Miracle-dz/UniFAR-FTUs huggingface dataset:
A Talenti-type comparison theorem for the $p$-Laplacian on $\mathrm{RCD}(K,N)$ spaces and some applications

In this paper, we prove a Talenti-type comparison theorem for the $p$-Laplacian with Dirichlet boundary conditions on open subsets of a $\mathrm{RCD}(K,N)$ space with $K>0$ and $N\in (1,\infty)$. The obtained Talenti-type comparison theorem is sharp, rigid and stable with respect to measured Gromov-Hausdorff topology. As an application of such Talenti-type comparison, we establish a sharp and rigid reverse H\"{o}lder inequality for first eigenfunctions of the $p$-Laplacian and a related quantitative stability result.
Operator Products in the SU($\infty$) Principal Chiral Model

The SU($N$) principal chiral model is asymptotically free and integrable in $1+1$ dimensions. In the large-$N$ limit, there is no scattering, but correlation functions are {\em not} those of a free field theory. We briefly review the derivation of form factors for local operators. Two-point functions for such operators are known exactly. The two-point function of scaling-field operators has the short-distance behavior expected from the renormalization group. We briefly discuss non-vacuum operator products. The ultimate goal is to derive the Lagrangian field theory from this axiomatic quantum-field-theory formalism.
Information-Theoretic State Variable Selection for Reinforcement Learning

Identifying the most suitable variables to represent the state is a fundamental challenge in Reinforcement Learning (RL). These variables must efficiently capture the information necessary for making optimal decisions. In order to address this problem, in this paper, we introduce the Transfer Entropy Redundancy Criterion (TERC), an information-theoretic criterion, which determines if there is \textit{entropy transferred} from state variables to actions during training. We define an algorithm based on TERC that provably excludes variables from the state that have no effect on the final performance of the agent, resulting in more sample efficient learning. Experimental results show that this speed-up is present across three different algorithm classes (represented by tabular Q-learning, Actor-Critic, and Proximal Policy Optimization (PPO)) in a variety of environments. Furthermore, to highlight the differences between the proposed methodology and the current state-of-the-art feature selection approaches, we present a series of controlled experiments on synthetic data, before generalizing to real-world decision-making tasks. We also introduce a representation of the problem that compactly captures the transfer of information from state variables to actions as Bayesian networks.
Differentiable Tree Search in Latent State Space

In decision-making problems with limited training data, policy functions approximated using deep neural networks often exhibit suboptimal performance. An alternative approach involves learning a world model from the limited data and determining actions through online search. However, the performance is adversely affected by compounding errors arising from inaccuracies in the learnt world model. While methods like TreeQN have attempted to address these inaccuracies by incorporating algorithmic structural biases into their architectures, the biases they introduce are often weak and insufficient for complex decision-making tasks. In this work, we introduce Differentiable Tree Search (DTS), a novel neural network architecture that significantly strengthens the inductive bias by embedding the algorithmic structure of a best-first online search algorithm. DTS employs a learnt world model to conduct a fully differentiable online search in latent state space. The world model is jointly optimised with the search algorithm, enabling the learning of a robust world model and mitigating the effect of model inaccuracies. We address potential Q-function discontinuities arising from naive incorporation of best-first search by adopting a stochastic tree expansion policy, formulating search tree expansion as a decision-making task, and introducing an effective variance reduction technique for the gradient computation. We evaluate DTS in an offline-RL setting with a limited training data scenario on Procgen games and grid navigation task, and demonstrate that DTS outperforms popular model-free and model-based baselines.
Sequential Model for Predicting Patient Adherence in Subcutaneous Immunotherapy for Allergic Rhinitis

