Miracle-dz/UniFAR-FTUs huggingface dataset:
Shifted Composition I: Harnack and Reverse Transport Inequalities

We formulate a new information-theoretic principle--the shifted composition rule--which bounds the divergence (e.g., Kullback-Leibler or R\'enyi) between the laws of two stochastic processes via the introduction of auxiliary shifts. In this paper, we apply this principle to prove reverse transport inequalities for diffusions which, by duality, imply F. -Y. Wang's celebrated dimension-free Harnack inequalities. Our approach bridges continuous-time coupling methods from geometric analysis with the discrete-time shifted divergence technique from differential privacy and sampling. It also naturally gives rise to (1) an alternative continuous-time coupling method based on optimal transport, which bypasses Girsanov transformations, (2) functional inequalities for discrete-time processes, and (3) a family of"reverse"Harnack inequalities.
Learning Dynamic Selection and Pricing of Out-of-Home Deliveries

Home delivery failures, traffic congestion, and relatively large handling times have a negative impact on the profitability of last-mile logistics. These external factors contribute to up to $28\%$ of the overall costs and $25\%$ of emissions for the home delivery supply chain. A potential solution, showing annual growth rates up to $36\%$, is the delivery to parcel lockers or parcel shops, denoted by out-of-home (OOH) delivery. In the academic literature, models of customer behavior with respect to OOH delivery were so far limited to deterministic settings, contrasting with the stochastic nature of actual customer choices. We model the sequential decision-making problem of which OOH location to offer against what incentive for each incoming customer, taking into account future customer arrivals and choices. We propose Dynamic Selection and Pricing of OOH (DSPO), an algorithmic pipeline that uses a novel spatial-temporal state encoding as input to a convolutional neural network. We demonstrate the performance of our method by benchmarking it against three state-of-the-art approaches. Our extensive numerical study, guided by real-world data, reveals that DSPO can save $20.8\%$ in costs compared to a situation without OOH locations, $8.1\%$ compared to a static selection and pricing policy, and $4.6\%$ compared to a state-of-the-art demand management benchmark. We provide comprehensive insights into the complex interplay between OOH delivery dynamics and customer behavior influenced by pricing strategies. The implications of our findings suggest practitioners to adopt dynamic selection and pricing policies as OOH delivery gains a larger market share.
On the continuity of the projection mapping from strategic measures to occupation measures in absorbing Markov decision processes

In this paper, we prove the following assertion for an absorbing Markov decision process (MDP) with the given initial distribution, which is also assumed to be semi-continuous: the continuity of the projection mapping from the space of strategic measures to the space of occupation measures, both endowed with their weak topologies, is equivalent to the MDP model being uniformly absorbing. An example demonstrates, among other interesting scenarios, that for an absorbing (but not uniformly absorbing) semi-continuous MDP with the given initial distribution, the space of occupation measures can fail to be compact in the weak topology.
Convergence Analysis for Learning Orthonormal Deep Linear Neural Networks

Enforcing orthonormal or isometric property for the weight matrices has been shown to enhance the training of deep neural networks by mitigating gradient exploding/vanishing and increasing the robustness of the learned networks. However, despite its practical performance, the theoretical analysis of orthonormality in neural networks is still lacking; for example, how orthonormality affects the convergence of the training process. In this letter, we aim to bridge this gap by providing convergence analysis for training orthonormal deep linear neural networks. Specifically, we show that Riemannian gradient descent with an appropriate initialization converges at a linear rate for training orthonormal deep linear neural networks with a class of loss functions. Unlike existing works that enforce orthonormal weight matrices for all the layers, our approach excludes this requirement for one layer, which is crucial to establish the convergence guarantee. Our results shed light on how increasing the number of hidden layers can impact the convergence speed. Experimental results validate our theoretical analysis.
TEA: Test-time Energy Adaptation

