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We obtain new controls for the Leray solutions $u$ of the incompressible Navier-Stokes equation in $\mathbb{R}^3$. Specifically, we estimate $u$, $\nabla u$, and $\nabla^2 u$ in suitable Lebesgue spaces $L^{\tilde r}_TL^r$, $r <+ \infty$ with some constraints on $\tilde r>0$. Our method is based on a Duhamel formula around a perturbed heat equation, allowing to thoroughly exploit the well-known energy estimates which balances the potential singularities. We also perform a new Bihari-LaSalle argument in this context. Eventually, we adapt our strategy to prove that $\sup_{t \in [0,T]} \int_{0}^t (t-s)^{-\theta} \|\nabla^k u(s,\cdot)\|_{L^r} ds<+ \infty$, for all $\theta< \frac{3-kr}{2r}$, $k \in [0,2]$, and $1

Course Outcome (CO) and Program Outcome (PO)/Program-Specific Outcome (PSO) alignment is a crucial task for ensuring curriculum coherence and assessing educational effectiveness. The construction of a Course Articulation Matrix (CAM), which quantifies the relationship between COs and POs/PSOs, typically involves assigning numerical values (0, 1, 2, 3) to represent the degree of alignment. In this study, We experiment with four models from the BERT family: BERT Base, DistilBERT, ALBERT, and RoBERTa, and use multiclass classification to assess the alignment between CO and PO/PSO pairs. We first evaluate traditional machine learning classifiers, such as Decision Tree, Random Forest, and XGBoost, and then apply transfer learning to evaluate the performance of the pretrained BERT models. To enhance model interpretability, we apply Explainable AI technique, specifically Local Interpretable Model-agnostic Explanations (LIME), to provide transparency into the decision-making process. Our system achieves accuracy, precision, recall, and F1-score values of 98.66%, 98.67%, 98.66%, and 98.66%, respectively. This work demonstrates the potential of utilizing transfer learning with BERT-based models for the automated generation of CAMs, offering high performance and interpretability in educational outcome assessment., Comment: 26 pages, 9 figures

In forensic genetics, short tandem repeats (STRs) are used for human identification (HID). Degraded biological trace samples with low amounts of short DNA fragments (low-quality DNA samples) pose a challenge for STR typing. Predefined single nucleotide polymorphisms (SNPs) can be amplified on short PCR fragments and used to generate SNP profiles from low-quality DNA samples. However, the stochastic results from low-quality DNA samples may result in frequent locus drop-outs and insufficient numbers of SNP genotypes for convincing identification of individuals. Shotgun DNA sequencing potentially analyses all DNA fragments in a sample in contrast to the targeted PCR-based sequencing methods and may be applied to DNA samples of very low quality, like heavily compromised crime-scene samples and ancient DNA samples. Here, we developed a statistical model for shotgun sequencing, sequence alignment, and genotype calling. Results from replicated shotgun sequencing of buccal swab (high-quality samples) and hair samples (low-quality samples) were arranged in a genotype-call confusion matrix to estimate the calling error probability by maximum likelihood and Bayesian inference. We developed formulas for calculating the evidential weight as a likelihood ratio (LR) based on data from dynamically selected SNPs from shotgun DNA sequencing. The method accounts for potential genotyping errors. Different genotype quality filters may be applied to account for genotyping errors. An error probability of zero resulted in the forensically commonly used LR formula. When considering a single SNP marker's contribution to the LR, error probabilities larger than zero reduced the LR contribution of matching genotypes and increased the LR in the case of a mismatch. We developed an open-source R package, wgsLR, which implements the method, including estimating the calling error probability and calculating LR values., Comment: 25 pages, 9 figures

Amemiya (1973) proposed a ``consistent initial estimator'' for the parameters in a censored regression model with normal errors. This paper demonstrates that a similar approach can be used to construct moment conditions for fixed--effects versions of the model considered by Amemiya. This result suggests estimators for models that have not previously been considered., Comment: This is a very old unpublished draft that is relevant for the recent literature that constructs moment conditions in nonlinear panel data models

We consider reconstruction of an ambient signal in a compressed sensing (CS) setup where the ambient signal has a neural network based generative model. The generative model has a sparse-latent input and we refer to the generated ambient signal as generative sparse-latent signal (GSL). The proposed sparsity inducing reconstruction algorithm is inherently non-convex, and we show that a gradient based search provides a good reconstruction performance. We evaluate our proposed algorithm using simulated data., Comment: Accepted at 31st European Signal Processing Conference, EUSIPCO 2023

