Very recently, Heng et al. studied a family of extended primitive cyclic codes. It was shown that the supports of all codewords with any fixed nonzero Hamming weight of this code supporting 2-designs. In this paper, we study this family of extended primitive cyclic codes in more details. The weight distribution is determined. The parameters of the related $2$-designs are also given. Moreover, we prove that the codewords with minimum Hamming weight supporting 3-designs, which gives an affirmative solution to Heng's conjecture.
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We present a novel unsupervised machine learning shock capturing algorithm based on Gaussian Mixture Models (GMMs). The proposed GMM sensor demonstrates remarkable accuracy in detecting shocks and is robust across diverse test cases without the need for parameter tuning. We compare the GMM-based sensor with state-of-the-art alternatives. All methods are integrated into a high-order compressible discontinuous Galerkin solver where artificial viscosity can be modulated to capture shocks. Supersonic test cases, including high Reynolds numbers, showcase the sensor's performance, demonstrating the same effectiveness as fine-tuned state-of-the-art sensors. %The nodal DG aproach allows for potential applications in sub-cell flux-differencing formulations, supersonic feature detection, and mesh refinement. The adaptive nature and ability to function without extensive training datasets make this GMM-based sensor suitable for complex geometries and varied flow configurations. Our study reveals the potential of unsupervised machine learning methods, exemplified by the GMM sensor, to improve the robustness and efficiency of advanced CFD codes.
We study the convergence and error estimates of a finite volume method for the compressible Navier-Stokes-Fourier system with Dirichlet boundary conditions. Physical fluid domain is typically smooth and needs to be approximated by a polygonal computational domain. This leads to domain-related discretization errors, the so-called variational crimes. To treat them efficiently we embed the fluid domain into a large enough cubed domain, and propose a finite volume scheme for the corresponding domain-penalized problem. Under the assumption that the numerical density and temperature are uniformly bounded, we derive the ballistic energy inequality, yielding a priori estimates and the consistency of the penalization finite volume approximations. Further, we show that the numerical solutions converge weakly to a generalized, the so-called dissipative measure-valued, solution of the corresponding Dirichlet problem. If a strong solution exists, we prove that our numerical approximations converge strongly with the rate 1/4. Additionally, assuming uniform boundedness of the approximate velocities, we obtain global existence of the strong solution. In this case we prove that the numerical solutions converge strongly to the strong solution with the optimal rate 1/2.
JADE is an educational game we have imagined, designed, built, and used successfully in various contexts. This board game enables learning and practicing software ergonomics concepts. It is intended for beginners. We use it every year during several hours with our second-year computer science students at Lyon 1 University. In this paper, we present the classical version of the game, as well as the design and evaluation process that we applied. We also present the hybrid version of JADE, which relies on the use of QR codes and videos. We also present its use in our teaching (with about 850 learners for a total duration of 54 hours, which totals more than 2500 student-hours). We then discuss the results obtained and present the considered evolutions.
Aiming for a mixbiotic society that combines freedom and solidarity among people with diverse values, I focused on nonviolent communication (NVC) that enables compassionate giving in various situations of social division and conflict, and tried a generative AI for it. Specifically, ChatGPT was used in place of the traditional certified trainer to test the possibility of mediating (modifying) input sentences in four processes: observation, feelings, needs, and requests. The results indicate that there is potential for the application of generative AI, although not yet at a practical level. Suggested improvement guidelines included adding model responses, relearning revised responses, specifying appropriate terminology for each process, and re-asking for required information. The use of generative AI will be useful initially to assist certified trainers, to prepare for and review events and workshops, and in the future to support consensus building and cooperative behavior in digital democracy, platform cooperatives, and cyber-human social co-operating systems. It is hoped that the widespread use of NVC mediation using generative AI will lead to the early realization of a mixbiotic society.
V. Levenshtein first proposed the sequence reconstruction problem in 2001. This problem studies the model where the same sequence from some set is transmitted over multiple channels, and the decoder receives the different outputs. Assume that the transmitted sequence is at distance $d$ from some code and there are at most $r$ errors in every channel. Then the sequence reconstruction problem is to find the minimum number of channels required to recover exactly the transmitted sequence that has to be greater than the maximum intersection between two metric balls of radius $r$, where the distance between their centers is at least $d$. In this paper, we study the sequence reconstruction problem of permutations under the Hamming distance. In this model we define a Cayley graph over the symmetric group, study its properties and find the exact value of the largest intersection of its two metric balls for $d=2r$. Moreover, we give a lower bound on the largest intersection of two metric balls for $d=2r-1$.
