Miracle-dz/UniFAR-FTUs huggingface dataset:
Higher order time discretization method for a class of semilinear stochastic partial differential equations with multiplicative noise

In this paper, we consider a new approach for semi-discretization in time and spatial discretization of a class of semi-linear stochastic partial differential equations (SPDEs) with multiplicative noise. The drift term of the SPDEs is only assumed to satisfy a one-sided Lipschitz condition and the diffusion term is assumed to be globally Lipschitz continuous. Our new strategy for time discretization is based on the Milstein method from stochastic differential equations. We use the energy method for its error analysis and show a strong convergence order of nearly $1$ for the approximate solution. The proof is based on new H\"older continuity estimates of the SPDE solution and the nonlinear term. For the general polynomial-type drift term, there are difficulties in deriving even the stability of the numerical solutions. We propose an interpolation-based finite element method for spatial discretization to overcome the difficulties. Then we obtain $H^1$ stability, higher moment $H^1$ stability, $L^2$ stability, and higher moment $L^2$ stability results using numerical and stochastic techniques. The nearly optimal convergence orders in time and space are hence obtained by coupling all previous results. Numerical experiments are presented to implement the proposed numerical scheme and to validate the theoretical results.
Variational Bayes latent class approach for EHR-based phenotyping with large real-world data

Bayesian approaches to clinical analyses for the purposes of patient phenotyping have been limited by the computational challenges associated with applying the Markov-Chain Monte-Carlo (MCMC) approach to large real-world data. Approximate Bayesian inference via optimization of the variational evidence lower bound, often called Variational Bayes (VB), has been successfully demonstrated for other applications. We investigate the performance and characteristics of currently available R and Python VB software for variational Bayesian Latent Class Analysis (LCA) of realistically large real-world observational data. We used a real-world data set, Optum\textsuperscript{TM} electronic health records (EHR), containing pediatric patients with risk indicators for type 2 diabetes mellitus that is a rare form in pediatric patients. The aim of this work is to validate a Bayesian patient phenotyping model for generality and extensibility and crucially that it can be applied to a realistically large real-world clinical data set. We find currently available automatic VB methods are very sensitive to initial starting conditions, model definition, algorithm hyperparameters and choice of gradient optimiser. The Bayesian LCA model was challenging to implement using VB but we achieved reasonable results with very good computational performance compared to MCMC.
Random-effects substitution models for phylogenetics via scalable gradient approximations.

Phylogenetic and discrete-trait evolutionary inference depend heavily on appropriate characterization of the underlying substitution process. In this paper, we present random-effects substitution models that extend common continuous-time Markov chain models into a richer class of processes capable of capturing a wider variety of substitution dynamics. As these random-effects substitution models often require many more parameters than their usual counterparts, inference can be both statistically and computationally challenging. Thus, we also propose an efficient approach to compute an approximation to the gradient of the data likelihood with respect to all unknown substitution model parameters. We demonstrate that this approximate gradient enables scaling of both sampling-based (Bayesian inference via HMC) and maximization-based inference (MAP estimation) under random-effects substitution models across large trees and state-spaces. Applied to a dataset of 583 SARS-CoV-2 sequences, an HKY model with random-effects shows strong signals of nonreversibility in the substitution process, and posterior predictive model checks clearly show that it is more adequate than a reversible model. When analyzing the pattern of phylogeographic spread of 1441 influenza A virus (H3N2) sequences between 14 regions, a random-effects phylogeographic substitution model infers that air travel volume adequately predicts almost all dispersal rates. A random-effects state-dependent substitution model reveals no evidence for an effect of arboreality on the swimming mode in the tree frog subfamily Hylinae. On a dataset of 28 taxa spanning the Metazoa, a random-effects amino acid substitution model finds evidence of notable departures from the current best-fit amino acid model in seconds. We show that our gradient-based inference approach is over an order of magnitude more time efficient than conventional approaches.
Weakly-supervised Single-view Image Relighting

We present a learning-based approach to relight a single image of Lambertian and low-frequency specular objects. Our method enables inserting objects from photographs into new scenes and relighting them under the new environment lighting, which is essential for AR applications. To relight the object, we solve both inverse rendering and re-rendering. To resolve the ill-posed inverse rendering, we propose a weakly-supervised method by a low-rank constraint. To facilitate the weakly-supervised training, we contribute Relit, a large-scale (750K images) dataset of videos with aligned objects under changing illuminations. For re-rendering, we propose a differentiable specular rendering layer to render low-frequency non-Lambertian materials under various illuminations of spherical harmonics. The whole pipeline is end-to-end and efficient, allowing for a mobile app implementation of AR object insertion. Extensive evaluations demonstrate that our method achieves state-of-the-art performance. Project page: https://renjiaoyi.github. io/relighting/.
APES: Approximate Posterior Ensemble Sampler