In-order to understand the results of recent observations of exoplanets, models have become increasingly complex. Unfortunately this increases both the computational cost and output size of said models. We intend to explore if AI-image-recognition can alleviate this burden. We used DYNAMICO to run a series of HD209458-like models with different orbital-radii. Training data for a number of features of interest was selected from the initial outputs of these models. This was used to train a pair of multi-categorisation convolutional-neural-networks (CNN), which we applied to our outer-atmosphere-equilibrated models. The features detected by our CNNs revealed that our models fall into two regimes: models with a shorter orbital-radii exhibit significant global mixing which shapes the entire atmospheres dynamics. Whereas, models with longer orbital-radii exhibit negligible mixing except at mid-pressures. Here, the initial non-detection of any trained features revealed a surprise: a night-side hot-spot. Analysis suggests that this occurs when rotational influence is sufficiently weak that divergent flows from the day-side to the night-side dominate over rotational-driven transport, such as the equatorial jet. We suggest that image-classification may play an important role in future, computational, atmospheric studies. However special care must be paid to the data feed into the model, from the colourmap, to training the CNN on features with enough breadth and complexity that the CNN can learn to detect them. However, by using preliminary-studies and prior-models, this should be more than achievable for future exascale calculations, allowing for a significant reduction in future workloads and computational resources., Comment: Accepted for publication in ApJ

We address the tasks of Bayesian state estimation and forecasting for a model-free process in an unsupervised learning setup. For a model-free process, we do not have any a-priori knowledge of the process dynamics. In the article, we propose DANSE -- a Data-driven Nonlinear State Estimation method. DANSE provides a closed-form posterior of the state of the model-free process, given linear measurements of the state. In addition, it provides a closed-form posterior for forecasting. A data-driven recurrent neural network (RNN) is used in DANSE to provide the parameters of a prior of the state. The prior depends on the past measurements as input, and then we find the closed-form posterior of the state using the current measurement as input. The data-driven RNN captures the underlying non-linear dynamics of the model-free process. The training of DANSE, mainly learning the parameters of the RNN, is executed using an unsupervised learning approach. In unsupervised learning, we have access to a training dataset comprising only a set of measurement data trajectories, but we do not have any access to the state trajectories. Therefore, DANSE does not have access to state information in the training data and can not use supervised learning. Using simulated linear and non-linear process models (Lorenz attractor and Chen attractor), we evaluate the unsupervised learning-based DANSE. We show that the proposed DANSE, without knowledge of the process model and without supervised learning, provides a competitive performance against model-driven methods, such as the Kalman filter (KF), extended KF (EKF), unscented KF (UKF), a data-driven deep Markov model (DMM) and a recently proposed hybrid method called KalmanNet. In addition, we show that DANSE works for high-dimensional state estimation., Comment: 12 pages, Accepted for publication in IEEE Transactions in Signal Processing

In this paper we consider a geothermal energy storage in which the spatio-temporal temperature distribution is modeled by a heat equation with a convection term. Such storages often are embedded in residential heating systems and control and management require the knowledge of some aggregated characteristics of that temperature distribution in the storage. They describe the input-output behaviour of the storage and the associated energy flows and their response to charging and discharging processes. We aim to derive an efficient approximative description of these characteristics by a low-dimensional system of ODEs. This leads to a model order reduction problem for a large scale linear system of ODEs arising from the semi-discretization of the heat equation combined with a linear algebraic output equation. In a first step we approximate the non time-invariant system of ODEs by a linear time-invariant system. Then we apply Lyapunov balanced truncation model order reduction to approximate the output by a reduced-order system with only a few state equations but almost the same input-output behavior. The paper presents results of extensive numerical experiments showing the efficiency of the applied model order reduction methods. It turns out that only a few suitable chosen ODEs are sufficient to produce good approximations of the input-output behaviour of the storage., Comment: arXiv admin note: text overlap with arXiv:2104.05116

We obtain a sharp limit H\"older continuity of the solution for the transport equations thanks to a vanishing viscosity analysis. We also derive the same control for parabolic equations and for inviscid Burgers' equation. Eventually, under a structural hypothesis on the coefficients, we provide existence and uniqueness of a H\"older continuous solution.

We obtain the well-posedness and Schauder estimates for a class of system of linear, quasi-linear and non-linear second order partial differential equations. We deduce existence and uniqueness of a global smooth solution of a non-linear and non-local equation that we call "semi" incompressible Navier Stokes equation in R 3 .

Two of Peter Schmidt's many contributions to econometrics have been to introduce a simultaneous logit model for bivariate binary outcomes and to study estimation of dynamic linear fixed effects panel data models using short panels. In this paper, we study a dynamic panel data version of the bivariate model introduced in Schmidt and Strauss (1975) that allows for lagged dependent variables and fixed effects as in Ahn and Schmidt (1995). We combine a conditional likelihood approach with a method of moments approach to obtain an estimation strategy for the resulting model. We apply this estimation strategy to a simple model for the intra-household relationship in employment. Our main conclusion is that the within-household dependence in employment differs significantly by the ethnicity composition of the couple even after one allows for unobserved household specific heterogeneity.