Objective: Subcutaneous Immunotherapy (SCIT) is the long-lasting causal treatment of allergic rhinitis. How to enhance the adherence of patients to maximize the benefit of allergen immunotherapy (AIT) plays a crucial role in the management of AIT. This study aims to leverage novel machine learning models to precisely predict the risk of non-adherence of patients and related systematic symptom scores, to provide a novel approach in the management of long-term AIT. Methods: The research develops and analyzes two models, Sequential Latent Actor-Critic (SLAC) and Long Short-Term Memory (LSTM), evaluating them based on scoring and adherence prediction capabilities. Results: Excluding the biased samples at the first time step, the predictive adherence accuracy of the SLAC models is from $60\,\%$ to $72\%$, and for LSTM models, it is $66\,\%$ to $84\,\%$, varying according to the time steps. The range of Root Mean Square Error (RMSE) for SLAC models is between $0.93$ and $2.22$, while for LSTM models it is between $1.09$ and $1.77$. Notably, these RMSEs are significantly lower than the random prediction error of $4.55$. Conclusion: We creatively apply sequential models in the long-term management of SCIT with promising accuracy in the prediction of SCIT nonadherence in Allergic Rhinitis (AR) patients. While LSTM outperforms SLAC in adherence prediction, SLAC excels in score prediction for patients undergoing SCIT for AR. The state-action-based SLAC adds flexibility, presenting a novel and effective approach for managing long-term AIT.
An Effective Cosmological Collider

Effective field theories (EFTs) of heavy particles coupled to the inflaton are rife with operator redundancies, frequently obscured by sensitivity to both boundary terms and field redefinitions. We initiate a systematic study of these redundancies by establishing a minimal operator basis for an archetypal example, the abelian gauge-Higgs-inflaton EFT. Working up to dimension 9, we show that certain low-dimensional operators are entirely redundant and identify new non-redundant operators with potentially interesting cosmological collider signals. Our methods generalize straightforwardly to other EFTs of heavy particles coupled to the inflaton.
Unraveling Attacks in Machine Learning-based IoT Ecosystems: A Survey and the Open Libraries Behind Them

The advent of the Internet of Things (IoT) has brought forth an era of unprecedented connectivity, with an estimated 80 billion smart devices expected to be in operation by the end of 2025. These devices facilitate a multitude of smart applications, enhancing the quality of life and efficiency across various domains. Machine Learning (ML) serves as a crucial technology, not only for analyzing IoT-generated data but also for diverse applications within the IoT ecosystem. For instance, ML finds utility in IoT device recognition, anomaly detection, and even in uncovering malicious activities. This paper embarks on a comprehensive exploration of the security threats arising from ML's integration into various facets of IoT, spanning various attack types including membership inference, adversarial evasion, reconstruction, property inference, model extraction, and poisoning attacks. Unlike previous studies, our work offers a holistic perspective, categorizing threats based on criteria such as adversary models, attack targets, and key security attributes (confidentiality, availability, and integrity). We delve into the underlying techniques of ML attacks in IoT environment, providing a critical evaluation of their mechanisms and impacts. Furthermore, our research thoroughly assesses 65 libraries, both author-contributed and third-party, evaluating their role in safeguarding model and data privacy. We emphasize the availability and usability of these libraries, aiming to arm the community with the necessary tools to bolster their defenses against the evolving threat landscape. Through our comprehensive review and analysis, this paper seeks to contribute to the ongoing discourse on ML-based IoT security, offering valuable insights and practical solutions to secure ML models and data in the rapidly expanding field of artificial intelligence in IoT.
On eigenvalues and eigenfunctions of the operators defining multidimensional scaling on some symmetric spaces

We study asymptotics of the eigenvalues and eigenfunctions of the operators used for constructing multidimensional scaling (MDS) on compact connected Riemannian manifolds, in particular on closed connected symmetric spaces. They are the limits of eigenvalues and eigenvectors of squared distance matrices of an increasing sequence of finite subsets covering the space densely in the limit. We show that for products of spheres and real projective spaces, the numbers of positive and negative eigenvalues of these operators are both infinite. We also find a class of spaces (namely $\mathbb{RP}^n$ with odd $n>1$) whose MDS defining operators are not trace class, and original distances cannot be reconstructed from the eigenvalues and eigenfunctions of these operators.
JWST Observations of K2-18b Can Be Explained by a Gas-rich Mini-Neptune with No Habitable Surface