This paper proposes a novel approach to generate samples from target distributions that are difficult to sample from using Markov Chain Monte Carlo (MCMC) methods. Traditional MCMC algorithms often face slow convergence due to the difficulty in finding proposals that suit the problem at hand. To address this issue, the paper introduces the Approximate Posterior Ensemble Sampler (APES) algorithm, which employs kernel density estimation and radial basis interpolation to create an adaptive proposal, leading to fast convergence of the chains. The APES algorithm’s scalability to higher dimensions makes it a practical solution for complex problems. The proposed method generates an approximate posterior probability that closely approximates the desired distribution and is easy to sample from, resulting in smaller autocorrelation times and a higher probability of acceptance by the chain. We compare the performance of the APES algorithm with the affine invariance ensemble sampler with the stretch move in various contexts, demonstrating the efficiency of the proposed method. For instance, on the Rosenbrock function, the APES presented an autocorrelation time 140 times smaller than the affine invariance ensemble sampler. The comparison showcases the effectiveness of the APES algorithm in generating samples from challenging distributions. This paper presents a practical solution to generating samples from complex distributions while addressing the challenge of finding suitable proposals. With new cosmological surveys set to deal with many new systematics, this method offers a practical solution for the upcoming era of cosmological analyses. The algorithms presented in this paper are available at https://github.com/NumCosmo/NumCosmo.
Solutions of an anisotropic nonlocal problem involving variable exponent

Abstract. The present paper deals with an anisotropic Kirchhoff problem under homogeneous Dirichlet boundary conditions, set in a bounded smooth domain of ℝN (). The problem studied is a stationary version of the original Kirchhoff equation, involving the anisotropic -Laplacian operator, in the framework of the variable exponent Lebesgue and Sobolev spaces. The question of the existence of weak solutions is treated. Applying the Mountain Pass Theorem of Ambrosetti and Rabinowitz, the existence of a nontrivial weak solution is obtained in the anisotropic variable exponent Sobolev space , provided that the positive parameter λ that multiplies the nonlinearity f is small enough.
ARKitTrack: A New Diverse Dataset for Tracking Using Mobile RGB-D Data

Compared with traditional RGB-only visual tracking, few datasets have been constructed for RGB-D tracking. In this paper, we propose ARKitTrack, a new RGB-D tracking dataset for both static and dynamic scenes captured by consumer-grade LiDAR scanners equipped on Apple's iPhone and iPad. ARKitTrack contains 300 RGB-D sequences, 455 targets, and 229.7K video frames in total. Along with the bounding box annotations and frame-level attributes, we also annotate this dataset with 123.9K pixel-level target masks. Besides, the camera intrinsic and camera pose of each frame are provided for future developments. To demonstrate the potential usefulness of this dataset, we further present a unified baseline for both box-level and pixel-level tracking, which integrates RGB features with bird's-eye-view representations to better explore cross-modality 3D geometry. In-depth empirical analysis has verified that the ARKitTrack dataset can significantly facilitate RGB-D tracking and that the proposed baseline method compares favorably against the state of the arts. The code and dataset is available at https://arkittrack.github. io.
Skip Connections in Spiking Neural Networks: An Analysis of Their Effect on Network Training

Spiking neural networks (SNNs) have gained attention as a promising alternative to traditional artificial neural networks (ANNs) due to their potential for energy efficiency and their ability to model spiking behavior in biological systems. However, the training of SNNs is still a challenging problem, and new techniques are needed to improve their performance. In this paper, we study the impact of skip connections on SNNs and propose a hyperparameter optimization technique that adapts models from ANN to SNN. We demonstrate that optimizing the position, type, and number of skip connections can significantly improve the accuracy and efficiency of SNNs by enabling faster convergence and increasing information flow through the network. Our results show an average +8% accuracy increase on CIFAR-10-DVS and DVS128 Gesture datasets adaptation of multiple state-of-the-art models.
Traveling salesman problem with time slots: Asymptotic analysis and resolution algorithm

We develop an asymptotic approximation and bounds for the traveling salesman problem with time slots, i.e. when the time windows of points to visit are a partition of a given time horizon. Although this problem is relevant in several delivery applications, operational research researchers did not pay close attention to it, contrary to the extensively studied general formulation with time windows. Exploiting the specificity of this problem allows to solve more efficiently instances which may be hard to solve by specifically designed algorithms for the traveling salesman problem with time windows. The asymptotic analysis of the traveling salesman problem with time slots is a step toward developing new approximations for the general problem with time windows.We discuss this case. We equally provide a formulation of the asymptotic approximation under a worst-case demand distribution of the points to visit, based on the principle of the maximum entropy. Computational results are given for the benchmarks of the literature for which the time slots are randomly generated.
Adversarial Attack and Defense for Medical Image Analysis: Methods and Applications