The amount of data generated by numerical simulations in various scientific domains such as molecular dynamics, climate modeling, biology, or astrophysics, led to a fundamental redesign of application workflows. The throughput and the capacity of storage subsystems have not evolved as fast as the computing power in extreme-scale supercomputers. As a result, the classical post-hoc analysis of simulation outputs became highly inefficient. In-situ workflows have then emerged as a solution in which simulation and data analytics are intertwined through shared computing resources, thus lower latencies. Determining the best allocation, i.e., how many resources to allocate to each component of an in-situ workflow; and mapping, i.e., where and at which frequency to run the data analytics component, is a complex task whose performance assessment is crucial to the efficient execution of in-situ workflows. However, such a performance evaluation of different allocation and mapping strategies usually relies either on directly running them on the targeted execution environments, which can rapidly become extremely time-and resource-consuming, or on resorting to the simulation of simplified models of the components of an in-situ workflow, which can lack of realism. In both cases, the validity of the performance evaluation is limited. To address this issue, we introduce SIM-SITU, a framework for the faithful simulation of in-situ workflows. This framework builds on the SimGrid toolkit and benefits of several important features of this versatile simulation tool. We designed SIM-SITU to reflect the typical structure of in-situ workflows and thanks to its modular design, SIM-SITU has the necessary flexibility to easily and faithfully evaluate the behavior and performance of various allocation and mapping strategies for in-situ workflows. We illustrate the simulation capabilities of SIM-SITU on a Molecular Dynamics use case. We study the impact of different allocation and mapping strategies on performance and show how users can leverage SIM-SITU to determine interesting tradeoffs when designing their in-situ workflow.

Magnetic tapes are often considered as an outdated storage technology, yet they are still used to store huge amounts of data. Their main interests are a large capacity and a low price per gigabyte, which come at the cost of a much larger file access time than on disks. With tapes, finding the right ordering of multiple file accesses is thus key to performance. Moving the reading head back and forth along a kilometer long tape has a non-negligible cost and unnecessary movements thus have to be avoided. However, the optimization of tape request ordering has then rarely been studied in the scheduling literature, much less than I/O scheduling on disks. For instance, minimizing the average service time for several read requests on a linear tape remains an open question. Therefore, in this paper, we aim at improving the quality of service experienced by users of tape storage systems, and not only the peak performance of such systems. To this end, we propose a reasonable polynomial-time exact algorithm while this problem and simpler variants have been conjectured NP-hard. We also refine the proposed model by considering U-turn penalty costs accounting for inherent mechanical accelerations. Then, we propose low-cost variants of our optimal algorithm by restricting the solution space, yet still yielding an accurate suboptimal solution. Finally, we compare our algorithms to existing solutions from the literature on logs of the mass storage management system of a major datacenter. This allows us to assess the quality of previous solutions and the improvement achieved by our low-cost algorithms. Aiming for reproducibility, we make available the complete implementation of the algorithms used in our evaluation, alongside the dataset of tape requests that is, to the best of our knowledge, the first of its kind to be publicly released.

Data augmentation is an important component in the robustness evaluation of models in natural language processing (NLP) and in enhancing the diversity of the data they are trained on. In this paper, we present NL-Augmenter, a new participatory Python-based natural language augmentation framework which supports the creation of both transformations (modifications to the data) and filters (data splits according to specific features). We describe the framework and an initial set of 117 transformations and 23 filters for a variety of natural language tasks. We demonstrate the efficacy of NL-Augmenter by using several of its transformations to analyze the robustness of popular natural language models. The infrastructure, datacards and robustness analysis results are available publicly on the NL-Augmenter repository (https://github.com/GEM-benchmark/NL-Augmenter)., Comment: 39 pages, repository at https://github.com/GEM-benchmark/NL-Augmenter

One factor of success in software development companies is their ability to deliver good quality products, fast. For this, they need to improve their software development practices. We work with a medium-sized company modernizing its development practices. The company introduced several practices recommended in agile development. If the benefits of these practices are well documented, the impact of such changes on the developers is less well known. We follow this modernization before and during the COVID-19 outbreak. This paper presents an empirical study of the perceived benefit and drawback of these practices as well as the impact of COVID-19 on the company's employees. One of the conclusions, is the additional difficulties created by obsolete technologies to adapt the technology itself and the development practices it encourages to modern standards., Comment: 10 pages, 3 figures, 2 tables