Miracle-dz/UniFAR-FTUs huggingface dataset:
On zero behavior of higher-order Sobolev-type discrete q-Hermite I orthogonal polynomials

In this work, we investigate the sequence of monic q-Hermite I-Sobolev type orthogonal polynomials of higher-order, denoted as $\{\mathbb{H}_{n}(x;q)\}_{n\geq 0}$, which are orthogonal with respect to the following non-standard inner product involving q-differences: \begin{equation*} \langle p,q\rangle_{\lambda }=\int_{-1}^{1}f\left( x\right) g\left(x\right) (qx,-qx;q)_{\infty }d_{q}(x)+\lambda \,(\mathscr{D}_{q}^{j}f)(\alpha)(\mathscr{D}_{q}^{j}g)(\alpha), \end{equation*} where $\alpha \in \mathbb{R}\backslash (-1,1)$, $\lambda $ belongs to the set of positive real numbers, $\mathscr{D}_{q}^{j}$ denotes the $j$-th $q $-discrete analogue of the derivative operator, and $(qx,-qx;q)_{\infty}d_{q}(x)$ denotes the orthogonality weight with its points of increase in a geometric progression. We proceed to obtain the hypergeometric representation of $\mathbb{H}_{n}(x;q)$ and explicit expressions for the corresponding ladder operators. From the latter, we obtain a novel kind of three-term recurrence formula with rational coefficients associated with these polynomial family. Moreover, for certain real values of $\alpha $, we present some results concerning the location of the zeros of $\mathbb{H}_n(x;q)$ and we perform a comprehensive analysis of their asymptotic behavior as the parameter $\lambda$ varies from zero to infinity.
Deconstructing the Goldilocks Zone of Neural Network Initialization

The second-order properties of the training loss have a massive impact on the optimization dynamics of deep learning models. Fort&Scherlis (2019) discovered that a high positive curvature and local convexity of the loss Hessian are associated with highly trainable initial points located in a region coined the"Goldilocks zone". Only a handful of subsequent studies touched upon this relationship, so it remains largely unexplained. In this paper, we present a rigorous and comprehensive analysis of the Goldilocks zone for homogeneous neural networks. In particular, we derive the fundamental condition resulting in non-zero positive curvature of the loss Hessian and argue that it is only incidentally related to the initialization norm, contrary to prior beliefs. Further, we relate high positive curvature to model confidence, low initial loss, and a previously unknown type of vanishing cross-entropy loss gradient. To understand the importance of positive curvature for trainability of deep networks, we optimize both fully-connected and convolutional architectures outside the Goldilocks zone and analyze the emergent behaviors. We find that strong model performance is not necessarily aligned with the Goldilocks zone, which questions the practical significance of this concept.
Resource-Aware Hierarchical Federated Learning in Wireless Video Caching Networks

Backhaul traffic congestion caused by the video traffic of a few popular files can be alleviated by storing the to-be-requested content at various levels in wireless video caching networks. Typically, content service providers (CSPs) own the content, and the users request their preferred content from the CSPs using their (wireless) internet service providers (ISPs). As these parties do not reveal their private information and business secrets, traditional techniques may not be readily used to predict the dynamic changes in users' future demands. Motivated by this, we propose a novel resource-aware hierarchical federated learning (RawHFL) solution for predicting user's future content requests. A practical data acquisition technique is used that allows the user to update its local training dataset based on its requested content. Besides, since networking and other computational resources are limited, considering that only a subset of the users participate in the model training, we derive the convergence bound of the proposed algorithm. Based on this bound, we minimize a weighted utility function for jointly configuring the controllable parameters to train the RawHFL energy efficiently under practical resource constraints. Our extensive simulation results validate the proposed algorithm's superiority, in terms of test accuracy and energy cost, over existing baselines.
Charge correlator expansion for free fermion negativity

Logarithmic negativity is a widely used entanglement measure in quantum information theories, which can also be efficiently computed in quantum many-body systems by replica trick or by relating to correlation matrices. In this paper, we demonstrate that in free-fermion systems with conserved charge, R\'enyi and logarithmic negativity can be expanded by connected charge correlators, analogous to the case for entanglement entropy in the context of full counting statistics (FCS). We confirm the rapid convergence of this expansion in random all-connected Hamiltonian through numerical verification, especially for systems with only local hopping. We find that the replica trick that get logarithmic negativity from the limit of R\'enyi negativity is valid in this method only for translational invariant systems. Using this expansion, we analyze the scaling behavior of negativity in extensive free-fermion systems. In particular, in 1+1 dimensional free-fermion systems, we observe that the scaling behavior of negativity from our expansion is consistent with known results from the method with Toeplitz matrix. These findings provide insights into the entanglement properties of free-fermion systems, and demonstrate the efficacy of the expansion approach in studying entanglement measures.
One-shot Neural Face Reenactment via Finding Directions in GAN's Latent Space

