Miracle-dz/UniFAR-FTUs huggingface dataset:
A multiparametric Murnaghan-Nakayama rule for Macdonald polynomials

We introduce a new family of operators as multi-parameter deformation of the one-row Macdonald polynomials. The matrix coefficients of these operators acting on the space of symmetric functions with rational coefficients in two parameters $q,t$ (denoted by $\Lambda[q,t]$) are computed by assigning some values to skew Macdonald polynomials in $\lambda$-ring notation. The new rule is utilized to provide new iterative formulas and also recover various existing formulas in a unified manner. Specifically the following applications are discussed: (i) A $(q,t)$-Murnaghan-Nakayama rule for Macdonald functions is given as a generalization of the $q$-Murnaghan-Nakayama rule; (ii) An iterative formula for the $(q,t)$-Green polynomial is deduced; (iii) A simple proof of the Murnaghan-Nakayama rule for the Hecke algebra and the Hecke-Clifford algebra is offered; (iv) A combinatorial inversion of the Pieri rule for Hall-Littlewood functions is derived with the help of the vertex operator realization of the Hall-Littlewood functions; (v) Two iterative formulae for the $(q,t)$-Kostka polynomials $K_{\lambda\mu}(q,t)$ are obtained from the dual version of our multiparametric Murnaghan-Nakayama rule, one of which yields an explicit formula for arbitrary $\lambda$ and $\mu$ in terms of the generalized $(q, t)$-binomial coefficient introduced independently by Lassalle and Okounkov.
Large Language Models are Temporal and Causal Reasoners for Video Question Answering

Large Language Models (LLMs) have shown remarkable performances on a wide range of natural language understanding and generation tasks. We observe that the LLMs provide effective priors in exploiting $\textit{linguistic shortcuts}$ for temporal and causal reasoning in Video Question Answering (VideoQA). However, such priors often cause suboptimal results on VideoQA by leading the model to over-rely on questions, $\textit{i.e.}$, $\textit{linguistic bias}$, while ignoring visual content. This is also known as `ungrounded guesses' or `hallucinations'. To address this problem while leveraging LLMs' prior on VideoQA, we propose a novel framework, Flipped-VQA, encouraging the model to predict all the combinations of $\langle$V, Q, A$\rangle$ triplet by flipping the source pair and the target label to understand their complex relationships, $\textit{i.e.}$, predict A, Q, and V given a VQ, VA, and QA pairs, respectively. In this paper, we develop LLaMA-VQA by applying Flipped-VQA to LLaMA, and it outperforms both LLMs-based and non-LLMs-based models on five challenging VideoQA benchmarks. Furthermore, our Flipped-VQA is a general framework that is applicable to various LLMs (OPT and GPT-J) and consistently improves their performances. We empirically demonstrate that Flipped-VQA not only enhances the exploitation of linguistic shortcuts but also mitigates the linguistic bias, which causes incorrect answers over-relying on the question. Code is available at https://github.com/mlvlab/Flipped-VQA.
Accessibility, planar graphs, and quasi-isometries

We prove that a connected, locally finite, quasi-transitive graph which is quasi-isometric to a planar graph is necessarily accessible. This leads to a complete classification of the finitely generated groups which are quasi-isometric to planar graphs. In particular, such groups are virtually free products of free and surface groups.
Symmetry-preserving graph attention network to solve routing problems at multiple resolutions

