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We investigate the physical properties and redshift evolution of simulated galaxies residing in protoclusters at cosmic noon, to understand the influence of the environment on galaxy formation. This work is to build clear expectations for the ongoing ODIN survey, devoted to mapping large-scale structures at z=2.4, 3.1, and 4.5 using Ly$\alpha$-emitting galaxies (LAEs) as tracers. From the IllustrisTNG simulations, we define subregions centered on the most massive clusters ranked by total stellar mass at z=0 and study the properties of galaxies within, including LAEs. To model the LAE population, we take a semi-analytical approach that assigns Ly$\alpha$ luminosity and equivalent width based on the UV luminosities to galaxies in a probabilistic manner. We investigate stellar mass, star formation rate, major mergers, and specific star formation rate of the population of star-forming galaxies and LAEs in the field and protocluster environment and trace their evolution. We find that the overall shape of the UV luminosity function (LF) in simulated protocluster environments is characterized by a shallower faint-end slope and an excess on the bright end, signaling different formation histories for galaxies therein. The difference is milder for the Ly$\alpha$ LF. While protocluster galaxies follow the same SFR-$M_{\odot}$ scaling relation as average field galaxies, a larger fraction appears to have experienced major mergers in the last 200 Myr and as a result shows enhanced star formation at a ~60% level, leading to a flatter distribution in both SFR and $M_{\odot}$ relative to galaxies in the average field. We find that protocluster galaxies, including LAEs, begin to quench much earlier (z~0.8-1.6) than field galaxies (z~0.5-0.9); our result is in agreement with recent observational results and highlights the importance of large-scale environment on the overall formation history of galaxies., Comment: 18 pages, 13 figures, to be submitted to Astronomy & Astrophysics, the abstract was reduced to meet character requirements; edits include: updating coauthor list and affiliations, updating citations in Sec 2.1

The aim of this paper is investigating the existence of at least one nontrivial bounded solution of the new asymptotically ``linear'' problem \[ \left\{ \begin{array}{ll} - {\rm div} \left[\left(A_0(x) + A(x) |u|^{ps}\right) |\nabla u|^{p-2} \nabla u\right] + s\ A(x) |u|^{ps-2} u\ |\nabla u|^p &\\ \qquad\qquad\qquad =\ \mu |u|^{p (s + 1) -2} u + g(x,u) & \hbox{in $\Omega$,}\\ u = 0 & \hbox{on $\partial{\Omega}$,} \end{array}\right.\] where $\Omega$ is a bounded domain in $\mathbb{R}^N$, $N \ge 2$, $1 < p < N$, $s > 1/p$, both the coefficients $A_0(x)$ and $A(x)$ are in $L^\infty(\Omega)$ and far away from 0, $\mu \in \mathbb{R}$, and the ``perturbation'' term $g(x,t)$ is a Carath\'{e}odory function on $\Omega \times \mathbb{R}$ which grows as $|t|^{r-1}$ with $1\le r < p (s + 1)$ and is such that $g(x,t) \approx \nu |t|^{p-2} t$ as $t \to 0$. By introducing suitable thresholds for the parameters $\nu$ and $\mu$, which are related to the coefficients $A_0(x)$, respectively $A(x)$, under suitable hypotheses on $g(x,t)$, the existence of a nontrivial weak solution is proved if either $\nu$ is large enough with $\mu$ small enough or $\nu$ is small enough with $\mu$ large enough. Variational methods are used and in the first case a minimization argument applies while in the second case a suitable Mountain Pass Theorem is used.

A much-studied problem posed by Motzkin asks to determine, given a finite set $D$ of integers, the so-called Motzkin density of $D$, i.e., the supremum of upper densities of sets of integers whose difference set avoids $D$. We study the natural analogue of this problem in compact abelian groups. Using ergodic-theoretic tools, this is shown to be equivalent to the following discrete problem: given a lattice $\Lambda\subset \mathbb{Z}^r$, letting $D$ be the image in $\mathbb{Z}^r/\Lambda$ of the standard basis, determine the Motzkin density of $D$ in $\mathbb{Z}^r/\Lambda$. We study in particular the periodicity question: is there a periodic $D$-avoiding set of maximal density in $\mathbb{Z}^r/\Lambda$? The Greenfeld--Tao counterexample to the periodic tiling conjecture implies that the answer can be negative. On the other hand, we prove that the answer is positive in several cases, including the case rank$(\Lambda)=1$ (in which we give a formula for the Motzkin density), the case rank$(\Lambda)=r-1$, and hence also the case $r\leq 3$. It follows that, for up to three missing differences, the Motzkin density in a compact abelian group is always a rational number., Comment: 19 pages