In this paper, we present our framework for neural face/head reenactment whose goal is to transfer the 3D head orientation and expression of a target face to a source face. Previous methods focus on learning embedding networks for identity and head pose/expression disentanglement which proves to be a rather hard task, degrading the quality of the generated images. We take a different approach, bypassing the training of such networks, by using (fine-tuned) pre-trained GANs which have been shown capable of producing high-quality facial images. Because GANs are characterized by weak controllability, the core of our approach is a method to discover which directions in latent GAN space are responsible for controlling head pose and expression variations. We present a simple pipeline to learn such directions with the aid of a 3D shape model which, by construction, inherently captures disentangled directions for head pose, identity, and expression. Moreover, we show that by embedding real images in the GAN latent space, our method can be successfully used for the reenactment of real-world faces. Our method features several favorable properties including using a single source image (one-shot) and enabling cross-person reenactment. Extensive qualitative and quantitative results show that our approach typically produces reenacted faces of notably higher quality than those produced by state-of-the-art methods for the standard benchmarks of VoxCeleb1 & 2.
Early prediction of onset of sepsis in Clinical Setting

This study proposes the use of Machine Learning models to predict the early onset of sepsis using deidentified clinical data from Montefiore Medical Center in Bronx, NY, USA. A supervised learning approach was adopted, wherein an XGBoost model was trained utilizing 80\% of the train dataset, encompassing 107 features (including the original and derived features). Subsequently, the model was evaluated on the remaining 20\% of the test data. The model was validated on prospective data that was entirely unseen during the training phase. To assess the model's performance at the individual patient level and timeliness of the prediction, a normalized utility score was employed, a widely recognized scoring methodology for sepsis detection, as outlined in the PhysioNet Sepsis Challenge paper. Metrics such as F1 Score, Sensitivity, Specificity, and Flag Rate were also devised. The model achieved a normalized utility score of 0.494 on test data and 0.378 on prospective data at threshold 0.3. The F1 scores were 80.8\% and 67.1\% respectively for the test data and the prospective data for the same threshold, highlighting its potential to be integrated into clinical decision-making processes effectively. These results bear testament to the model's robust predictive capabilities and its potential to substantially impact clinical decision-making processes.
U-shaped Vision Mamba for Single Image Dehazing

Currently, Transformer is the most popular architecture for image dehazing, but due to its large computational complexity, its ability to handle long-range dependency is limited on resource-constrained devices. To tackle this challenge, we introduce the U-shaped Vision Mamba (UVM-Net), an efficient single-image dehazing network. Inspired by the State Space Sequence Models (SSMs), a new deep sequence model known for its power to handle long sequences, we design a Bi-SSM block that integrates the local feature extraction ability of the convolutional layer with the ability of the SSM to capture long-range dependencies. Extensive experimental results demonstrate the effectiveness of our method. Our method provides a more highly efficient idea of long-range dependency modeling for image dehazing as well as other image restoration tasks. The URL of the code is \url{https://github.com/zzr-idam/UVM-Net}. Our method takes only \textbf{0.009} seconds to infer a $325 \times 325$ resolution image (100FPS) without I/O handling time.
On gauge freedom, conservativity and intrinsic dimensionality estimation in diffusion models

Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward continuous denoising process, which can be described by a time-dependent vector field and is used as a generative model. In the original formulation of the diffusion model, this vector field is assumed to be the score function (i.e. it is the gradient of the log-probability at a given time in the diffusion process). Curiously, on the practical side, most studies on diffusion models implement this vector field as a neural network function and do not constrain it be the gradient of some energy function (that is, most studies do not constrain the vector field to be conservative). Even though some studies investigated empirically whether such a constraint will lead to a performance gain, they lead to contradicting results and failed to provide analytical results. Here, we provide three analytical results regarding the extent of the modeling freedom of this vector field. {Firstly, we propose a novel decomposition of vector fields into a conservative component and an orthogonal component which satisfies a given (gauge) freedom. Secondly, from this orthogonal decomposition, we show that exact density estimation and exact sampling is achieved when the conservative component is exactly equals to the true score and therefore conservativity is neither necessary nor sufficient to obtain exact density estimation and exact sampling. Finally, we show that when it comes to inferring local information of the data manifold, constraining the vector field to be conservative is desirable.
An ALMA Molecular Inventory of Warm Herbig Ae Disks. II. Abundant Complex Organics and Volatile Sulphur in the IRS 48 Disk

