use them to show that they also share multiple nonisomorphic Whitney dual posets. In addition to EW-labelings, we also find two new EL-labelings for $\Pi_n^\bullet$ answering a question of Chapoton and Vallette. Using these EL-labelings of $\Pi_n^\bullet$, and an EL-labeling of $\Pi_n^w$ introduced by the first author and Wachs, we give combinatorial descriptions of bases for the operads $\mathcal{P}re\mathcal{L}ie, \mathcal{P}erm,$ and $\mathcal{C}om^2$. We also show that the bases for $\mathcal{P}erm$ and $\mathcal{C}om^2$ are PBW bases.
First-Principles Study of Electronic Structure and Optical Properties of Silicon/Carbon Nanotube

A supercell of a nanotube formed by a carbon nanotube (CNT) and a silicon nanotube (SiNT) is established. The electronic structure and optical properties are implemented through the first-principles method based on the density functional theory (DFT) with the generalized gradient approximation (GGA). The calculated results show that (6, 6) - (6, 6) silicon/carbon nanotubes (Si/CNTs) presented a direct band gap of 0.093 eV, (4, 4) - (6, 6) silicon/carbon nanotubes presented a direct band gap of 0.563 eV. The top of valence band was fundamentally determined by the Si-3p states and C-2p states, and the bottom of conduction band was primarily occupied by the C-2p states and Si-3p states in the Si/CNTs. It was found that (6, 6) - (6, 6) Si/CNTs have smaller energy band gap and better conductivity. Besides, Si/CNTs have satisfactory absorption characteristics and luminous efficiency in ultraviolet band.
Optimal Symmetric Strategies in Multi-Agent Systems with Decentralized Information

We consider a cooperative multi-agent system consisting of a team of agents with decentralized information. Our focus is on the design of symmetric (i.e. identical) strategies for the agents in order to optimize a finite horizon team objective. We start with a general information structure and then consider some special cases. The constraint of using symmetric strategies introduces new features and complications in the team problem. For example, we show in a simple example that randomized symmetric strategies may outperform deterministic symmetric strategies. We also discuss why some of the known approaches for reducing agents' private information in teams may not work under the constraint of symmetric strategies. We then adopt the common information approach for our problem and modify it to accommodate the use of symmetric strategies. This results in a common information based dynamic program where each step involves minimization over a single function from the space of an agent's private information to the space of probability distributions over actions. We present specialized models where private information can be reduced using simple dynamic program based arguments.
Deep learning-based reduced order model for three-dimensional unsteady flow using mesh transformation and stitching

Artificial intelligence-based three-dimensional(3D) fluid modeling has gained significant attention in recent years. However, the accuracy of such models is often limited by the processing of irregular flow data. In order to bolster the credibility of near-wall flow prediction, this paper presents a deep learning-based reduced order model for three-dimensional unsteady flow using the transformation and stitching of multi-block structured meshes. To begin with, full-order flow data is provided by numerical simulations that rely on multi-block structured meshes. A mesh transformation technique is applied to convert each structured grid with data into a corresponding uniform and orthogonal grid, which is subsequently stitched and filled. The resulting snapshots in the transformed domain contain accurate flow information for multiple meshes and can be directly fed into a structured neural network without requiring any interpolation operation. Subsequently, a network model based on a fully convolutional neural network is constructed to predict flow dynamics accurately. To validate the strategy's feasibility, the flow around a sphere with Re=300 was investigated, and the results obtained using traditional Cartesian interpolation were used as the baseline for comparison. All the results demonstrate the preservation and accurate prediction of flow details near the wall, with the pressure correlation coefficient on the wall achieving an impressive value of 0.9985. Moreover, the periodic behavior of flow fields can be faithfully predicted during long-term inference.
Nonparametric truncated spline regression model on the data of human development index (HDI) in indonesia