The James Webb Space Telescope (JWST) recently measured the transmission spectrum of K2-18b, a habitable-zone sub-Neptune exoplanet, detecting CH4 and CO2 in its atmosphere. The discovery paper argued the data are best explained by a habitable “Hycean” world, consisting of a relatively thin H2-dominated atmosphere overlying a liquid water ocean. Here, we use photochemical and climate models to simulate K2-18b as both a Hycean planet and a gas-rich mini-Neptune with no defined surface. We find that a lifeless Hycean world is hard to reconcile with the JWST observations because photochemistry only supports <1 part-per-million CH4 in such an atmosphere while the data suggest about ∼1% of the gas is present. Sustaining percent-level CH4 on a Hycean K2-18b may require the presence of a methane-producing biosphere, similar to microbial life on Earth ∼3 billion years ago. On the other hand, we predict that a gas-rich mini-Neptune with 100× solar metallicity should have 4% CH4 and nearly 0.1% CO2, which are compatible with the JWST data. The CH4 and CO2 are produced thermochemically in the deep atmosphere and mixed upward to the low pressures sensitive to transmission spectroscopy. The model predicts H2O, NH3, and CO abundances broadly consistent with the nondetections. Given the additional obstacles to maintaining a stable temperate climate on Hycean worlds due to H2 escape and potential supercriticality at depth, we favor the mini-Neptune interpretation because of its relative simplicity and because it does not need a biosphere or other unknown source of methane to explain the data.
LKFormer: Large Kernel Transformer for Infrared Image Super-Resolution

Given the broad application of infrared technology across diverse fields, there is an increasing emphasis on investigating super-resolution techniques for infrared images within the realm of deep learning. Despite the impressive results of current Transformer-based methods in image super-resolution tasks, their reliance on the self-attentive mechanism intrinsic to the Transformer architecture results in images being treated as one-dimensional sequences, thereby neglecting their inherent two-dimensional structure. Moreover, infrared images exhibit a uniform pixel distribution and a limited gradient range, posing challenges for the model to capture effective feature information. Consequently, we suggest a potent Transformer model, termed Large Kernel Transformer (LKFormer), to address this issue. Specifically, we have designed a Large Kernel Residual Attention (LKRA) module with linear complexity. This mainly employs depth-wise convolution with large kernels to execute non-local feature modeling, thereby substituting the standard self-attentive layer. Additionally, we have devised a novel feed-forward network structure called Gated-Pixel Feed-Forward Network (GPFN) to augment the LKFormer's capacity to manage the information flow within the network. Comprehensive experimental results reveal that our method surpasses the most advanced techniques available, using fewer parameters and yielding considerably superior performance.The source code will be available at https://github.com/sad192/large-kernel-Transformer.
Federated Learning with Dual Attention for Robust Modulation Classification under Attacks

Federated learning (FL) allows distributed participants to train machine learning models in a decentralized manner. It can be used for radio signal classification with multiple receivers due to its benefits in terms of privacy and scalability. However, the existing FL algorithms usually suffer from slow and unstable convergence and are vulnerable to poisoning attacks from malicious participants. In this work, we aim to design a versatile FL framework that simultaneously promotes the performance of the model both in a secure system and under attack. To this end, we leverage attention mechanisms as a defense against attacks in FL and propose a robust FL algorithm by integrating the attention mechanisms into the global model aggregation step. To be more specific, two attention models are combined to calculate the amount of attention cast on each participant. It will then be used to determine the weights of local models during the global aggregation. The proposed algorithm is verified on a real-world dataset and it outperforms existing algorithms, both in secure systems and in systems under data poisoning attacks.
A Survey of Advances in Optimization Methods for Wireless Communication System Design