Species distribution models (SDMs) are increasingly applied across macroscales. Such models typically assume that a single set of regression coefficients can adequately describe species-environment relationships and/or population trends. However, such relationships often show nonlinear and/or spatially-varying patterns that arise from complex interactions with abiotic and biotic processes that operate at different scales. Spatially-varying coefficient (SVC) models can readily account for variability in the effects of environmental covariates. Yet, their use in ecology is relatively scarce due to gaps in understanding the inferential benefits that SVC models can provide compared to simpler frameworks. Here we demonstrate the inferential benefits of SVC SDMs, with a particular focus on how this approach can be used to generate and test ecological hypotheses regarding the drivers of spatial variability in population trends and species-environment relationships. We illustrate the inferential benefits of SVC SDMs with simulations and two case studies: one that assesses spatially-varying trends of 51 forest bird species in the eastern US over two decades and a second that evaluates spatial variability in the effects of five decades of land cover change on Grasshopper Sparrow occurrence across the continental US. We found strong support for SVC SDMs compared to simpler alternatives in both empirical case studies. These applications display the utility of SVC SDMs to help reveal the environmental factors that drive species distributions across both local and broad scales. We conclude by discussing the potential applications of SVC SDMs in ecology and conservation.
In this paper, we consider the problem of parameter estimating for a family of exponential distributions. We develop the improved estimation method, which generalized the James--Stein approach for a wide class of distributions. The proposed estimator dominates the classical maximum likelihood estimator under the quadratic risk. The estimating procedure is applied to special cases of distributions. The numerical simulations results are given.
Large enterprises face a crucial imperative to achieve the Sustainable Development Goals (SDGs), especially goal 13, which focuses on combating climate change and its impacts. To mitigate the effects of climate change, reducing enterprise Scope 3 (supply chain emissions) is vital, as it accounts for more than 90\% of total emission inventories. However, tracking Scope 3 emissions proves challenging, as data must be collected from thousands of upstream and downstream suppliers.To address the above mentioned challenges, we propose a first-of-a-kind framework that uses domain-adapted NLP foundation models to estimate Scope 3 emissions, by utilizing financial transactions as a proxy for purchased goods and services. We compared the performance of the proposed framework with the state-of-art text classification models such as TF-IDF, word2Vec, and Zero shot learning. Our results show that the domain-adapted foundation model outperforms state-of-the-art text mining techniques and performs as well as a subject matter expert (SME). The proposed framework could accelerate the Scope 3 estimation at Enterprise scale and will help to take appropriate climate actions to achieve SDG 13.
We study the online overlapping batch-means covariance estimator for Stochastic Gradient Descent (SGD) under Markovian sampling. We show that the convergence rates of the covariance estimator are $O\big(\sqrt{d}\,n^{-1/8}(\log n)^{1/4}\big)$ and $O\big(\sqrt{d}\,n^{-1/8}\big)$ under state-dependent and state-independent Markovian sampling, respectively, with $d$ representing dimensionality and $n$ denoting the number of observations or SGD iterations. Remarkably, these rates match the best-known convergence rate previously established for the independent and identically distributed ($\iid$) case by \cite{zhu2021online}, up to logarithmic factors. Our analysis overcomes significant challenges that arise due to Markovian sampling, leading to the introduction of additional error terms and complex dependencies between the blocks of the batch-means covariance estimator. Moreover, we establish the convergence rate for the first four moments of the $\ell_2$ norm of the error of SGD dynamics under state-dependent Markovian data, which holds potential interest as an independent result. To validate our theoretical findings, we provide numerical illustrations to derive confidence intervals for SGD when training linear and logistic regression models under Markovian sampling. Additionally, we apply our approach to tackle the intriguing problem of strategic classification with logistic regression, where adversaries can adaptively modify features during the training process to increase their chances of being classified in a specific target class.
Navigating automated driving systems (ADSs) through complex driving environments is difficult. Predicting the driving behavior of surrounding human-driven vehicles (HDVs) is a critical component of an ADS. This paper proposes an enhanced motion-planning approach for an ADS in a highway-merging scenario. The proposed enhanced approach utilizes the results of two aspects: the driving behavior and long-term trajectory of surrounding HDVs, which are coupled using a hierarchical model that is used for the motion planning of an ADS to improve driving safety.
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