The standard measurement for country’s human development is Human Development Index (HDI). Several factors allegedly affect it, such as life expectancy, gross domestic regional product (GDRP), the number of poor people, and the percentage of an illeterate people. If the HDI’s data and those factors is plotted, then the plot do not form a specific pattern, so the HDI’s data can be applied with nonparametric truncated spline regression model. The best of nonparametric truncated spline regression model is influenced by the order and knot points selection. In this article, nonparametric truncated spline regression model on the data of HDI in Indonesia is applied at first order with 3,4 and 5 knot points. Based on the result, the best nonparametric truncated spline regression model on the data of HDI in Indonesia is obtained by the combination of 5-5-5-4 knot points. There were 2 of 4 allegedly factors significant to HDI in Indonesia based on parameter significance test followed in this research.
A framework to test interval arithmetic libraries and their IEEE 1788‐2015 compliance

As developers of libraries implementing interval arithmetic, we faced the same difficulties when it comes to testing our libraries. What must be tested? How can we devise relevant test cases for unit testing? How can we ensure a high (and possibly 100%) test coverage? Before considering these questions, we briefly recall the main features of interval arithmetic and of the IEEE 1788‐2015 standard for interval arithmetic. After listing the different aspects that, in our opinion, must be tested, we contribute a first step towards offering a test suite for an interval arithmetic library. First we define a format that enables the exchange of test cases, so that they can be read and tried easily. Then we offer a first set of test cases, for a selected set of mathematical functions. Next, we examine how the Julia interval arithmetic library, IntervalArithmetic.jl, actually performs to these tests. As this is an ongoing work, we list extra tests that we deem important to perform.
An Incremental Span-Program-Based Algorithm and the Fine Print of Quantum Topological Data Analysis

We introduce a new quantum algorithm for computing the Betti numbers of a simplicial complex. In contrast to previous quantum algorithms that work by estimating the eigenvalues of the combinatorial Laplacian, our algorithm is an instance of the generic Incremental Algorithm for computing Betti numbers that incrementally adds simplices to the simplicial complex and tests whether or not they create a cycle. In contrast to existing quantum algorithms for computing Betti numbers that work best when the complex has close to the maximal number of simplices, our algorithm works best for sparse complexes. To test whether a simplex creates a cycle, we introduce a quantum span-program algorithm. We show that the query complexity of our span program is parameterized by quantities called the effective resistance and effective capacitance of the boundary of the simplex. Unfortunately, we also prove upper and lower bounds on the effective resistance and capacitance, showing both quantities can be exponentially large with respect to the size of the complex, implying that our algorithm would have to run for exponential time to exactly compute Betti numbers. However, as a corollary to these bounds, we show that the spectral gap of the combinatorial Laplacian can be exponentially small. As the runtime of all previous quantum algorithms for computing Betti numbers are parameterized by the inverse of the spectral gap, our bounds show that all quantum algorithms for computing Betti numbers must run for exponentially long to exactly compute Betti numbers. Finally, we prove some novel formulas for effective resistance and effective capacitance to give intuition for these quantities.
Structured Pruning of Neural Networks for Constraints Learning

In recent years, the integration of Machine Learning (ML) models with Operation Research (OR) tools has gained popularity across diverse applications, including cancer treatment, algorithmic configuration, and chemical process optimization. In this domain, the combination of ML and OR often relies on representing the ML model output using Mixed Integer Programming (MIP) formulations. Numerous studies in the literature have developed such formulations for many ML predictors, with a particular emphasis on Artificial Neural Networks (ANNs) due to their significant interest in many applications. However, ANNs frequently contain a large number of parameters, resulting in MIP formulations that are impractical to solve, thereby impeding scalability. In fact, the ML community has already introduced several techniques to reduce the parameter count of ANNs without compromising their performance, since the substantial size of modern ANNs presents challenges for ML applications as it significantly impacts computational efforts during training and necessitates significant memory resources for storage. In this paper, we showcase the effectiveness of pruning, one of these techniques, when applied to ANNs prior to their integration into MIPs. By pruning the ANN, we achieve significant improvements in the speed of the solution process. We discuss why pruning is more suitable in this context compared to other ML compression techniques, and we identify the most appropriate pruning strategies. To highlight the potential of this approach, we conduct experiments using feed-forward neural networks with multiple layers to construct adversarial examples. Our results demonstrate that pruning offers remarkable reductions in solution times without hindering the quality of the final decision, enabling the resolution of previously unsolvable instances.
AudioInceptionNeXt: TCL AI LAB Submission to EPIC-SOUND Audio-Based-Interaction-Recognition Challenge 2023