Mathematical optimization is now widely regarded as an indispensable modeling and solution tool for the design of wireless communications systems. While optimization has played a significant role in the revolutionary progress in wireless communication and networking technologies from 1G to 5G and onto the future 6G, the innovations in wireless technologies have also substantially transformed the nature of the underlying mathematical optimization problems upon which the system designs are based and have sparked significant innovations in the development of methodologies to understand, to analyze, and to solve those problems. In this paper, we provide a comprehensive survey of recent advances in mathematical optimization theory and algorithms for wireless communication system design. We begin by illustrating common features of mathematical optimization problems arising in wireless communication system design. We discuss various scenarios and use cases and their associated mathematical structures from an optimization perspective. We then provide an overview of recent advances in mathematical optimization theory and algorithms, from nonconvex optimization, global optimization, and integer programming, to distributed optimization and learning-based optimization. The key to successful solution of mathematical optimization problems is in carefully choosing and/or developing suitable optimization algorithms (or neural network architectures) that can exploit the underlying problem structure. We conclude the paper by identifying several open research challenges and outlining future research directions.
A Nonlinear Observer Design for the Discrete-time Systems: Exploiting Matrix-Multiplier-based LMI Approach

This letter focuses on the $\mathcal{H}_\infty$ observer design for a class of nonlinear discrete systems under the presence of measurement noise or external disturbances. A novel Linear Matrix Inequality (LMI) condition is developed in this method through the utilisation of the reformulated Lipschitz property, a new variant of Young inequality and the well-known Linear Parameter Varying (LPV) approach. One of the key components of the proposed LMI is the generalised matrix multipliers. The deliberate use of these multipliers enables us to introduce more numbers of decision variables inside LMIs than the one illustrated in the literature. It aids in adding some extra degrees of freedom from a feasibility point of view, thus enhancing the LMI conditions. Thus, the proposed LMIs are less conservative than existing ones. Later on, the effectiveness of the developed LMIs and observer is highlighted through the numerical example and an application of state of charge (SoC) estimation in the Li-ion battery model.
Hecke orbits and the Mordell-Lang conjecture in distinguished categories

Inspired by recent work of Aslanyan and Daw, we introduce the notion of $\Sigma$-orbits in the general framework of distinguished categories. In the setting of connected Shimura varieties, this concept contains many instances of (generalized) Hecke orbits from the literature. In the setting of semiabelian varieties, a $\Sigma$-orbit is a subgroup of finite rank. We show that our $\Sigma$-orbits have useful functorial properties and we use them to formulate two general statements of Mordell-Lang type (a weak one and an apparently stronger one). We prove an analogue of a recent theorem of Aslanyan and Daw in this general setting, which we apply to deduce an unconditional result about unlikely intersections in a fibered power of the Legendre family.
Data-Driven Target Localization: Benchmarking Gradient Descent Using the Cramér-Rao Bound

In modern radar systems, precise target localization using azimuth and velocity estimation is paramount. Traditional unbiased estimation methods have utilized gradient descent algorithms to reach the theoretical limits of the Cramer Rao Bound (CRB) for the error of the parameter estimates. As an extension, we demonstrate on a realistic simulated example scenario that our earlier presented data-driven neural network model outperforms these traditional methods, yielding improved accuracies in target azimuth and velocity estimation. We emphasize, however, that this improvement does not imply that the neural network outperforms the CRB itself. Rather, the enhanced performance is attributed to the biased nature of the neural network approach. Our findings underscore the potential of employing deep learning methods in radar systems to achieve more accurate localization in cluttered and dynamic environments.
Rethinking Centered Kernel Alignment in Knowledge Distillation

