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While overparameterization is known to benefit generalization, its impact on Out-Of-Distribution (OOD) detection is less understood. This paper investigates the influence of model complexity in OOD detection. We propose an expected OOD risk metric to evaluate classifiers confidence on both training and OOD samples. Leveraging Random Matrix Theory, we derive bounds for the expected OOD risk of binary least-squares classifiers applied to Gaussian data. We show that the OOD risk depicts an infinite peak, when the number of parameters is equal to the number of samples, which we associate with the double descent phenomenon. Our experimental study on different OOD detection methods across multiple neural architectures extends our theoretical insights and highlights a double descent curve. Our observations suggest that overparameterization does not necessarily lead to better OOD detection. Using the Neural Collapse framework, we provide insights to better understand this behavior. To facilitate reproducibility, our code will be made publicly available upon publication.

In this study, we systematically investigate the dynamics of various hadrons namely \( \pi^+ \), \( \pi^- \), \( K^+ \), \( K^- \), \( p \), \( \bar{p} \), \( \Lambda \), \( \bar{\Lambda} \), \( \Xi^- \) and \( \bar{\Xi}^+ \) produced in central Au-Au collisions. We analyze data of AGS and RHIC, which span a broad range of collision energies, ranging from \( \sqrt{s_{NN}}\) = 1.9 to 200 GeV. To analyze the transverse momentum (\( p_T \)) and transverse mass (\( m_T \)) distributions, we employ a two-component standard distribution function, achieving a very good representation of the experimental data across these energy regimes. We extract key thermodynamic parameters, including the effective temperature \( T \), the mean transverse momentum \( \langle p_T \rangle \), and the initial temperature \( T_i \), and analyze their dependence on the values of collision energy and particle mass. Our findings reveal a distinct transition behaviour around \( \sqrt{s_{NN}} = 19.6 \) GeV. Below \( \sqrt{s_{NN}} = 19.6 \) GeV, the values of \( T \), \( \langle p_T \rangle \), and \( T_i \) increase monotonically for all hadrons due to higher energy transfer into the system. Above this energy threshold, these extracted parameters plateau, suggesting that the additional energy is utilized as latent heat for phase transition rather than increasing the system's temperature. These observations delineate two distinct regions: a hadron-dominated region at lower energies and a parton-dominated region at higher energies, each potentially indicative of different phases of matter, with the latter possibly signalling the onset of a Quark-Gluon Plasma (QGP). The study thus provides critical insights into the complex interplay of thermodynamics, phase transitions, and particle interactions in high-energy Au-Au collisions., Comment: 17 pages, 3 figures

Tunisian Arabic (ISO 693-3: aeb) isa distinct variety native to Tunisia, derived from Arabic and enriched by various historical influences. This research introduces the "Normalized Orthography for Tunisian Arabic" (NOTA), an adaptation of CODA* guidelines for transcribing Tunisian Arabic using Arabic script. The aim is to enhance language resource development by ensuring user-friendliness and consistency. The updated standard addresses challenges in accurately representing Tunisian phonology and morphology, correcting issues from transcriptions based on Modern Standard Arabic., Comment: Final Report for the Derja Association. Camera-Ready for LPKM 2024

We consider the spaces $\mathcal{F}_\mu$ of polynomial $\mu$-densities on the line as $\mathfrak{sl}(2)$-modules and then we compute the cohomological spaces $\mathrm{H}^2_\mathrm{diff}(\mathfrak{sl}(2), \mathcal{D}_{\bar{\lambda},\mu})$, where $\mu\in \mathbb{R}$, $\bar{\lambda}=(\lambda_1,\dots,\lambda_n) \in\mathbb{R}^n$ and $\mathcal{D}_{\bar{\lambda},\mu}$ is the space of $n$-ary differential operators from $\mathcal{F}_{\lambda_1}\otimes\cdots\otimes \mathcal{F}_{\lambda_n}$ to $\mathcal{F}_\mu$., Comment: 15 pages