Test-time adaptation (TTA) aims to improve model generalizability when test data diverges from training distribution, offering the distinct advantage of not requiring access to training data and processes, especially valuable in the context of large pre-trained models. However, current TTA methods fail to address the fundamental issue: covariate shift, i.e., the decreased generalizability can be attributed to the model's reliance on the marginal distribution of the training data, which may impair model calibration and introduce confirmation bias. To address this, we propose a novel energy-based perspective, enhancing the model's perception of target data distributions without requiring access to training data or processes. Building on this perspective, we introduce $\textbf{T}$est-time $\textbf{E}$nergy $\textbf{A}$daptation ($\textbf{TEA}$), which transforms the trained classifier into an energy-based model and aligns the model's distribution with the test data's, enhancing its ability to perceive test distributions and thus improving overall generalizability. Extensive experiments across multiple tasks, benchmarks and architectures demonstrate TEA's superior generalization performance against state-of-the-art methods. Further in-depth analyses reveal that TEA can equip the model with a comprehensive perception of test distribution, ultimately paving the way toward improved generalization and calibration.
Leaching of Nitrate-N (NO3-N) from cropped and fallow soil - a lysimeter study with ambient and imposed rainfall regimes

A three-year investigation into the effects of nitrogen (N) fertiliser rates and rainfall on nitrate-N (NO3-N) leaching from spring barley and Fallow was carried out in a lysimeter unit. The soil was well drained, moderately deep and similar to soils used to grow cereals in Ireland. Levels of fertiliser N applied were in the range 0-120kg per ha with rainfall amounts varying from 90 to 159 percent of ambient. The Fallow treatment resulted in large removals of N in the drainage water with high concentrations of NO3-N. The load of N removed in the water draining from the barley crop was, in general terms, related to drainage volume (R2=~0.7) while NO3-N concentrations, where N was applied, were inversely related to drainage volume (R2=0.6). Mean NO3-N concentration in drainage water from barley receiving fertiliser N was >MAC in two years out of three. The relative importance of the results to the designation of Nitrate Vulnerable Zones and possible mitigation strategies are discussed.
Lipschitz regularity of almost minimizers in a Bernoulli problem with non-standard growth

In this work we establish the optimal Lipschitz regularity for non-negative almost minimizers of the one-phase Bernoulli-type functional $$ \mathcal{J}_{\mathrm{G}}(u,\Omega) := \int_\Omega \left(\mathrm{G}(|\nabla u|)+\chi_{\{u>0\}}\right)\,dx $$ where $\Omega \subset \mathbb{R}^n$ is a bounded domain and $\mathrm{G}: [0, \infty) \to [0, \infty) $ is a Young function with $\mathrm{G}^{\prime}=g$ satisfying the Lieberman's classical conditions. Moreover, of independent mathematical interest, we also address a H\"{o}der regularity characterization via Campanato-type estimates in the context of Orlicz modulars, which is new for such a class of non-standard growth functionals.
Hybrid quantum-classical reservoir computing for simulating chaotic systems

Forecasting chaotic systems is a notably complex task, which in recent years has been approached with reasonable success using reservoir computing (RC), a recurrent network with fixed random weights (the reservoir) used to extract the spatio-temporal information of the system. This work presents a hybrid quantum reservoir-computing (HQRC) framework, which replaces the reservoir in RC with a quantum circuit. The modular structure and measurement feedback in the circuit are used to encode the complex system dynamics in the reservoir states, from which classical learning is performed to predict future dynamics. The noiseless simulations of HQRC demonstrate valid prediction times comparable to state-of-the-art classical RC models for both the Lorenz63 and double-scroll chaotic paradigmatic systems and adhere to the attractor dynamics long after the forecasts have deviated from the ground truth.
Bose-Einstein condensate stars in combined Rastall-Rainbow gravity

