Miracle-dz/UniFAR-FTUs huggingface dataset:
Improved bounds for the bracketing number of orthants or revisiting an algorithm of Thiémard to compute bounds for the star discrepancy

We improve the best known upper bound for the bracketing number of $d$-dimensional axis-parallel boxes anchored in $0$ (or, put differently, of lower left orthants intersected with the $d$-dimensional unit cube $[0,1]^d$). More precisely, we provide a better upper bound for the cardinality of an algorithmic bracketing cover construction due to Eric Thi\'emard, which forms the core of his algorithm to approximate the star discrepancy of arbitrary point sets from [E. Thi\'emard, An algorithm to compute bounds for the star discrepancy, J.~Complexity 17 (2001), 850 -- 880]. Moreover, the new upper bound for the bracketing number of anchored axis-parallel boxes yields an improved upper bound for the bracketing number of arbitrary axis-parallel boxes in $[0,1]^d$. In our upper bounds all constants are fully explicit.
A Simple Construction of Tournaments with Finite and Uncountable Dichromatic Number

The dichromatic number $\chi(\vec{G})$ of a digraph $\vec{G}$ is the minimum number of colors needed to color the vertices $V(\vec{G})$ in such a way that no monochromatic directed cycle is obtained. In this note, for any $k\in \mathbb{N}$, we give a simple construction of tournaments with dichromatic number exactly equal to $k$. The proofs are based on a combinatorial lemma on partitioning a checkerboard which may be of independent interest. We also generalize our finite construction to give an elementary construction of a complete digraph of cardinality equal to the cardinality of $\mathbb{R}$ and having an uncountable dichromatic number. Furthermore, we also construct an oriented balanced complete $n$-partite graph $\vec{K}^{(m)}_n$, such that the minimum number of colors needed to color its vertices such that there is no monochromatic directed triangle is greater than or equal to $nm/(n+2m-2)$.
Approximation algorithms for Job Scheduling with reconfigurable resources

We consider here the MultiBot problem for the scheduling and the resource parametrization of jobs related to the production or the transportation of different products inside a given time horizon. Those jobs must meet known in advance demands. The time horizon is divided into several discrete identical periods representing each the time needed to proceed a job. The objective is to find a parametrization and a schedule for the jobs in such a way they require as less resources as possible. Though this problem derived from the applicative context of reconfigurable robots, we focus here on fundamental issues. We show that the resulting strongly NP-hard Multibot problem may be handled in a greedy way with an approximation ratio of $\frac{4}{3}$.
Quantum and Classical Communication Complexity of Permutation-Invariant Functions

This paper gives a nearly tight characterization of the quantum communication complexity of the permutation-invariant Boolean functions. With such a characterization, we show that the quantum and randomized communication complexity of the permutation-invariant Boolean functions are quadratically equivalent (up to a logarithmic factor). Our results extend a recent line of research regarding query complexity \cite{AA14, Cha19, BCG+20} to communication complexity, showing symmetry prevents exponential quantum speedups. Furthermore, we show the Log-rank Conjecture holds for any non-trivial total permutation-invariant Boolean function. Moreover, we establish a relationship between the quantum/classical communication complexity and the approximate rank of permutation-invariant Boolean functions. This implies the correctness of the Log-approximate-rank Conjecture for permutation-invariant Boolean functions in both randomized and quantum settings (up to a logarithmic factor).
On Sparse Canonical Correlation Analysis

The classical Canonical Correlation Analysis (CCA) identifies the correlations between two sets of multivariate variables based on their covariance, which has been widely applied in diverse fields such as computer vision, natural language processing, and speech analysis. Despite its popularity, CCA can encounter challenges in explaining correlations between two variable sets within high-dimensional data contexts. Thus, this paper studies Sparse Canonical Correlation Analysis (SCCA) that enhances the interpretability of CCA. We first show that SCCA generalizes three well-known sparse optimization problems, sparse PCA, sparse SVD, and sparse regression, which are all classified as NP-hard problems. This result motivates us to develop strong formulations and efficient algorithms. Our main contributions include (i) the introduction of a combinatorial formulation that captures the essence of SCCA and allows the development of approximation algorithms; (ii) the derivation of an equivalent mixed-integer semidefinite programming model that facilitates a specialized branch-and-cut algorithm with analytical cuts; and (iii) the establishment of the complexity results for two low-rank special cases of SCCA. The effectiveness of our proposed formulations and algorithms is validated through numerical experiments.
Brain-Conditional Multimodal Synthesis: A Survey and Taxonomy

