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Ovoids of the hyperbolic quadric $Q^+(7,q)$ of $\mathrm{PG}(7,q)$ have been extensively studied over the past 40 years, partly due to their connections with other combinatorial objects. It is well known that the points of an ovoid of $Q^+(7,q)$ can be parametrized by three polynomials $f_1(X,Y,Z)$, $f_2(X,Y,Z)$, $f_3(X,Y,Z)$. In this paper, we classify ovoids of $Q^+(7,q)$ of low degree, specifically under the assumption that $f_1(X,Y,Z)$, $f_2(X,Y,Z)$, $f_3(X,Y,Z)$ have degree at most 3. Our approach relies on the analysis of an algebraic hypersurface associated with the ovoid.

Bayesian optimization (BO) is one of the most powerful strategies to solve computationally expensive-to-evaluate blackbox optimization problems. However, BO methods are conventionally used for optimization problems of small dimension because of the curse of dimensionality. In this paper, a high-dimensionnal optimization method incorporating linear embedding subspaces of small dimension is proposed to efficiently perform the optimization. An adaptive learning strategy for these linear embeddings is carried out in conjunction with the optimization. The resulting BO method, named efficient global optimization coupled with random and supervised embedding (EGORSE), combines in an adaptive way both random and supervised linear embeddings. EGORSE has been compared to state-of-the-art algorithms and tested on academic examples with a number of design variables ranging from 10 to 600. The obtained results show the high potential of EGORSE to solve high-dimensional blackbox optimization problems, in terms of both CPU time and the limited number of calls to the expensive blackbox simulation.

Choosing the right system architecture for the problem at hand is challenging due to the large design space and high uncertainty in the early stage of the design process. Formulating the architecting process as an optimization problem may mitigate some of these challenges. This work investigates strategies for solving System Architecture Optimization (SAO) problems: expensive, black-box, hierarchical, mixed-discrete, constrained, multi-objective problems that may be subject to hidden constraints. Imputation ratio, correction ratio, correction fraction, and max rate diversity metrics are defined for characterizing hierar chical design spaces. This work considers two classes of optimization algorithms for SAO: Multi-Objective Evolutionary Algorithms (MOEA) such as NSGA-II, and Bayesian Optimization (BO) algorithms. A new Gaussian process kernel is presented that enables modeling hierarchical categorical variables, extending previous work on modeling continuous and integer hierarchical variables. Next, a hierarchical sampling algorithm that uses design space hierarchy to group design vectors by active design variables is developed. Then, it is demonstrated that integrating more hierarchy information in the optimization algorithms yields better optimization results for BO algorithms. Several realistic single-objective and multi-objective test problems are used for investigations. Finally, the BO algorithm is applied to a jet engine architecture optimization problem. This work shows that the developed BO algorithm can effectively solve the problem with one order of magnitude less function evaluations than NSGA-II. The algorithms and problems used in this work are implemented in the open-source Python library SBArchOpt., Comment: J Glob Optim (2024)

Reconfigurable Intelligent Surfaces (RIS) represent transformative technologies for next-generation wireless communications, offering advanced control over electromagnetic wave propagation. While RIS have been extensively studied, Stacked Intelligent Metasurfaces (SIM), which extend the RIS concept to multi-layered systems, present significant modeling and optimization challenges. This work addresses these challenges by introducing an optimization framework for SIM that, unlike previous approaches, is based on a comprehensive model without relying on specific assumptions, allowing for broader applicability of the results. We first present a model based on multi-port network theory for characterizing a general electromagnetic collaborative object (ECO) and derive a general framework for ECO optimization. We then introduce the SIM as an ECO with a specific architecture, providing insights into SIM optimization for various architectures and discussing the complexity in each case. Finally, we analyze the impact of commonly used assumptions, demonstrating that employing a complete model - one that does not rely on the unilateral hypothesis and accounts for mutual coupling among SIM elements - can yield better performance, using the realization of a 2D DFT as a case study., Comment: 13 pages, 8 figures