We study zero and finite temperature static Bose-Einstein condensate (BEC) stars in the combined Rastall-Rainbow (RR) theory of gravity by considering different BEC equation of states (EoSs). We obtain the global properties of BEC stars by solving the modified Tolman-Oppenheimer-Volkoff equations with values of Rastall parameter $\kappa$ and Rainbow function $\Sigma$ chosen accordingly to get the results in theories of Rastall, Rainbow and RR. We observe that the parameter $\kappa$ has negligible effect on the maximum mass of the stars considered, whereas $\Sigma$ alters it significantly, and increasing the value of $\kappa$ beyond a certain limit results in unstable solutions for any value of $\Sigma$. We report that the inclusion of temperature in our analysis expands the parameter space by including more values of $\kappa$. However, temperature has negligible effect on the maximum mass of the stellar profiles in all the three theories. We find that the maximum masses and radii of the stars within RR theory can have good agreement with the observational data on pulsars for all the EoSs considered and in particular, the Colpi-Wasserman-Shapiro EoS, which was ruled out in General Relativity (GR). We also find that, in contrast to the results of GR, BEC stars consistent with observations can be realised in the RR theory with smaller bosonic self-interaction strength.
Binarized 3D Whole-body Human Mesh Recovery

3D whole-body human mesh recovery aims to reconstruct the 3D human body, face, and hands from a single image. Although powerful deep learning models have achieved accurate estimation in this task, they require enormous memory and computational resources. Consequently, these methods can hardly be deployed on resource-limited edge devices. In this work, we propose a Binarized Dual Residual Network (BiDRN), a novel quantization method to estimate the 3D human body, face, and hands parameters efficiently. Specifically, we design a basic unit Binarized Dual Residual Block (BiDRB) composed of Local Convolution Residual (LCR) and Block Residual (BR), which can preserve full-precision information as much as possible. For LCR, we generalize it to four kinds of convolutional modules so that full-precision information can be propagated even between mismatched dimensions. We also binarize the face and hands box-prediction network as Binaried BoxNet, which can further reduce the model redundancy. Comprehensive quantitative and qualitative experiments demonstrate the effectiveness of BiDRN, which has a significant improvement over state-of-the-art binarization algorithms. Moreover, our proposed BiDRN achieves comparable performance with full-precision method Hand4Whole while using just 22.1% parameters and 14.8% operations. We will release all the code and pretrained models.
Electron and Proton Energization in 3D Reconnecting Current Sheets in Semirelativistic Plasma with Guide Magnetic Field

Using 3D particle-in-cell simulation, we characterize energy conversion, as a function of guide magnetic field, in a thin current sheet in semirelativistic plasma, with relativistic electrons and subrelativistic protons. There, magnetic reconnection, the drift-kink instability (DKI), and the flux-rope kink instability all compete and interact in their nonlinear stages to convert magnetic energy to plasma energy. We compare fully 3D simulations with 2D in two different planes to isolate reconnection and DKI effects. In zero guide field, these processes yield distinct energy conversion signatures: ions gain more energy than electrons in 2Dxy (reconnection), while the opposite is true in 2Dyz (DKI), and the 3D result falls in between. The flux-rope instability, which occurs only in 3D, allows more magnetic energy to be released than in 2D, but the rate of energy conversion in 3D tends to be lower. Increasing the guide magnetic field strongly suppresses DKI, and in all cases slows and reduces the overall amount of energy conversion; it also favors electron energization through a process by which energy is first stored in the motional electric field of flux ropes before energizing particles. Understanding the evolution of the energy partition thus provides insight into the role of various plasma processes, and is important for modeling radiation from astrophysical sources such as accreting black holes and their jets.
Robustness and measurement-induced percolation of the surface code