Autonomous selection of optimal options for data collection from multiple alternatives is challenging in uncertain environments. When secondary information about options is accessible, such problems can be framed as contextual multi-armed bandits (CMABs). Neuro-inspired active inference has gained interest for its ability to balance exploration and exploitation using the expected free energy objective function. Unlike previous studies that showed the effectiveness of active inference based strategy for CMABs using synthetic data, this study aims to apply active inference to realistic scenarios, using a simulated mineralogical survey site selection problem. Hyperspectral data from AVIRIS-NG at Cuprite, Nevada, serves as contextual information for predicting outcome probabilities, while geologists' mineral labels represent outcomes. Monte Carlo simulations assess the robustness of active inference against changing expert preferences. Results show that active inference requires fewer iterations than standard bandit approaches with real-world noisy and biased data, and performs better when outcome preferences vary online by adapting the selection strategy to align with expert shifts., Comment: 10 pages, 12 figures, submitted to IEEE Transactions on Robotics

We investigate the possible production of a MeV-scale sterile fermion through the up-scattering of neutrinos on nuclei and atomic electrons at different facilities. We consider a phenomenological model that adds a new fermion to the particle content of the Standard Model and we allow for all possible Lorentz-invariant non-derivative interactions (scalar, pseudoscalar, vector, axial-vector and tensor) of neutrinos with electrons and first-generation quarks. We first explore the sensitivity of the DUNE experiment to this scenario, by simulating elastic neutrino-electron scattering events in the near detector. We consider both options of a standard and a tau-optimized neutrino beams, and investigate the impact of a mobile detector that can be moved off-axis with respect to the beam. Next, we infer constraints on the typical coupling, new fermion and mediator masses from elastic neutrino-electron scattering events induced by solar neutrinos in two current dark matter direct detection experiments, XENONnT and LZ. Under the assumption that the new mediators couple also to first-generation quarks, we further set constraints on the up-scattering production of the sterile fermion using coherent elastic neutrino-nucleus scattering data from the COHERENT experiment. Moreover, we set additional constraints assuming that the sterile fermion may decay within the detector. We finally compare our results and discuss how these facilities are sensitive to different regions of the relevant parameter space due to kinematics arguments and can hence provide complementary information on the up-scattering production of a sterile fermion., Comment: 29 pages, 9 figures, 1 table; spin-dependent cross sections corrected, typos corrected, references added

Large-scale face recognition datasets are collected by crawling the Internet and without individuals' consent, raising legal, ethical, and privacy concerns. With the recent advances in generative models, recently several works proposed generating synthetic face recognition datasets to mitigate concerns in web-crawled face recognition datasets. This paper presents the summary of the Synthetic Data for Face Recognition (SDFR) Competition held in conjunction with the 18th IEEE International Conference on Automatic Face and Gesture Recognition (FG 2024) and established to investigate the use of synthetic data for training face recognition models. The SDFR competition was split into two tasks, allowing participants to train face recognition systems using new synthetic datasets and/or existing ones. In the first task, the face recognition backbone was fixed and the dataset size was limited, while the second task provided almost complete freedom on the model backbone, the dataset, and the training pipeline. The submitted models were trained on existing and also new synthetic datasets and used clever methods to improve training with synthetic data. The submissions were evaluated and ranked on a diverse set of seven benchmarking datasets. The paper gives an overview of the submitted face recognition models and reports achieved performance compared to baseline models trained on real and synthetic datasets. Furthermore, the evaluation of submissions is extended to bias assessment across different demography groups. Lastly, an outlook on the current state of the research in training face recognition models using synthetic data is presented, and existing problems as well as potential future directions are also discussed., Comment: The 18th IEEE International Conference on Automatic Face and Gesture Recognition (FG 2024)

Within the field of Humanities, there is a recognized need for educational innovation, as there are currently no reported tools available that enable individuals to interact with their environment to create an enhanced learning experience in the humanities (e.g., immersive spaces). This project proposes a solution to address this gap by integrating technology and promoting the development of teaching methodologies in the humanities, specifically by incorporating emotional monitoring during the learning process of humanistic context inside an immersive space. In order to achieve this goal, a real-time emotion detection EEG-based system was developed to interpret and classify specific emotions. These emotions aligned with the early proposal by Descartes (Passions), including admiration, love, hate, desire, joy, and sadness. This system aims to integrate emotional data into the Neurohumanities Lab interactive platform, creating a comprehensive and immersive learning environment. This work developed a ML, real-time emotion detection model that provided Valence, Arousal, and Dominance (VAD) estimations every 5 seconds. Using PCA, PSD, RF, and Extra-Trees, the best 8 channels and their respective best band powers were extracted; furthermore, multiple models were evaluated using shift-based data division and cross-validations. After assessing their performance, Extra-Trees achieved a general accuracy of 96%, higher than the reported in the literature (88% accuracy). The proposed model provided real-time predictions of VAD variables and was adapted to classify Descartes' six main passions. However, with the VAD values obtained, more than 15 emotions can be classified (reported in the VAD emotion mapping) and extend the range of this application., Comment: 20 pages, 7 figures. Submitted to Frontiers in Human Neuroscience