In the era of Artificial Intelligence Generated Content (AIGC), conditional multimodal synthesis technologies (e.g., text-to-image, text-to-video, text-to-audio, etc) are gradually reshaping the natural content in the real world. The key to multimodal synthesis technology is to establish the mapping relationship between different modalities. Brain signals, serving as potential reflections of how the brain interprets external information, exhibit a distinctive One-to-Many correspondence with various external modalities. This correspondence makes brain signals emerge as a promising guiding condition for multimodal content synthesis. Brian-conditional multimodal synthesis refers to decoding brain signals back to perceptual experience, which is crucial for developing practical brain-computer interface systems and unraveling complex mechanisms underlying how the brain perceives and comprehends external stimuli. This survey comprehensively examines the emerging field of AIGC-based Brain-conditional Multimodal Synthesis, termed AIGC-Brain, to delineate the current landscape and future directions. To begin, related brain neuroimaging datasets, functional brain regions, and mainstream generative models are introduced as the foundation of AIGC-Brain decoding and analysis. Next, we provide a comprehensive taxonomy for AIGC-Brain decoding models and present task-specific representative work and detailed implementation strategies to facilitate comparison and in-depth analysis. Quality assessments are then introduced for both qualitative and quantitative evaluation. Finally, this survey explores insights gained, providing current challenges and outlining prospects of AIGC-Brain. Being the inaugural survey in this domain, this paper paves the way for the progress of AIGC-Brain research, offering a foundational overview to guide future work.
A unified structure-preserving parametric finite element method for anisotropic surface diffusion

We propose and analyze a unified structure-preserving parametric finite element method (SP-PFEM) for the anisotropic surface diffusion of curves in two dimensions $(d=2)$ and surfaces in three dimensions $(d=3)$ with an arbitrary anisotropic surface energy density $\gamma(\boldsymbol{n})$, where $\boldsymbol{n}\in \mathbb{S}^{d-1}$ represents the outward unit vector. By introducing a novel unified surface energy matrix $\boldsymbol{G}_k(\boldsymbol{n})$ depending on $\gamma(\boldsymbol{n})$, the Cahn--Hoffman $\boldsymbol{\xi}$-vector and a stabilizing function $k(\boldsymbol{n}):\ \mathbb{S}^{d-1}\to {\mathbb R}$, we obtain a unified and conservative variational formulation for the anisotropic surface diffusion via different surface differential operators including the surface gradient operator, the surface divergence operator and the surface Laplace--Beltrami operator. A SP-PFEM discretization is presented for the variational problem. In order to establish the unconditional energy stability of the proposed SP-PFEM under a very mild condition on $\gamma(\boldsymbol{n})$, we propose a new framework via {\sl local energy estimate} for proving energy stability/structure-preserving properties of the parametric finite element method for the anisotropic surface diffusion. This framework sheds light on how to prove unconditional energy stability of other numerical methods for geometric partial differential equations. Extensive numerical results are reported to demonstrate the efficiency and accuracy as well as structure-preserving properties of the proposed SP-PFEM for the anisotropic surface diffusion with arbitrary anisotropic surface energy density $\gamma(\boldsymbol{n})$ arising from different applications.
Cavitation bubble dynamics inside a droplet suspended in a different host fluid