We examine the robustness of a logical qubit in the planar surface code subject to 'measurement-errors', i.e., to local Pauli measurements at known positions. This yields a measurement-only dynamics, which is driven by the competition between local Pauli measurements and stabilizer measurements. The setup differs from the conventional surface code for which errors are caused by decoherence and their positions are unknown. Yet, our setting allows us to examine the dynamics of the encoded logical qubit by using a combination of analytical arguments based on percolation theory and numerical simulations. Firstly, we show that for a single round of Pauli measurements only, the threshold corresponding to the irreversible loss of the logical qubit depends only on the rate of $ \hat X$- and $\hat Z$-measurements, and that this loss of logical quantum information is equivalent to the bond percolation transition in a 2D square lattice. Local $\hat Y$-measurements, which affect both $X$ and $Z$ stabilizers, erase the logical qubit only if all physical qubits along one of the diagonals are measured, and are thus negligible at large code distance. Secondly, we examine the dynamics in the code by considering the interplay between rounds of Pauli measurements and rounds of stabilizer measurements. Focusing on the lifetime of the logical qubit, we obtain a rich phase diagram featuring different dynamical regimes. We argue that the loss of the logical qubit in this setting can still be understood by percolation theory and underpin our arguments with numerical simulations.
Robust and Interpretable COVID-19 Diagnosis on Chest X-ray Images using Adversarial Training

The novel 2019 Coronavirus disease (COVID-19) global pandemic is a defining health crisis. Recent efforts have been increasingly directed towards achieving quick and accurate detection of COVID-19 across symptomatic patients to mitigate the intensity and spread of the disease. Artificial intelligence (AI) algorithms applied to chest X-ray (CXR) images have emerged as promising diagnostic tools, and previous work has demonstrated impressive classification performances. However, such methods have faced criticisms from physicians due to their black-box reasoning process and unpredictable nature. In contrast to professional radiologist diagnosis, AI systems often lack generalizability, explainability, and robustness in the clinical decision making process. In our work, we address these issues by first proposing an extensive baseline study, training and evaluating 21 convolutional neural network (CNN) models on a diverse set of 33,000+ CXR images to classify between healthy, COVID-19, and non-COVID-19 pneumonia CXRs. Our resulting models achieved a 3-way classification accuracy, recall, and precision of up to 97.03\%, 97.97\%, and 99.95\%, respectively. Next, we investigate the effectiveness of adversarial training on model robustness and explainability via Gradient-weighted Class Activation Mapping (Grad-CAM) heatmaps. We find that adversarially trained models not only significantly outperform their standard counterparts on classifying perturbed images, but also yield saliency maps that 1) better specify clinically relevant features, 2) are robust against extraneous artifacts, and 3) agree considerably more with expert radiologist findings.
Progressive Learning with Visual Prompt Tuning for Variable-Rate Image Compression

In this paper, we propose a progressive learning paradigm for transformer-based variable-rate image compression. Our approach covers a wide range of compression rates with the assistance of the Layer-adaptive Prompt Module (LPM). Inspired by visual prompt tuning, we use LPM to extract prompts for input images and hidden features at the encoder side and decoder side, respectively, which are fed as additional information into the Swin Transformer layer of a pre-trained transformer-based image compression model to affect the allocation of attention region and the bits, which in turn changes the target compression ratio of the model. To ensure the network is more lightweight, we involves the integration of prompt networks with less convolutional layers. Exhaustive experiments show that compared to methods based on multiple models, which are optimized separately for different target rates, the proposed method arrives at the same performance with 80% savings in parameter storage and 90% savings in datasets. Meanwhile, our model outperforms all current variable bitrate image methods in terms of rate-distortion performance and approaches the state-of-the-art fixed bitrate image compression methods trained from scratch.
An overview on the local limit of non-local conservation laws, and a new proof of a compactness estimate

Consider a non-local (i.e., involving a convolution term) conservation law: when the convolution term converges to a Dirac delta, in the limit we formally recover a classical (or"local") conservation law. In this note we overview recent progress on this so-called non-local to local limit and in particular we discuss the case of anistropic kernels, which is extremely relevant in view of applications to traffic models. We also provide a new proof of a related compactness estimate.
StableSSM: Alleviating the Curse of Memory in State-space Models through Stable Reparameterization