The Nobel Prize winning Black-Scholes equation for stock options and the heat equation can both be written in the form \[ \frac{\partial u}{\partial t}=P_2(A)u, \] where $P_2(z)=\alpha z^2+ \beta z+\gamma$ is a quadratic polynomial with $\alpha > 0$. In fact, taking $A = x\frac{\partial}{\partial x}$ on functions on $[0,\infty) \times [0,\infty)$ the previous equality reduces to the Black-Scholes equation, while taking $A = \frac{\partial}{\partial x}$ for functions on $\mathbb{R} \times [0,\infty)$ it becomes the heat equation. Here, we ``connect'' the two previous problems by considering the generalized operator $A= x^a\frac{\partial}{\partial x}$ for functions on $[0,\infty) \times [0,\infty)$ with $0

In recent work, Jamneshan, Shalom and Tao proved an inverse theorem for the Gowers $U^{k+1}$-norm on finite abelian groups of fixed torsion $m$, where the final correlating harmonic is a polynomial phase function of degree at most $C(k,m)$. They also posed a related central question, namely, whether the bound $C$ can be reduced to the optimal value $k$ for every $m$. We make progress on this question using nilspace theory. First we connect the question to the study of finite nilspaces whose structure groups have torsion $m$. Then we prove one of the main results of this paper: a primary decomposition theorem for finite nilspaces, extending the Sylow decomposition in group theory. Thus we give an analogue for nilspaces of an ergodic-theoretic Sylow decomposition in the aforementioned work of Jamneshan-Shalom-Tao. We deduce various consequences which illustrate the following general idea: the primary decomposition enables a reduction of higher-order Fourier analysis in the $m$-torsion setting to the case of abelian $p$-groups. These consequences include a positive answer to the question of Jamneshan-Shalom-Tao when $m$ is squarefree, and also a new relation between uniformity norms and certain generalized cut norms on products of abelian groups of coprime orders. Another main result in this paper is a positive answer to the above central question for the $U^3$-norm, proving that $C(2,m)=2$ for all $m$. Finally, we give a partial answer to the question for all $k$ and $m$, proving an inverse theorem involving extensions of polynomial phase functions which were introduced by the third-named author, known as projected phase polynomials of degree $k$. A notable aspect is that this inverse theorem implies that of Jamneshan-Shalom-Tao, while involving projected phase polynomials of degree $k$, which are genuine obstructions to having small $U^{k+1}$-norm., Comment: 26 pages. Comments from Jamneshan, Shalom and Tao incorporated

A soft random graph $G(n,r,p)$ can be obtained from the random geometric graph $G(n,r)$ by keeping every edge in $G(n,r)$ with probability $p$. This random graph is a particular case of the soft random graph model introduced by Penrose, in which the probability between 2 vertices is a function that depends on the distance between them. In this article, we define models for random simplicial complexes built over the soft random graph $G(n,r,p)$, which also present randomness in all other dimensions. Furthermore, we study the homology of those random simplicial complexes in different regimes of $n,r$, and $p$ by giving asymptotic formulas for the expectation of the Betti numbers in the sparser regimes, and bounds in the denser regimes., Comment: 20 pages. arXiv admin note: text overlap with arXiv:2311.10625

A soft random graph $G(n,r,p)$ can be obtained from the random geometric graph $G(n,r)$ by keeping every edge in $G(n,r)$ with probability $p$. The soft random simplicial complexes is a model for random simplicial complexes built over the soft random graph $G(n,r,p)$. This new model depends on a probability vector $\rho$ which allows the simplicial complexes to present randomness in all dimensions. In this article, we use a normal approximation theorem to prove central limit theorems for the number of $k$-faces and for the Euler's characteristic for soft random simplicial complexes., Comment: 28 pages

Despite the widespread adoption of face recognition technology around the world, and its remarkable performance on current benchmarks, there are still several challenges that must be covered in more detail. This paper offers an overview of the Face Recognition Challenge in the Era of Synthetic Data (FRCSyn) organized at WACV 2024. This is the first international challenge aiming to explore the use of synthetic data in face recognition to address existing limitations in the technology. Specifically, the FRCSyn Challenge targets concerns related to data privacy issues, demographic biases, generalization to unseen scenarios, and performance limitations in challenging scenarios, including significant age disparities between enrollment and testing, pose variations, and occlusions. The results achieved in the FRCSyn Challenge, together with the proposed benchmark, contribute significantly to the application of synthetic data to improve face recognition technology., Comment: 10 pages, 1 figure, WACV 2024 Workshops