This report presents the technical details of our submission to the 2023 Epic-Kitchen EPIC-SOUNDS Audio-Based Interaction Recognition Challenge. The task is to learn the mapping from audio samples to their corresponding action labels. To achieve this goal, we propose a simple yet effective single-stream CNN-based architecture called AudioInceptionNeXt that operates on the time-frequency log-mel-spectrogram of the audio samples. Motivated by the design of the InceptionNeXt, we propose parallel multi-scale depthwise separable convolutional kernels in the AudioInceptionNeXt block, which enable the model to learn the time and frequency information more effectively. The large-scale separable kernels capture the long duration of activities and the global frequency semantic information, while the small-scale separable kernels capture the short duration of activities and local details of frequency information. Our approach achieved 55.43% of top-1 accuracy on the challenge test set, ranked as 1st on the public leaderboard. Codes are available anonymously at https://github.com/StevenLauHKHK/AudioInceptionNeXt.git.
Approximately optimal trade execution strategies under fast mean-reversion

In a fixed time horizon, appropriately executing a large amount of a particular asset -- meaning a considerable portion of the volume traded within this frame -- is challenging. Especially for illiquid or even highly liquid but also highly volatile ones, the role of"market quality"is quite relevant in properly designing execution strategies. Here, we model it by considering uncertain volatility and liquidity; hence, moments of high or low price impact and risk vary randomly throughout the trading period. We work under the central assumption: although there are these uncertain variations, we assume they occur in a fast mean-reverting fashion. We thus employ singular perturbation arguments to study approximations to the optimal strategies in this framework. By using high-frequency data, we provide estimation methods for our model in face of microstructure noise, as well as numerically assess all of our results.
MorphPiece : Moving away from Statistical Language Representation

Tokenization is a critical part of modern NLP pipelines. However, contemporary tokenizers for Large Language Models, are based on statistical analysis of text corpora, without much consideration to the linguistic features. We propose a linguistically motivated tokenization scheme, MorphPiece, which is based partly on morphological segmentation of the underlying text. A GPT-style causal language model trained on this tokenizer (called MorphGPT) shows superior convergence compared to the same architecture trained on a standard BPE tokenizer. Speciﬁcally we get Language Modeling performance comparable to a 6 times larger model. Additionally, we evaluate Mor-phGPT on a variety of NLP tasks in supervised and unsupervised settings and ﬁnd superior performance across the board, compared to GPT-2 model.
Implementation of the Density-functional Theory on Quantum Computers with Linear Scaling with respect to the Number of Atoms

Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing the Hamiltonian, for which a classical algorithm typically requires a computational complexity that scales cubically with respect to the number of electrons. This limits DFT's applicability to large-scale problems with complex chemical environments and microstructures. This article presents a quantum algorithm that has a linear scaling with respect to the number of atoms, which is much smaller than the number of electrons. Our algorithm leverages the quantum singular value transformation (QSVT) to generate a quantum circuit to encode the density-matrix, and an estimation method for computing the output electron density. In addition, we present a randomized block coordinate fixed-point method to accelerate the self-consistent field calculations by reducing the number of components of the electron density that needs to be estimated. The proposed framework is accompanied by a rigorous error analysis that quantifies the function approximation error, the statistical fluctuation, and the iteration complexity. In particular, the analysis of our self-consistent iterations takes into account the measurement noise from the quantum circuit. These advancements offer a promising avenue for tackling large-scale DFT problems, enabling simulations of complex systems that were previously computationally infeasible.
Hypothesis Transfer Learning with Surrogate Classification Losses