The Atacama Large Millimeter/submillimeter Array (ALMA) can probe the molecular content of planet-forming disks with unprecedented sensitivity. These observations allow us to build up an inventory of the volatiles available for forming planets and comets. Herbig Ae transition disks are fruitful targets due to the thermal sublimation of complex organic molecules (COMs) and likely H2O-rich ices in these disks. The IRS 48 disk shows a particularly rich chemistry that can be directly linked to its asymmetric dust trap. Here, we present ALMA observations of the IRS 48 disk where we detect 16 different molecules and make the first robust detections of H 2 13 CO , 34SO, 33SO, and c-H2COCH2 (ethylene oxide) in a protoplanetary disk. All of the molecular emissions, aside from CO, are co-located with the dust trap, and this includes newly detected simple molecules such as HCO+, HCN , and CS. Interestingly, there are spatial offsets between different molecular families, including between the COMs and sulfur-bearing species, with the latter being more azimuthally extended and radially located further from the star. The abundances of the newly detected COMs relative to CH3OH are higher than the expected protostellar ratios, which implies some degree of chemical processing of the inherited ices during the disk lifetime. These data highlight IRS 48 as a unique astrochemical laboratory to unravel the full volatile reservoir at the epoch of planet and comet formation and the role of the disk in (re)setting chemical complexity.
Quotients of Leavitt path algebras over rings by $I$-basic graded ideals

In this paper, the quotient of a Leavitt path algebra of an arbitrary graph by an $I$-basic graded ideal, and the quotient of a Leavitt path algebra of a row-finite graph by an arbitrary graded ideal are considered. The result of the quotient of a Leavitt path algebra by an arbitrary graded ideal is extended by using the function $\varphi$. Examples are given to illustrate the results.
Determination of the growth and herbicide sensitivity of some invasive plants under different carbon dioxide, temperature and nitrogen conditions

DETERMINATION OF THE GROWTH AND HERBICIDE SENSITIVITY OF SOME INVASIVE PLANTS UNDER DIFFERENT CARBON DIOXIDE, TEMPERATURE AND NITROGEN CONDITIONS Khawar JABRAN Ph.D. Thesis, Department of Plant Protection Supervisor: Prof. Dr. M. Nedim DOĞAN 2016, 90 pages Global climate changes are supposed to impact the global ecosystems including those of plants. Invasive plants present a serious threat to plants, environment and, human and animal health. The global climate changes may impact the growth, invasion and management of invasive weed species. Hence, these studies were conducted to investigate the impact of recent climate changes on growth, control and nitrogen uptake of invasive species. In these two-years glasshouse experiments, we studied the effects of temperature, carbon dioxide (CO2), nitrogen and herbicide application on biomass, growth, control and leaf tissue nitrogen concentration of four invasive weed species. High CO2-concentration, high CO2concentration+high temperature improved the biomass and growth parameters of weeds including Bromus tectorum L. , Hordeum murinum L. , and Lactuca serriola L. , while Capsella bursa-pastoris (L.) Medik. responded differently to climatic conditions compared with the other weeds. In general, high temperature had a negative or neutral effect on all the weed species in our studies. Nitrogen application had little effects on grasses while the broadleaved weeds mostly had a positive response to nitrogen application. Climatic conditions had no effect on activity of herbicide (glyphosate). This research work conclude that high-CO2 concentration improved the growth of most of the invasive weeds in the experiment while elevated temperature mostly had negative or neutral effect on invasive weeds. Herbicide application provided equal and effective weed control under either of the CO2 or temperature levels while N fertilization had improved very few growth parameters of invasive weeds under different climatic conditions.
Simulating the epoch of Helium Reionization in photon-conserving semi-numerical code SCRIPT

The reionization of the second electron of helium (HeII) leaves important imprints on the thermal and ionization state of the intergalactic medium (IGM). Observational evidence suggests that HeII reionization ended at $z \simeq 3$ due to ionizing photons emitted predominantly by quasars. We present efficient semi-numerical simulations of helium reionization in a $230 \ \mathrm{h^{-1}~Mpc}$ box, that takes into account the spatial patchiness of reionization coupled with photoheating of the IGM. Dark matter haloes are assigned quasars using empirical measurements of the quasar luminosity function, assuming a universal quasar lifetime consistent with duty cycle values inferred from measurements of the quasar clustering. The ionizing photon field from quasars is then included in the semi-numerical Code for ReionIzation with PhoTon conservation (SCRIPT), which was originally developed for modeling hydrogen reionization. In this work, we make appropriate modifications to SCRIPT for modeling inhomogenous HeII reionization and the corresponding thermal history of the IGM is modelled via a subgrid prescription. Our model has three main free parameters i.e. the global clumping factor $\mathcal{C}_{HeIII}$, the temperature increase due to photoheating $T^{re}_{He}$ and the quasar spectral energy distribution (SED) index, $\alpha_{UV}$. Our fiducial model with $\mathcal{C}_{HeIII}=15.6$ and $T^{re}_{He} \sim 6000 \ K$ gives reasonable values for the empirical measurements of the temperature density equation of state at these redshifts, assuming that quasars brighter than $\mathrm{M_{1450}}<-21$ and having $\alpha_{UV}=1.7$ contribute to HeII reionization. The efficiency of our code shows promising prospects for performing parameter estimation in future, for models of HeII reionization using observations of the Ly$\alpha$ forest.
Finite volumes for the Gross-Pitaevskii equation