Travelling Salesperson Problems (TSPs) and Vehicle Routing Problems (VRPs) have achieved reasonable improvement in accuracy and computation time with the adaptation of Machine Learning (ML) methods. However, none of the previous works completely respects the symmetries arising from TSPs and VRPs including rotation, translation, permutation, and scaling. In this work, we introduce the first-ever completely equivariant model and training to solve combinatorial problems. Furthermore, it is essential to capture the multiscale structure (i.e. from local to global information) of the input graph, especially for the cases of large and long-range graphs, while previous methods are limited to extracting only local information that can lead to a local or sub-optimal solution. To tackle the above limitation, we propose a Multiresolution scheme in combination with Equivariant Graph Attention network (mEGAT) architecture, which can learn the optimal route based on low-level and high-level graph resolutions in an efficient way. In particular, our approach constructs a hierarchy of coarse-graining graphs from the input graph, in which we try to solve the routing problems on simple low-level graphs first, then utilize that knowledge for the more complex high-level graphs. Experimentally, we have shown that our model outperforms existing baselines and proved that symmetry preservation and multiresolution are important recipes for solving combinatorial problems in a data-driven manner. Our source code is publicly available at https://github.com/HySonLab/Multires-NP-hard
A Generalized Adjusted Min-Sum Decoder for 5G LDPC Codes: Algorithm and Implementation

5G New Radio (NR) has stringent demands on both performance and complexity for the design of low-density parity-check (LDPC) decoding algorithms and corresponding VLSI implementations. Furthermore, decoders must fully support the wide range of all 5G NR blocklengths and code rates, which is a significant challenge. In this paper, we present a high-performance and low-complexity LDPC decoder, tailor-made to fulfill the 5G requirements. First, to close the gap between belief propagation (BP) decoding and its approximations in hardware, we propose an extension of adjusted min-sum decoding, called generalized adjusted min-sum (GA-MS) decoding. This decoding algorithm flexibly truncates the incoming messages at the check node level and carefully approximates the non-linear functions of BP decoding to balance the error-rate and hardware complexity. Numerical results demonstrate that the proposed fixed-point GAMS has only a minor gap of 0.1 dB compared to floating-point BP under various scenarios of 5G standard specifications. Secondly, we present a fully reconfigurable 5G NR LDPC decoder implementation based on GA-MS decoding. Given that memory occupies a substantial portion of the decoder area, we adopt multiple data compression and approximation techniques to reduce 42.2% of the memory overhead. The corresponding 28nm FD-SOI ASIC decoder has a core area of 1.823 mm2 and operates at 895 MHz. It is compatible with all 5G NR LDPC codes and achieves a peak throughput of 24.42 Gbps and a maximum area efficiency of 13.40 Gbps/mm2 at 4 decoding iterations.
On minimal graphs of sublinear growth over manifolds with non-negative Ricci curvature

We prove that entire solutions of the minimal hypersurface equation \[ \mathrm{div}\left(\frac{Du}{\sqrt{1+|Du|^2}}\right) = 0 \] on a complete manifold with $\mathrm{Ric} \ge 0$, whose negative part grows like $\mathcal{O}(r/\log r)$ ($r$ the distance from a fixed origin), are constant. This extends the Bernstein Theorem for entire positive minimal graphs established in recent years. The proof depends on a new technique to get gradient bounds by means of integral estimates, which does not require any further geometric assumption on $M$.
RIS-based IMT-2030 Testbed for MmWave Multi-stream Ultra-massive MIMO Communications

As one enabling technique of the future sixth generation (6G) network, ultra-massive multiple-input-multiple-output (MIMO) can support high-speed data transmissions and cell coverage extension. However, it is hard to realize the ultra-massive MIMO via traditional phased arrays due to unacceptable power consumption. To address this issue, reconfigurable intelligent surface-based (RIS-based) antennas are an energy-efficient enabler of the ultra-massive MIMO, since they are free of energy-hungry phase shifters. In this article, we report the performances of the RIS-enabled ultra-massive MIMO via a project called Verification of MmWave Multi-stream Transmissions Enabled by RIS-based Ultra-massive MIMO for 6G (V4M), which was proposed to promote the evolution towards IMT-2030. In the V4M project, we manufacture RIS-based antennas with 1024 one-bit elements working at 26 GHz, based on which an mmWave dual-stream ultra-massive MIMO prototype is implemented for the first time. To approach practical settings, the Tx and Rx of the prototype are implemented by one commercial new radio base station and one off-the-shelf user equipment, respectively. The measured data rate of the dual-stream prototype approaches the theoretical peak rate. Our contributions to the V4M project are also discussed by presenting technological challenges and corresponding solutions.
On 2-distance 16-coloring of planar graphs with maximum degree at most five