In this paper, we present a theoretical, experimental and numerical study of the dynamics of cavitation bubbles inside a droplet suspended in another host fluid. On the theoretical side, we provided a modified Rayleigh collapse time and natural frequency for spherical bubbles in our particular context, characterized by the density ratio between the two liquids and the bubble-to-droplet size ratio. Regarding the experimental aspect, experiments were carried out for laser-induced cavitation bubbles inside oil-in-water (O/W) or water-in-oil (W/O) droplets. Two distinct fluid-mixing mechanisms were unveiled in the two systems, respectively. In the case of O/W droplets, a liquid jet emerges around the end of the bubble collapse phase, effectively penetrating the droplet interface. We offer a detailed analysis of the criteria governing jet penetration, involving the standoff parameter and impact velocity of the bubble jet on the droplet surface. Conversely, in the scenario involving W/O droplets, the bubble traverses the droplet interior, inducing global motion and eventually leading to droplet pinch-off when the local Weber number exceeds a critical value. This phenomenon is elucidated through the equilibrium between interfacial and kinetic energies. Lastly, our boundary integral model faithfully reproduces the essential physics of the non-spherical bubble dynamics observed in the experiments. We conduct a parametric study spanning a wide parameter space to investigate bubble–droplet interactions. The insights from this study could serve as a valuable reference for practical applications in the field of ultrasonic emulsification, pharmacy, etc.
Fast decisions reflect biases, slow decisions do not

Decisions are often made by heterogeneous groups of individuals, each with distinct initial biases and access to information of different quality. We show that in large groups of independent agents who accumulate evidence the first to decide are those with the strongest initial biases. Their decisions align with their initial bias, regardless of the underlying truth. In contrast, agents who decide last make decisions as if they were initially unbiased, and hence make better choices. We obtain asymptotic expressions in the large population limit that quantify how agents’ initial inclinations shape early decisions. Our analysis shows how bias, information quality, and decision order interact in non-trivial ways to determine the reliability of decisions in a group.
A multipartite analogue of Dilworth's Theorem

We prove that every partially ordered set on $n$ elements contains $k$ subsets $A_{1},A_{2},\dots,A_{k}$ such that either each of these subsets has size $\Omega(n/k^{5})$ and, for every $i<j$, every element in $A_{i}$ is less than or equal to every element in $A_{j}$, or each of these subsets has size $\Omega(n/(k^{2}\log n))$ and, for every $i \not = j$, every element in $A_{i}$ is incomparable with every element in $A_{j}$ for $i\ne j$. This answers a question of the first author from 2006. As a corollary, we prove for each positive integer $h$ there is $C_h$ such that for any $h$ partial orders $<_{1},<_{2},\dots,<_{h}$ on a set of $n$ elements, there exists $k$ subsets $A_{1},A_{2},\dots,A_{k}$ each of size at least $n/(k\log n)^{C_{h}}$ such that for each partial order $<_{\ell}$, either $a_{1}<_{\ell}a_{2}<_{\ell}\dots<_{\ell}a_{k}$ for any tuple of elements $(a_1,a_2,\dots,a_k) \in A_1\times A_2\times \dots \times A_k$, or $a_{1}>_{\ell}a_{2}>_{\ell}\dots>_{\ell}a_{k}$ for any $(a_1,a_2,\dots,a_k) \in A_1\times A_2\times \dots \times A_k$, or $a_i$ is incomparable with $a_j$ for any $i\ne j$, $a_i\in A_i$ and $a_j\in A_j$. This improves on a 2009 result of Pach and the first author motivated by problems in discrete geometry.
Density bounds for unit ball packings relative to their outer parallel domains

We prove that the highest density of non-overlapping translates of a given centrally symmetric convex domain relative to its outer parallel domain of given outer radius is attained by a lattice packing in the Euclidean plane. This generalizes some earlier (classical) results. Sharp upper bounds are proved for the analogue problem on congruent circular disks in the spherical (resp., hyperbolic) plane and on congruent balls in Euclidean $3$-space.
Blockchain and Deep Learning-Based IDS for Securing SDN-Enabled Industrial IoT Environments