Building on previous work in the nilspace-theoretic approach to the study of Host-Kra factors of measure-preserving systems, we prove that every ergodic $\mathbb{F}_p^\omega$-system of order $k$ is a factor of an Abramov $\mathbb{F}_p^\omega$-system of order $k$. This answers a question of Jamneshan, Shalom and Tao., Comment: 15 pages

The topology of the Internet and its geographic properties received significant attention during the last years, not only because they have a deep impact on the performance experienced by users, but also because of legal, political, and economic reasons. In this paper, the global Internet is studied in terms of path locality, where a path is defined as local if it does not cross the borders of the region where the source and destination hosts are located. The phenomenon is studied from the points of view of two metrics, one based on the size of the address space of the autonomous systems where the endpoints are located and the other one on the amount of served population. Results show that the regions of the world are characterized by significant differences in terms of path locality. The main elements contributing to the path locality, and non-locality, of the regions and countries, are identified and discussed. Finally, we present the most significant dependency relationships between countries caused by non-local paths.

In this work, the novel Image Transformation Sequence Retrieval (ITSR) task is presented, in which a model must retrieve the sequence of transformations between two given images that act as source and target, respectively. Given certain characteristics of the challenge such as the multiplicity of a correct sequence or the correlation between consecutive steps of the process, we propose a solution to ITSR using a general model-based Reinforcement Learning such as Monte Carlo Tree Search (MCTS), which is combined with a deep neural network. Our experiments provide a benchmark in both synthetic and real domains, where the proposed approach is compared with supervised training. The results report that a model trained with MCTS is able to outperform its supervised counterpart in both the simplest and the most complex cases. Our work draws interesting conclusions about the nature of ITSR and its associated challenges.

Operationalizing AI fairness at LinkedIn's scale is challenging not only because there are multiple mutually incompatible definitions of fairness but also because determining what is fair depends on the specifics and context of the product where AI is deployed. Moreover, AI practitioners need clarity on what fairness expectations need to be addressed at the AI level. In this paper, we present the evolving AI fairness framework used at LinkedIn to address these three challenges. The framework disentangles AI fairness by separating out equal treatment and equitable product expectations. Rather than imposing a trade-off between these two commonly opposing interpretations of fairness, the framework provides clear guidelines for operationalizing equal AI treatment complemented with a product equity strategy. This paper focuses on the equal AI treatment component of LinkedIn's AI fairness framework, shares the principles that support it, and illustrates their application through a case study. We hope this paper will encourage other big tech companies to join us in sharing their approach to operationalizing AI fairness at scale, so that together we can keep advancing this constantly evolving field.

Compact finite-rank nilspaces have become central in the nilspace approach to higher-order Fourier analysis, notably through their role in a general form of the inverse theorem for the Gowers norms. This paper studies these nilspaces per se, and in connection with further refinements of this inverse theorem that have been conjectured recently. Our first main result states that every compact finite-rank nilspace is obtained by taking a free nilspace (a nilspace based on an abelian group of the form $\mathbb{Z}^{r}\times \mathbb{R}^s$) and quotienting this by a discrete group action of a specific type, describable in terms of polynomials. We call these group actions "higher-order lattice actions", as they generalize actions of lattices in $\mathbb{Z}^r\times \mathbb{R}^s$. The second main result (which relies on the first one) represents every compact finite-rank nilspace as a double-coset space $K\backslash G / \Gamma$ where $G$ is a nilpotent Lie group of a specific kind. Our third main result extends the aforementioned results to $k$-step compact nilspaces (not necessarily of finite rank), by representing any such nilspace as a quotient of infinite products of free nilspaces and also as double coset spaces $K\backslash G/\Gamma$ where $G$ is a degree-$k$ nilpotent pro-Lie group. These results open the study of compact nilspaces to areas more classical than nilspace theory, such as the theory of topological group actions. The results also require developing the theory of topological non-compact nilspaces, for which we provide groundwork in this paper. Applications include new inverse theorems for Gowers norms on any finite abelian group. These theorems are purely group theoretic in that the correlating harmonics are based on double-coset spaces. This yields progress towards the Jamneshan-Tao conjecture., Comment: 81 pages

We consider the possible production of a new MeV-scale fermion at the COHERENT experiment. The new fermion, belonging to a dark sector, can be produced through the up-scattering process of neutrinos off the nuclei and the electrons of the detector material, via the exchange of a light vector or scalar mediator. We perform a detailed statistical analysis of the combined COHERENT CsI and LAr data sets and obtain up-to-date constraints on the couplings and masses of the dark fermion and mediators. We finally briefly comment about the stability of the dark fermion., Comment: 26 pages, 10 figures, 1 table; typos corrected, references added