A vertex coloring of a graph G is called a 2-distance coloring if any two vertices at a distance at most 2 from each other receive different colors. Suppose that G is a planar graph with a maximum degree at most 5. We prove that G admits a 2-distance 16 coloring, which improves the result given by Hou et al. (Graphs and Combinatorics 39:20, 2023).
A general nonuniqueness result for Yamabe-type problems for conformally variational Riemannian invariants

Given a conformally variational scalar Riemannian invariant $I$, we identify a sufficient condition for a closed Riemannian manifold to admit finite regular coverings with many nonhomothetic conformal rescalings with $I$ constant. We also identify a sufficient condition for the universal cover to admit infinitely many geometrically distinct periodic conformal rescalings with $I$ constant. Using these conditions, we improve known nonuniqueness results for the $Q$-curvatures of orders two, four, and six, and establish nonuniqueness results for higher-order $Q$-curvatures and renormalized volume coefficients.
Irreducible Curriculum for Language Model Pretraining

Automatic data selection and curriculum design for training large language models is challenging, with only a few existing methods showing improvements over standard training. Furthermore, current schemes focus on domain-level selection, overlooking the more fine-grained contributions of each individual training point. It is difficult to apply traditional datapoint selection methods on large language models: most online batch selection methods perform two-times forward or backward passes, which introduces considerable extra costs with large-scale models. To mitigate these obstacles, we propose irreducible curriculum as a curriculum learning algorithm for language model pretraining, which prioritizes samples with higher learnability. Specifically, to avoid prohibitive extra computation overhead, we simulate the sample loss along the main model's training trajectory using a small-scale proxy model. Our experiments on the RedPajama-1B dataset demonstrate a consistent improvement on validation perplexity across all 7 domains compared to random uniform baseline and the anti-curriculum strategy. Our method also reduces the sharpness of the network and illustrates a better 5-shot accuracy on MMLU benchmarks.
Thermodynamics and Rate Thermodynamics

Approach of mesoscopic state variables to time independent equilibrium sates (zero law of thermodynamics) gives birth to the classical equilibrium thermodynamics. Approach of fluxes and forces to fixed points (equilibrium fluxes and forces) that drive reduced mesoscopic dynamics gives birth to the rate thermodynamics that is applicable to driven systems. We formulate the rate thermodynamics and dynamics, investigate its relation to the classical thermodynamics, to extensions involving more details, to the hierarchy reformulations of dynamical theories, and to the Onsager variational principle. We also compare thermodynamic and dynamic critical behavior observed in closed and open systems. Dynamics and thermodynamics of the van der Waals gas provides an illustration.
A short proof of the Almkvist-Meurman theorem

We give a short generating function proof of the Almkvist-Meurman theorem: For integers $h$ and $k\ne0$, define the numbers $M_n(h,k)$ by $kx(e^{hx}-1)/(e^{kx}-1)=\sum_{n=0}^\infty M_n(h,k) x^n/n! $. Equivalently, $M_n(h,k) = k^n(B_n(h/k) - B_n)$, where $B_n(u)$ is the Bernoulli polynomial. Then $M_n(h,k)$ is an integer. The proof is related to Postnikov's functional equation for the generating function for intransitive trees.
Optimal Structured Matrix Approximation for Robustness to Incomplete Biosequence Data

We propose a general method for optimally approximating an arbitrary matrix $\mathbf{M}$ by a structured matrix $\mathbf{T}$ (circulant, Toeplitz/Hankel, etc.) and examine its use for estimating the spectra of genomic linkage disequilibrium matrices. This application is prototypical of a variety of genomic and proteomic problems that demand robustness to incomplete biosequence information. We perform a simulation study and corroborative test of our method using real genomic data from the Mouse Genome Database. The results confirm the predicted utility of the method and provide strong evidence of its potential value to a wide range of bioinformatics applications. Our optimal general matrix approximation method is expected to be of independent interest to an even broader range of applications in applied mathematics and engineering.
Quantitative errors in the Cochrane review on"Physical interventions to interrupt or reduce the spread of respiratory viruses"