The industrial Internet of Things (IIoT) involves the integration of Internet of Things (IoT) technologies into industrial settings. However, given the high sensitivity of the industry to the security of industrial control system networks and IIoT, the use of software-defined networking (SDN) technology can provide improved security and automation of communication processes. Despite this, the architecture of SDN can give rise to various security threats. Therefore, it is of paramount importance to consider the impact of these threats on SDN-based IIoT environments. Unlike previous research, which focused on security in IIoT and SDN architectures separately, we propose an integrated method including two components that work together seamlessly for better detecting and preventing security threats associated with SDN-based IIoT architectures. The two components consist in a convolutional neural network-based Intrusion Detection System (IDS) implemented as an SDN application and a Blockchain-based system (BS) to empower application layer and network layer security, respectively. A significant advantage of the proposed method lies in jointly minimizing the impact of attacks such as command injection and rule injection on SDN-based IIoT architecture layers. The proposed IDS exhibits superior classification accuracy in both binary and multiclass categories.
Steering of Vortices by Magnetic Field Tilting in Open Superconductor Nanotubes

In planar superconductor thin films, the places of nucleation and arrangements of moving vortices are determined by structural defects. However, various applications of superconductors require reconfigurable steering of fluxons, which is hard to realize with geometrically predefined vortex pinning landscapes. Here, on the basis of the time-dependent Ginzburg–Landau equation, we present an approach for the steering of vortex chains and vortex jets in superconductor nanotubes containing a slit. The idea is based on the tilting of the magnetic field B at an angle α in the plane perpendicular to the axis of a nanotube carrying an azimuthal transport current. Namely, while at α=0∘, vortices move paraxially in opposite directions within each half-tube; an increase in α displaces the areas with the close-to-maximum normal component |Bn| to the close(opposite)-to-slit regions, giving rise to descending (ascending) branches in the induced-voltage frequency spectrum fU(α). At lower B values, upon reaching the critical angle αc, the close-to-slit vortex chains disappear, yielding fU of the nf1 type (n≥1: an integer; f1: the vortex nucleation frequency). At higher B values, fU is largely blurry because of multifurcations of vortex trajectories, leading to the coexistence of a vortex jet with two vortex chains at α=90∘. In addition to prospects for the tuning of GHz-frequency spectra and the steering of vortices as information bits, our findings lay the foundation for on-demand tuning of vortex arrangements in 3D superconductor membranes in tilted magnetic fields.
Temporal Validity Change Prediction

Temporal validity is an important property of text that is useful for many downstream applications, such as recommender systems, conversational AI, or story understanding. Existing benchmarking tasks often require models to identify the temporal validity duration of a single statement. However, in many cases, additional contextual information, such as sentences in a story or posts on a social media profile, can be collected from the available text stream. This contextual information may greatly alter the duration for which a statement is expected to be valid. We propose Temporal Validity Change Prediction, a natural language processing task benchmarking the capability of machine learning models to detect contextual statements that induce such change. We create a dataset consisting of temporal target statements sourced from Twitter and crowdsource sample context statements. We then benchmark a set of transformer-based language models on our dataset. Finally, we experiment with temporal validity duration prediction as an auxiliary task to improve the performance of the state-of-the-art model.
Multiform Evolution for High-Dimensional Problems with Low Effective Dimensionality

In this paper, we scale evolutionary algorithms to high-dimensional optimization problems that deceptively possess a low effective dimensionality (certain dimensions do not significantly affect the objective function). To this end, an instantiation of the multiform optimization paradigm is presented, where multiple low-dimensional counterparts of a target high-dimensional task are generated via random embeddings. Since the exact relationship between the auxiliary (low-dimensional) tasks and the target is a priori unknown, a multiform evolutionary algorithm is developed for unifying all formulations into a single multi-task setting. The resultant joint optimization enables the target task to efficiently reuse solutions evolved across various low-dimensional searches via cross-form genetic transfers, hence speeding up overall convergence characteristics. To validate the overall efficacy of our proposed algorithmic framework, comprehensive experimental studies are carried out on well-known continuous benchmark functions as well as a set of practical problems in the hyper-parameter tuning of machine learning models and deep learning models in classification tasks and Predator-Prey games, respectively.
1st Place Solution for 5th LSVOS Challenge: Referring Video Object Segmentation