Detecting out-of-distribution (OOD) data is a critical challenge in machine learning due to model overconfidence, often without awareness of their epistemological limits. We hypothesize that ``neural collapse'', a phenomenon affecting in-distribution data for models trained beyond loss convergence, also influences OOD data. To benefit from this interplay, we introduce NECO, a novel post-hoc method for OOD detection, which leverages the geometric properties of ``neural collapse'' and of principal component spaces to identify OOD data. Our extensive experiments demonstrate that NECO achieves state-of-the-art results on both small and large-scale OOD detection tasks while exhibiting strong generalization capabilities across different network architectures. Furthermore, we provide a theoretical explanation for the effectiveness of our method in OOD detection. Code is available at https://gitlab.com/drti/neco, Comment: Accepted to ICLR2024

We report on ferromagnetic resonant mode hybridization in re-entrant cavities made with a commercial three-dimensional (3D) printer, followed by conventional 3D metalization with copper and tin. The cavity volume was only 7% that of a standard cavity resonating at the same frequency, while maintaining a high quality factor. Simulations were in very good agreement. We obtained an effective coupling of about 40 MHz in two cavities at room temperature. These experimental results demonstrate the utility of tunable filters based on complex 3D printed cavities.

We consider a nonlinear representation of a Lie algebra which is regular on an abelian ideal, we define a normal form which generalizes that defined in [D. Arnal, M. Ben Ammar, M. Selmi, {\rm Normalisation d'une repr\'esentation non lin\'eaire d'une alg\`ebre de Lie}. {\it Annales de la Facult\'e des Sciences de Toulouse}, 5e s\'erie, tome 9, No 3, 1988, p 355--379.]

We classify deformations of $\mathfrak{osp}(2|2)-$module structure on the spaces of symbols $\mathfrak{S}_d^2$ of differential operators acting on the space of weighted densities $\mathfrak{F}_{\lambda}^{2}$., Comment: 14 pages

Graph databases (GDB) have recently been arisen to overcome the limits of traditional databases for storing and managing data with graph-like structure. Today, they represent a requirement for many applications that manage graph-like data, like social networks. Most of the techniques, applied to optimize queries in graph databases, have been used in traditional databases, distribution systems... or they are inspired from graph theory. However, their reuse in graph databases should take care of the main characteristics of graph databases, such as dynamic structure, highly interconnected data, and ability to efficiently access data relationships. In this paper, we survey the query optimization techniques in graph databases. In particular, we focus on the features they have introduced to improve querying graph-like data.

We consider the $\mu$-densities spaces $\mathcal{F}_\mu$ with $\mu\in\mathbb{R}$, we compute the space $\mathrm{H}^1_\mathrm{diff}(\mathfrak{aff}(1),\mathrm{D}_{\lambda,\mu})$ where $\lambda=(\lambda_1,\dots,\lambda_n)\in\mathbb{R}^n$ and $\mathrm{D}_{\lambda,\mu}$ is the space of $n$-ary differential operators from $\mathcal{F}_{\lambda_1}\otimes\cdots\otimes\mathcal{F}_{\lambda_n}$ to $\mathcal{F}_\mu$. We also compute the super analog space $\mathrm{H}^1_\mathrm{diff}(\mathfrak{aff}(1|1),\mathfrak{D}_{\lambda,\mu})$., Comment: 14 pages. arXiv admin note: text overlap with arXiv:0911.2769, arXiv:1512.02847

We consider the spaces $\mathcal{F}_\mu$ of polynomial $\mu$-densities on the line as $\mathfrak{sl}(2)$-modules and then we compute the cohomological spaces $\mathrm{H}^1_\mathrm{diff}(\mathfrak{sl}(2), \mathcal{D}_{\bar{\lambda},\mu})$, where $\mu\in \mathbb{R}$, $\bar{\lambda}=(\lambda_1,\dots,\lambda_n) \in\mathbb{R}^n$ and $\mathcal{D}_{\bar{\lambda},\mu}$ is the space of $n$-ary differential operators from $\mathcal{F}_{\lambda_1}\otimes\cdots\otimes \mathcal{F}_{\lambda_n}$ to $\mathcal{F}_\mu$.