Hypothesis transfer learning (HTL) contrasts domain adaptation by allowing for a previous task leverage, named the source, into a new one, the target, without requiring access to the source data. Indeed, HTL relies only on a hypothesis learnt from such source data, relieving the hurdle of expansive data storage and providing great practical benefits. Hence, HTL is highly beneficial for real-world applications relying on big data. The analysis of such a method from a theoretical perspective faces multiple challenges, particularly in classification tasks. This paper deals with this problem by studying the learning theory of HTL through algorithmic stability, an attractive theoretical framework for machine learning algorithms analysis. In particular, we are interested in the statistical behaviour of the regularized empirical risk minimizers in the case of binary classification. Our stability analysis provides learning guarantees under mild assumptions. Consequently, we derive several complexity-free generalization bounds for essential statistical quantities like the training error, the excess risk and cross-validation estimates. These refined bounds allow understanding the benefits of transfer learning and comparing the behaviour of standard losses in different scenarios, leading to valuable insights for practitioners.
Introduction to ‘Artificial intelligence in failure analysis of transportation infrastructure and materials'

Transportation infrastructures, including roads, bridges, tunnels, stations, airports and subways, play fundamental roles in modern society. Engineering failures of transportation infrastructures may result in significant damage to the public. The traditional methods are to monitor, store and analyse the information during the infrastructure and material design, testing, construction, numerical simulations, evaluation, operation, maintenance and preservation, using mechanistic-based, material-based and statistics-based approaches. In recent decades, artificial intelligence (AI) has drawn the attention of many researchers and has been used as a powerful tool to understand and analyse the engineering failures in transportation infrastructure and materials. AI has the advantages of conveniently characterizing infrastructure materials in multi-scale, extracting failure information from images and cloud points, evaluating performance from the signals of sensors, predicting the long-term performance of infrastructure based on big data and optimizing infrastructure maintenance strategies, etc. In the future, AI techniques will be more effective and promising for data collection, transmission, fusion, mining and analysis, which will help engineers quickly detect, analyse and finally prevent the engineering failures of transportation infrastructure and materials. This theme issue presents the latest developments of AI in failure analysis of transportation infrastructure and materials. This article is part of the theme issue 'Artificial intelligence in failure analysis of transportation infrastructure and materials'.
Formation and evolution of vortex rings with weak to moderate swirl

Abstract The formation of swirling vortex rings and their early time evolution, resulting from the controlled discharge of an incompressible, Newtonian fluid into a stationary equivalent fluid bulk, is explored for weak to moderate swirl number $S \in [0, 1]$. Two practically realisable inlet conditions are investigated with swirl simultaneously superposed onto a linear momentum discharge; the corresponding circulation based Reynolds number is 7500. The results obtained reveal that for $S > 1/2$, the addition of swirl promotes the breakdown of the leading primary vortex ring structure, giving rise to the striking feature of significant negative azimuthal vorticity generation in the region surrounding the primary vortex ring core, whose strength scales with ${S}^2$. Through a nonlinear interaction with the vortex breakdown, the radius of the primary toroidal vortex core is rapidly increased; consequently, the self-induced propagation velocity of the leading ring decreases with $S$ and vortex stretching along the circular primary vortex core increases counteracting viscous diffusion effects. The latter governs the evolution of the peak vorticity intensity and the swirl velocity magnitude in the primary ring core, the circulation growth rate of the primary ring, as well as the vorticity intensity of the trailing jet and hence its stability. This combination of effects leads to an increased dimensionless kinetic energy for the primary ring with increasing $S$ and results in an almost linearly decreasing circulation based formation number, $F$.
Selective autophagy regulates chloroplast protein import and promotes plant stress tolerance

Chloroplasts are plant organelles responsible for photosynthesis and environmental sensing. Most chloroplast proteins are imported from the cytosol through the translocon at the outer envelope membrane of chloroplasts (TOC). Previous work has shown that TOC components are regulated by the ubiquitin‐proteasome system (UPS) to control the chloroplast proteome, which is crucial for the organelle's function and plant development. Here, we demonstrate that the TOC apparatus is also subject to K63‐linked polyubiquitination and regulation by selective autophagy, potentially promoting plant stress tolerance. We identify NBR1 as a selective autophagy adaptor targeting TOC components, and mediating their relocation into vacuoles for autophagic degradation. Such selective autophagy is shown to control TOC protein levels and chloroplast protein import and to influence photosynthetic activity as well as tolerance to UV‐B irradiation and heat stress in Arabidopsis plants. These findings uncover the vital role of selective autophagy in the proteolytic regulation of specific chloroplast proteins, and how dynamic control of chloroplast protein import is critically important for plants to cope with challenging environments.