Deep learning techniques have achieved superior performance in computer-aided medical image analysis, yet they are still vulnerable to imperceptible adversarial attacks, resulting in potential misdiagnosis in clinical practice. Oppositely, recent years have also witnessed remarkable progress in defense against these tailored adversarial examples in deep medical diagnosis systems. In this exposition, we present a comprehensive survey on recent advances in adversarial attack and defense for medical image analysis with a novel taxonomy in terms of the application scenario. We also provide a unified theoretical framework for different types of adversarial attack and defense methods for medical image analysis. For a fair comparison, we establish a new benchmark for adversarially robust medical diagnosis models obtained by adversarial training under various scenarios. To the best of our knowledge, this is the first survey paper that provides a thorough evaluation of adversarially robust medical diagnosis models. By analyzing qualitative and quantitative results, we conclude this survey with a detailed discussion of current challenges for adversarial attack and defense in medical image analysis systems to shed light on future research directions.
Machine Psychology: Investigating Emergent Capabilities and Behavior in Large Language Models Using Psychological Methods

Large language models (LLMs) are currently at the forefront of intertwining AI systems with human communication and everyday life. Due to rapid technological advances and their extreme versatility, LLMs nowadays have millions of users and are at the cusp of being the main go-to technology for information retrieval, content generation, problem-solving, etc. Therefore, it is of great importance to thoroughly assess and scrutinize their capabilities. Due to increasingly complex and novel behavioral patterns in current LLMs, this can be done by treating them as participants in psychology experiments that were originally designed to test humans. For this purpose, the paper introduces a new field of research called"machine psychology". The paper outlines how different subfields of psychology can inform behavioral tests for LLMs. It defines methodological standards for machine psychology research, especially by focusing on policies for prompt designs. Additionally, it describes how behavioral patterns discovered in LLMs are to be interpreted. In sum, machine psychology aims to discover emergent abilities in LLMs that cannot be detected by most traditional natural language processing benchmarks.
Object Motion Sensitivity: A Bio-inspired Solution to the Ego-motion Problem for Event-based Cameras

Neuromorphic (event-based) image sensors draw inspiration from the human-retina to create an electronic device that can process visual stimuli in a way that closely resembles its biological counterpart. These sensors process information significantly different than the traditional RGB sensors. Specifically, the sensory information generated by event-based image sensors are orders of magnitude sparser compared to that of RGB sensors. The first generation of neuromorphic image sensors, Dynamic Vision Sensor (DVS), are inspired by the computations confined to the photoreceptors and the first retinal synapse. In this work, we highlight the capability of the second generation of neuromorphic image sensors, Integrated Retinal Functionality in CMOS Image Sensors (IRIS), which aims to mimic full retinal computations from photoreceptors to output of the retina (retinal ganglion cells) for targeted feature-extraction. The feature of choice in this work is Object Motion Sensitivity (OMS) that is processed locally in the IRIS sensor. Our results show that OMS can accomplish standard computer vision tasks with similar efficiency to conventional RGB and DVS solutions but offers drastic bandwidth reduction. This cuts the wireless and computing power budgets and opens up vast opportunities in high-speed, robust, energy-efficient, and low-bandwidth real-time decision making.
DisC-Diff: Disentangled Conditional Diffusion Model for Multi-Contrast MRI Super-Resolution

Multi-contrast magnetic resonance imaging (MRI) is the most common management tool used to characterize neurological disorders based on brain tissue contrasts. However, acquiring high-resolution MRI scans is time-consuming and infeasible under specific conditions. Hence, multi-contrast super-resolution methods have been developed to improve the quality of low-resolution contrasts by leveraging complementary information from multi-contrast MRI. Current deep learning-based super-resolution methods have limitations in estimating restoration uncertainty and avoiding mode collapse. Although the diffusion model has emerged as a promising approach for image enhancement, capturing complex interactions between multiple conditions introduced by multi-contrast MRI super-resolution remains a challenge for clinical applications. In this paper, we propose a disentangled conditional diffusion model, DisC-Diff, for multi-contrast brain MRI super-resolution. It utilizes the sampling-based generation and simple objective function of diffusion models to estimate uncertainty in restorations effectively and ensure a stable optimization process. Moreover, DisC-Diff leverages a disentangled multi-stream network to fully exploit complementary information from multi-contrast MRI, improving model interpretation under multiple conditions of multi-contrast inputs. We validated the effectiveness of DisC-Diff on two datasets: the IXI dataset, which contains 578 normal brains, and a clinical dataset with 316 pathological brains. Our experimental results demonstrate that DisC-Diff outperforms other state-of-the-art methods both quantitatively and visually.
Dancing the Quantum Waltz: Compiling Three-Qubit Gates on Four Level Architectures