In this paper, we investigate the long-term memory learning capabilities of state-space models (SSMs) from the perspective of parameterization. We prove that state-space models without any reparameterization exhibit a memory limitation similar to that of traditional RNNs: the target relationships that can be stably approximated by state-space models must have an exponential decaying memory. Our analysis identifies this"curse of memory"as a result of the recurrent weights converging to a stability boundary, suggesting that a reparameterization technique can be effective. To this end, we introduce a class of reparameterization techniques for SSMs that effectively lift its memory limitations. Besides improving approximation capabilities, we further illustrate that a principled choice of reparameterization scheme can also enhance optimization stability. We validate our findings using synthetic datasets and language models.
Numerical Generalized Randomized HMC processes for restricted domains

We propose a generic approach for numerically efficient simulation from analytically intractable distributions with constrained support. Our approach relies upon Generalized Randomized Hamiltonian Monte Carlo (GRHMC) processes and combines these with a randomized transition kernel that appropriately adjusts the Hamiltonian flow at the boundary of the constrained domain, ensuring that it remains within the domain. The numerical implementation of this constrained GRHMC process exploits the sparsity of the randomized transition kernel and the specific structure of the constraints so that the proposed approach is numerically accurate, computationally fast and operational even in high-dimensional applications. We illustrate this approach with posterior distributions of several Bayesian models with challenging parameter domain constraints in applications to real-word data sets. Building on the capability of GRHMC processes to efficiently explore otherwise challenging and high-dimensional posteriors, the proposed method expands the set of Bayesian models that can be analyzed by using the standard Markov-Chain Monte-Carlo (MCMC) methodology, As such, it can advance the development and use of Bayesian models with useful constrained priors, which are difficult to handle with existing methods. The article is accompanied by an R-package (\url{https://github.com/torekleppe/pdmphmc}), which allows for automatically implementing GRHMC processes for arbitrary target distributions and domain constraints.
Hydrodynamically Induced Aggregation in Two-Dimensional Active Systems

We investigate a system of co-oriented active particles interacting only via hydrodynamic and steric interactions. We offer a new method of calculating the flow created by any active particle in a 2D fluid, focusing on the dynamics of flow fields with a high-order spatial decay, which we analyze using a geometric Hamiltonian. We show that when orientational degrees of freedom are quenched, and the flow has a single, odd power decay, such many-particle systems lead to stable, fractal-like aggregation, with the only exceptions being the force dipole. We discuss how our results can easily be generalized to more complicated force distributions and to other effective two-dimensional systems.
A special class of $k$-harmonic maps inducing calibrated fibrations

We consider two special classes of $k$-harmonic maps between Riemannian manifolds which are related to calibrated geometry, satisfying a first order fully nonlinear PDE. The first is a special type of weakly conformal map $u \colon (L^k, g) \to (M^n, h)$ where $k \leq n$ and $\alpha$ is a calibration $k$-form on $M$. Away from the critical set, the image is an $\alpha$-calibrated submanifold of $M$. These were previously studied by Cheng-Karigiannis-Madnick when $\alpha$ was associated to a vector cross product, but we clarify that such a restriction is unnecessary. The second, which is new, is a special type of weakly horizontally conformal map $u \colon (M^n, h) \to (L^k, g)$ where $n \geq k$ and $\alpha$ is a calibration $(n-k)$-form on $M$. Away from the critical set, the fibres $u^{-1} \{ u(x) \}$ are $\alpha$-calibrated submanifolds of $M$. We also review some previously established analytic results for the first class; we exhibit some explicit noncompact examples of the second class, where $(M, h)$ are the Bryant-Salamon manifolds with exceptional holonomy; we remark on the relevance of this new PDE to the Strominger-Yau-Zaslow conjecture for mirror symmetry in terms of special Lagrangian fibrations and to the $\mathrm{G}_2$ version by Gukov-Yau-Zaslow in terms of coassociative fibrations; and we present several open questions for future study.