The recent transformer-based models have dominated the Referring Video Object Segmentation (RVOS) task due to the superior performance. Most prior works adopt unified DETR framework to generate segmentation masks in query-to-instance manner. In this work, we integrate strengths of that leading RVOS models to build up an effective paradigm. We first obtain binary mask sequences from the RVOS models. To improve the consistency and quality of masks, we propose Two-Stage Multi-Model Fusion strategy. Each stage rationally ensembles RVOS models based on framework design as well as training strategy, and leverages different video object segmentation (VOS) models to enhance mask coherence by object propagation mechanism. Our method achieves 75.7% J&F on Ref-Youtube-VOS validation set and 70% J&F on test set, which ranks 1st place on 5th Large-scale Video Object Segmentation Challenge (ICCV 2023) track 3. Code is available at https://github.com/RobertLuo1/iccv2023_RVOS_Challenge.
AI and Tempo Estimation: A Review

The author's goal in this paper is to explore how artificial intelligence (AI) has been utilised to inform our understanding of and ability to estimate at scale a critical aspect of musical creativity - musical tempo. The central importance of tempo to musical creativity can be seen in how it is used to express specific emotions (Eerola and Vuoskoski 2013), suggest particular musical styles (Li and Chan 2011), influence perception of expression (Webster and Weir 2005) and mediate the urge to move one's body in time to the music (Burger et al. 2014). Traditional tempo estimation methods typically detect signal periodicities that reflect the underlying rhythmic structure of the music, often using some form of autocorrelation of the amplitude envelope (Lartillot and Toiviainen 2007). Recently, AI-based methods utilising convolutional or recurrent neural networks (CNNs, RNNs) on spectral representations of the audio signal have enjoyed significant improvements in accuracy (Aarabi and Peeters 2022). Common AI-based techniques include those based on probability (e.g., Bayesian approaches, hidden Markov models (HMM)), classification and statistical learning (e.g., support vector machines (SVM)), and artificial neural networks (ANNs) (e.g., self-organising maps (SOMs), CNNs, RNNs, deep learning (DL)). The aim here is to provide an overview of some of the more common AI-based tempo estimation algorithms and to shine a light on notable benefits and potential drawbacks of each. Limitations of AI in this field in general are also considered, as is the capacity for such methods to account for idiosyncrasies inherent in tempo perception, i.e., how well AI-based approaches are able to think and act like humans.
Internet of Harvester Nano Things: A Future Prospects

The advancements in nanotechnology, material science, and electrical engineering have shrunk the sizes of electronic devices down to the micro/nanoscale. This brings the opportunity of developing the Internet of Nano Things (IoNT), an extension of the Internet of Things (IoT). With nanodevices, numerous new possibilities emerge in the biomedical, military fields, and industrial products. However, a continuous energy supply is needed for these devices to work. At the micro/nanoscale, batteries cannot supply this demand due to size limitations and the limited energy contained in the batteries. Internet of Harvester Nano Things (IoHNT), a concept of Energy Harvesting (EH), which converts the existing different energy sources, which otherwise would be dissipated to waste, into electrical energy via electrical generators. Sources for EH are abundant, from sunlight, sound, water, and airflow to living organisms. IoHNT methods are significant assets to ensure the proper operation of the IoNT; thus, in this review, we comprehensively investigate the most useful energy sources and IoHNT principles to power the nano/micro-scaled electronic devices with the scope of IoNT. We discuss the IoHNT principles, material selections, challenges, and state-of-the-art applications of each energy source for both in-vivo and in vitro applications. Finally, we present the latest challenges of EH along with future research directions to solve the problems regarding constructing continuous IoNT containing various self-powered nanodevices. Therefore, IoHNT represents a significant shift in nanodevice power supply, leading us towards a future where wireless technology is widespread. Hence, it will motivate researchers to envision and contribute to the advancement of the following power revolution in IoNT, providing unmatched simplicity and efficiency.