The COVID-19 pandemic has heightened the urgency to understand and prevent pathogen transmission, specifically regarding infectious airborne particles. Extensive studies validate the understanding of larger (droplets) and smaller (aerosols) particles in disease transmission. Similarly, N95 respirators, and other forms of respiratory protection, have proven efficacy in reducing the risk of infection across various environments. Even though multiple studies confirm their protective effect when adopted in healthcare and public settings for infection prevention, studies on their adoption over the last several decades in both clinical trials and observational studies have not provided as clear an understanding. Here we show that the standard analytical equations used in the analysis of these studies do not accurately represent the random variables impacting study results. By correcting these equations, it is demonstrated that conclusions drawn from these studies are heavily biased and uncertain, providing little useful information. Despite these limitations, we show that when outcome measures are properly analyzed, existing results consistently point to the benefit of N95 respirators over medical masks, and masking over its absence. Correcting errors in widely reported meta-analyses also yields statistically significant estimates. These findings have important implications for study design and using existing evidence for infection control policy guidelines.
Learning Fair Representations with High-Confidence Guarantees

Representation learning is increasingly employed to generate representations that are predictive across multiple downstream tasks. The development of representation learning algorithms that provide strong fairness guarantees is thus important because it can prevent unfairness towards disadvantaged groups for all downstream prediction tasks. To prevent unfairness towards disadvantaged groups in all downstream tasks, it is crucial to provide representation learning algorithms that provide fairness guarantees. In this paper, we formally define the problem of learning representations that are fair with high confidence. We then introduce the Fair Representation learning with high-confidence Guarantees (FRG) framework, which provides high-confidence guarantees for limiting unfairness across all downstream models and tasks, with user-defined upper bounds. After proving that FRG ensures fairness for all downstream models and tasks with high probability, we present empirical evaluations that demonstrate FRG's effectiveness at upper bounding unfairness for multiple downstream models and tasks.
Pricing of water: Optimal departures from the inverse elasticity rule

We consider the problem of water usage, developing a model to analyze the optimal pricing of water within a second‐best economy. A benevolent supplier provides water to multiple user groups and chooses sectoral prices to maximize social welfare subject revenue and resource constraints. We first analyze the optimal pricing rule in a static setup, and examine when it is optimal to deviate from the inverse elasticity rule. Then, we investigate the effects of both revenue and resource constraints in the dynamic model. We find that it could be possible to for the supplier to charge a higher price to the more elastic demand, when water gets scarce.
Tilted Circumbinary Planetary Systems as Efficient Progenitors of Free-floating Planets

The dominant mechanism for generating free-floating planets has so far remained elusive. One suggested mechanism is that planets are ejected from planetary systems due to planet–planet interactions. Instability around a single star requires a very compactly spaced planetary system. We find that around binary star systems instability can occur even with widely separated planets that are on tilted orbits relative to the binary orbit due to combined effects of planet–binary and planet–planet interactions, especially if the binary is on an eccentric orbit. We investigate the orbital stability of planetary systems with various planet masses and architectures. We find that the stability of the system depends upon the mass of the highest-mass planet. The order of the planets in the system does not significantly affect stability, but, generally, the most massive planet remains stable and the lower-mass planets are ejected. The minimum planet mass required to trigger the instability is about that of Neptune for a circular orbit binary and a super-Earth of about 10 Earth masses for highly eccentric binaries. Hence, we suggest that planet formation around inclined binaries can be an efficient formation mechanism for free-floating planets. While most observed free-floating planets are giant planets, we predict that there should be more low-mass free-floating planets that are as of yet unobserved than higher-mass planets.
Adapted Thermodynamical Model for the Prediction of Adsorption in Nanoporous Materials