Superconducting quantum devices are a leading technology for quantum computation, but they face several challenges. Gate errors, coherence errors and a lack of connectivity all contribute to low fidelity results. In particular, connectivity restrictions enforce a gate set that requires three-qubit gates to be decomposed into one- or two-qubit gates. This substantially increases the number of two-qubit gates that need to be executed. However, many quantum devices have access to higher energy levels. We can expand the qubit abstraction of |0〉 and |1〉 to a ququart which has access to the |2〉 and |3〉 state, but with shorter coherence times. This allows for two qubits to be encoded in one ququart, enabling increased virtual connectivity between physical units from two adjacent qubits to four fully connected qubits. This connectivity scheme allows us to more efficiently execute three-qubit gates natively between two physical devices. We present direct-to-pulse implementations of several three-qubit gates, synthesized via optimal control, for compilation of three-qubit gates onto a superconducting-based architecture with access to four-level devices with the first experimental demonstration of four-level ququart gates designed through optimal control. We demonstrate strategies that temporarily use higher level states to perform Toffoli gates and always use higher level states to improve fidelities for quantum circuits. We find that these methods improve expected fidelities with increases of 2x across circuit sizes using intermediate encoding, and increases of 3x for fully-encoded ququart compilation.
A Constructive Proof of the Nash Bargaining Solution

This paper o ers a constructive proof of the Nash Bargaining solution. We start by proving that Nashs solution is representable based on its continuity. This property along with the linearity of the choice function will then allow us to identify the function representing Nashs bargaining choice. Finally, supported on the result for two players, we will generalize it to n-players.
Neural network quantum states analysis of the Shastry-Sutherland model

We utilize neural network quantum states (NQS) to investigate the ground state properties of the Heisenberg model on a Shastry-Sutherland lattice using the variational Monte Carlo method. We show that already relatively simple NQSs can be used to approximate the ground state of this model in its different phases and regimes. We first compare several types of NQSs with each other on small lattices and benchmark their variational energies against the exact diagonalization results. We argue that when precision, generality, and computational costs are taken into account, a good choice for addressing larger systems is a shallow restricted Boltzmann machine NQS. We then show that such NQS can describe the main phases of the model in zero magnetic field. Moreover, NQS based on a restricted Boltzmann machine correctly describes the intriguing plateaus forming in magnetization of the model as a function of increasing magnetic field.
Quantization revisited: a mathematical and computational model

A nascent theory of near division is presented, from which an efficient quantization algorithm for rhythm intervals is derived. Based on a number theoretic analysis of the uniqueness and convergence of this first algorithm, a generalized algorithm is presented. An empirical study of the algorithm's performance reveals a readily computable criterion within which the perceived ratio may reliably be produced on real performance data. Distribution properties are shown to be reasonable for computation.
A general convergence result for a functional related to the theory of homogenization

The convergence, as $\varepsilon \downarrow 0$, of the functional $F_\varepsilon (\Psi ) = \int _{\mathbb{R}^N } u_\varepsilon (x)\Psi (x,{x / \varepsilon })$ associated with a given $L^2 $ function $u_\varepsilon $ with support in a fixed compact set is studied. The test functions $\Psi (x,y)$ are continuous on $\mathbb{R}^N \times \mathbb{R}^N $ and periodic in y. A convergence theorem is proved under the weaker assumption that $u_\varepsilon $ remains in a bounded subset of $L^2 $. Finally, the use of multiple-scale expansions in homogenization is justified, and a new approach is proposed for the mathematical analysis of homogenization problems.
Grf10 regulates the response to copper, iron, and phosphate in Candida albicans

Abstract The pathogenic yeast, Candida albicans, and other microbes must be able to handle drastic changes in nutrient availability within the human host. Copper, iron, and phosphate are essential micronutrients for microbes that are sequestered by the human host as nutritional immunity; yet high copper levels are employed by macrophages to induce toxic oxidative stress. Grf10 is a transcription factor important for regulating genes involved in morphogenesis (filamentation, chlamydospore formation) and metabolism (adenylate biosynthesis, 1-carbon metabolism). The grf10Δ mutant exhibited resistance to excess copper in a gene dosage-dependent manner but grew the same as the wild type in response to other metals (calcium, cobalt, iron, manganese, and zinc). Point mutations in the conserved residues D302 and E305, within a protein interaction region, conferred resistance to high copper and induced hyphal formation similar to strains with the null allele. The grf10Δ mutant misregulated genes involved with copper, iron, and phosphate uptake in YPD medium and mounted a normal transcriptional response to high copper. The mutant accumulated lower levels of magnesium and phosphorus, suggesting that copper resistance is linked to phosphate metabolism. Our results highlight new roles for Grf10 in copper and phosphate homeostasis in C. albicans and underscore the fundamental role of Grf10 in connecting these with cell survival.