Knowledge distillation has emerged as a highly effective method for bridging the representation discrepancy between large-scale models and lightweight models. Prevalent approaches involve leveraging appropriate metrics to minimize the divergence or distance between the knowledge extracted from the teacher model and the knowledge learned by the student model. Centered Kernel Alignment (CKA) is widely used to measure representation similarity and has been applied in several knowledge distillation methods. However, these methods are complex and fail to uncover the essence of CKA, thus not answering the question of how to use CKA to achieve simple and effective distillation properly. This paper first provides a theoretical perspective to illustrate the effectiveness of CKA, which decouples CKA to the upper bound of Maximum Mean Discrepancy~(MMD) and a constant term. Drawing from this, we propose a novel Relation-Centered Kernel Alignment~(RCKA) framework, which practically establishes a connection between CKA and MMD. Furthermore, we dynamically customize the application of CKA based on the characteristics of each task, with less computational source yet comparable performance than the previous methods. The extensive experiments on the CIFAR-100, ImageNet-1k, and MS-COCO demonstrate that our method achieves state-of-the-art performance on almost all teacher-student pairs for image classification and object detection, validating the effectiveness of our approaches.
Four Gluon Vertex from Lattice QCD

A lattice QCD calculation for the four gluon one-particle irreducible Green function in the Landau gauge is discussed. Results for some of the associated form factors are reported for kinematical configurations with a single momentum scale. Our results show that the computation of this Green function requires large statistical ensembles with 10K or larger number of gauge configurations. The simulations considered herein have a clear Monte Carlo signal for momenta up to $\sim 1$ GeV. The form factors show an hierarchy, with the form factor associated with the tree level Feynman rule being dominant and essentially constant for the range of momenta accessed. The remaining form factors seem to increase as the momentum decreases, suggesting that a possible $\log$ divergence may occur. The computed form factors are, at least, in qualitative agreement with the results obtained with continuum approaches to this vertex, when available.
MotionMix: Weakly-Supervised Diffusion for Controllable Motion Generation

Controllable generation of 3D human motions becomes an important topic as the world embraces digital transformation. Existing works, though making promising progress with the advent of diffusion models, heavily rely on meticulously captured and annotated (e.g., text) high-quality motion corpus, a resource-intensive endeavor in the real world. This motivates our proposed MotionMix, a simple yet effective weakly-supervised diffusion model that leverages both noisy and unannotated motion sequences. Specifically, we separate the denoising objectives of a diffusion model into two stages: obtaining conditional rough motion approximations in the initial T-T* steps by learning the noisy annotated motions, followed by the unconditional refinement of these preliminary motions during the last T* steps using unannotated motions. Notably, though learning from two sources of imperfect data, our model does not compromise motion generation quality compared to fully supervised approaches that access gold data. Extensive experiments on several benchmarks demonstrate that our MotionMix, as a versatile framework, consistently achieves state-of-the-art performances on text-to-motion, action-to-motion, and music-to-dance tasks.
Entangled biphoton generation in myelin sheath

Consciousness within the brain hinges on the synchronized activities of millions of neurons, but the mechanism responsible for orchestrating such synchronization remains elusive. In this study, we employ cavity quantum electrodynamics (cQED) to explore entangled biphoton generation through cascade emission in the vibration spectrum of C-H bonds within the lipid molecules' tails. The results indicate that the cylindrical cavity formed by a myelin sheath can facilitate spontaneous photon emission from the vibrational modes and generate a significant number of entangled photon pairs. The abundance of C-H bond vibration units in neurons can therefore serve as a source of quantum entanglement resources for the nervous system. The finding may offer insight into the brain's ability to leverage these resources for quantum information transfer, thereby elucidating a potential source for the synchronized activity of neurons.
A Randomized Runge-Kutta Method for time-irregular delay differential equations

In this paper we investigate the existence, uniqueness and approximation of solutions of delay differential equations (DDEs) with the right-hand side functions $f=f(t,x,z)$ that are Lipschitz continuous with respect to $x$ but only H\"older continuous with respect to $(t,z)$. We give a construction of the randomized two-stage Runge-Kutta scheme for DDEs and investigate its upper error bound in the $L^p(\Omega)$-norm for $p\in [2,+\infty)$. Finally, we report on results of numerical experiments.