In this paper, we introduce a novel, adapted approach for computing gas adsorption properties in porous materials. We analyze the Dubinin-Polanyi's adsorption model and investigate various frameworks to estimate its required essential components. Those are linked to physicochemical properties of the adsorbates, such as the vapor saturation pressure and density in the adsorbed state. To conduct this analysis, we obtain adsorption isotherms for several metal-organic frameworks, encompassing a range of pore sizes, shapes, and chemical compositions. We then apply and evaluate multiple combinations of models for saturation pressure and density. After the evaluation of the method, we propose a working thermodynamic model for computing adsorption isotherms, which entails using the critical isochore as an approximation of the saturation pressure above the critical point and applying Hauer's method with a universal thermal expansion coefficient for density in the adsorbed state. This framework is applicable not only to simulated isotherms but also to experimental data from the literature for various molecules and structures, demonstrating robust predictive capabilities and high transferability. Our method showcases superior performance in terms of accuracy, generalizability, and simplicity compared to existing methods currently in use. For the first time, a method starting from a single adsorption curve and based on physically interpretable parameters can predict adsorption properties across a wide range of operating conditions.
Facial Data Minimization: Shallow Model as Your Privacy Filter

Face recognition service has been used in many fields and brings much convenience to people. However, once the user's facial data is transmitted to a service provider, the user will lose control of his/her private data. In recent years, there exist various security and privacy issues due to the leakage of facial data. Although many privacy-preserving methods have been proposed, they usually fail when they are not accessible to adversaries' strategies or auxiliary data. Hence, in this paper, by fully considering two cases of uploading facial images and facial features, which are very typical in face recognition service systems, we proposed a data privacy minimization transformation (PMT) method. This method can process the original facial data based on the shallow model of authorized services to obtain the obfuscated data. The obfuscated data can not only maintain satisfactory performance on authorized models and restrict the performance on other unauthorized models but also prevent original privacy data from leaking by AI methods and human visual theft. Additionally, since a service provider may execute preprocessing operations on the received data, we also propose an enhanced perturbation method to improve the robustness of PMT. Besides, to authorize one facial image to multiple service models simultaneously, a multiple restriction mechanism is proposed to improve the scalability of PMT. Finally, we conduct extensive experiments and evaluate the effectiveness of the proposed PMT in defending against face reconstruction, data abuse, and face attribute estimation attacks. These experimental results demonstrate that PMT performs well in preventing facial data abuse and privacy leakage while maintaining face recognition accuracy.
An accelerated first-order regularized momentum descent ascent algorithm for stochastic nonconvex-concave minimax problems

Stochastic nonconvex minimax problems have attracted wide attention in machine learning, signal processing and many other fields in recent years. In this paper, we propose an accelerated first-order regularized momentum descent ascent algorithm (FORMDA) for solving stochastic nonconvex-concave minimax problems. The iteration complexity of the algorithm is proved to be $\tilde{\mathcal{O}}(\varepsilon ^{-6.5})$ to obtain an $\varepsilon$-stationary point, which achieves the best-known complexity bound for single-loop algorithms to solve the stochastic nonconvex-concave minimax problems under the stationarity of the objective function.
Quantifying Photoproduction Corrections to J/\psi Measurements in Au+Au and Cu+Cu Collisions at $\sqrt{s_{NN}} = 200$ GeV

The contribution of J/\psi production from coherent and incoherent photon-induced production is calculated in Au+Au and Cu+Cu collisions at $\sqrt{s_{NN}} = 200$ GeV. The yield and nuclear modification factors ($R_{AA}$) contributed by photoproduction are presented as functions of transverse momentum ($p_T$) and centrality at both mid- and forward rapidity. The $R_{AA}$ of J/\psi from photoproduction is found to be as high as 0.6 in the lowest $p_{T}$ bin ($0<p_{T}<1$ GeV/$c$) at mid-rapidity in 60-92\% Au+Au collisions. The $R_{AA}$ measured in Au+Au and Cu+Cu collisions at $\sqrt{s_{NN}} = 200$ GeV are corrected by subtracting the calculated photoproduction contribution.