We study the approximation by a Voronoi finite-volume scheme of the Gross-Pitaevskii equation with time-dependent potential in two and three dimensions. We perform an explicit splitting scheme for the time integration alongside a two-point flux approximation scheme in space. We rigorously analyze the error bounds relying on discrete uniform Sobolev inequalities. We also prove the convergence of the pseudo-vorticity of the wave function. We finally perform some numerical simulations to illustrate our theoretical results.
Deep-Learning Estimation of Weight Distribution Using Joint Kinematics for Lower-Limb Exoskeleton Control

In the control of lower-limb exoskeletons with feet, the phase in the gait cycle can be identified by monitoring the weight distribution at the feet. This phase information can be used in the exoskeleton's controller to compensate the dynamics of the exoskeleton and to assign impedance parameters. Typically the weight distribution is calculated using data from sensors such as treadmill force plates or insole force sensors. However, these solutions increase both the setup complexity and cost. For this reason, we propose a deep-learning approach that uses a short time window of joint kinematics to predict the weight distribution of an exoskeleton in real time. The model was trained on treadmill walking data from six users wearing a four-degree-of-freedom exoskeleton and tested in real time on three different users wearing the same device. This test set includes two users not present in the training set to demonstrate the model's ability to generalize across individuals. Results show that the proposed method is able to fit the actual weight distribution with R2=0.9 and is suitable for real-time control with prediction times less than 1 ms. Experiments in closed-loop exoskeleton control show that deep-learning-based weight distribution estimation can be used to replace force sensors in overground and treadmill walking.
Geometric theory of (extended) time-reversal symmetries in stochastic processes -- Part I: finite dimension

In this article, we analyze three classes of time-reversal of a Markov process with Gaussian noise on a manifold. We first unveil a commutativity constraint for the most general of these time-reversals to be well defined. Then we give a triad of necessary and sufficient conditions for the stochastic process to be time-reversible. While most reversibility conditions in the literature require knowledge of the stationary probability, our conditions do not, and therefore can be analytically checked in a systematic way. We then show that the mathematical objects whose cancellation is required by our reversibility conditions play the role of independent sources of entropy production. Furthermore, we give a geometric interpretation of the so-called irreversible cycle-affinity as the vorticity of a certain vector field for a Riemannian geometry given by the diffusion tensor. We also discuss the relation between the time-reversability of the stochastic process and that of an associated deterministic dynamics: its Stratonovitch average. Finally, we show that a suitable choice of a reference measure - that can be considered as a prior or a gauge, depending on the context - allows to study a stochastic process in a way that is both coordinate-free and independent of the prescription used to define stochastic integrals. When this reference measure plays the role of a gauge choice, we interpret our previous results through the lens of gauge theory and prove them to be gauge-invariant.
Attention Meets Post-hoc Interpretability: A Mathematical Perspective

Attention-based architectures, in particular transformers, are at the heart of a technological revolution. Interestingly, in addition to helping obtain state-of-the-art results on a wide range of applications, the attention mechanism intrinsically provides meaningful insights on the internal behavior of the model. Can these insights be used as explanations? Debate rages on. In this paper, we mathematically study a simple attention-based architecture and pinpoint the differences between post-hoc and attention-based explanations. We show that they provide quite different results, and that, despite their limitations, post-hoc methods are capable of capturing more useful insights than merely examining the attention weights.
Decentralized Sporadic Federated Learning: A Unified Methodology with Generalized Convergence Guarantees

Decentralized Federated Learning (DFL) has received significant recent research attention, capturing settings where both model updates and model aggregations -- the two key FL processes -- are conducted by the clients. In this work, we propose Decentralized Sporadic Federated Learning ($\texttt{DSpodFL}$), a DFL methodology which generalizes the notion of sporadicity in both of these processes, modeling the impact of different forms of heterogeneity that manifest in realistic DFL settings. $\texttt{DSpodFL}$ unifies many of the prominent decentralized optimization methods, e.g., distributed gradient descent (DGD), randomized gossip (RG), and decentralized federated averaging (DFedAvg), under a single modeling framework. We analytically characterize the convergence behavior of $\texttt{DSpodFL}$, showing, among other insights, that we can match a geometric convergence rate to a finite optimality gap under more general assumptions than in existing works. Through experiments, we demonstrate that $\texttt{DSpodFL}$ achieves significantly improved training speeds and robustness to variations in system parameters compared to the state-of-the-art.