Brillouin Microscopy is a novel label-free optical technique that enables the measurement of a material's mechanical properties at the sub-micron scale in a non-invasive and non-contact way; in the last few years, its applications in the life sciences have extensively expanded. To date, many custom-built Brillouin Microscopes suffer from temporal instabilities that impact their performances, showing drifts in the acquired spectra during time that may lead to inconsistencies between data acquired at different days. A further challenge for standard Brillouin Microscopes is the calibration of the spectrometer: the currently accepted protocol in literature uses known Brillouin shifts of water and methanol to reconstruct the dispersion curve, but this approach is highly influenced by external factors that are unrelated to spectrometer's performances. Manual and frequent realignments of the spectrometer and repeated calibrations with standard materials are thus needed to address these issues. Here, we show an innovative method to remove temporal instabilities of a standard Brillouin Microscope by inserting an Electro-Optic Modulator (EOM) that can be used: i) as a reference signal during measurements; ii) as a calibrator, allowing the reconstruction of the spectrometer dispersion curve with high precision, in an automatic pipeline and without the need for reference samples; iii) as a tool to detect and compensate for temporal drifts through a feedback control in a closed loop. We here show that our Brillouin Microscope, equipped with an EOM and a tuneable laser, is able to automatically acquire data for more than 2 days without the need to realign the spectrometer; retrieved Brillouin shifts and widths showed superior stability in time than standard Brillouin Microscopes.

A novel framework for covert communications aided by Reconfigurable Intelligent Surfaces (RIS) is proposed. In this general framework, the use of multiport network theory for modelling the RIS consider various aspects that traditional RIS models in communication theory often overlook, including mutual coupling between elements and the impact of structural scattering. Moreover, the transmitter has only limited knowledge about the channels of the warden and the intended receiver. The proposed approach is validated through numerical results, demonstrating that communication with the legitimate user is successfully achieved while satisfying the covertness constraint., Comment: 13 pages, 7 figures, journal paper

In most applications, robots need to adapt to new environments and be multi-functional without forgetting previous information. This requirement gains further importance in real-world scenarios where robots operate in coexistence with humans. In these complex environments, human actions inevitably lead to changes, requiring robots to adapt accordingly. To effectively address these dynamics, the concept of continual learning proves essential. It not only enables learning models to integrate new knowledge while preserving existing information but also facilitates the acquisition of insights from diverse contexts. This aspect is particularly relevant to the issue of context-switching, where robots must navigate and adapt to changing situational dynamics. Our approach introduces a novel approach to effectively tackle the problem of context drifts by designing a Streaming Graph Neural Network that incorporates both regularization and rehearsal techniques. Our Continual\_GTM model enables us to retain previous knowledge from different contexts, and it is more effective than traditional fine-tuning approaches. We evaluated the efficacy of Continual\_GTM in predicting human routines within household environments, leveraging spatio-temporal object dynamics across diverse scenarios.

This document is comprised of a collection of updated preliminary parameters for the key parts of the muon collider. The updated preliminary parameters follow on from the October 2023 Tentative Parameters Report. Particular attention has been given to regions of the facility that are believed to hold greater technical uncertainty in their design and that have a strong impact on the cost and power consumption of the facility. The data is collected from a collaborative spreadsheet and transferred to overleaf.

In this note we show (for a large enough dimension of the underlying field) a conjecture of [C. Beierle, C. Carlet, G. Leander, L. Perrin, {\em A further study of quadratic APN permutations in dimension nine}, Finite Fields Appl. 81 (2022), 102049] on a trivariate permutation. This function is a global representation of two new sporadic quadratic APN permutations in dimension $9$ found by [C. Beierle, G. Leander, {\em New instances of quadratic APN functions}, IEEE Trans. Inf. Theory 68(1) (2022), 670--678].

In this paper we use algebraic curves and other algebraic number theory methods to show the validity of a permutation polynomial conjecture regarding $f(X)=X^{q(p-1)+1} +\alpha X^{pq}+X^{q+p-1}$, on finite fields $\mathbb{F}_{q^2}, q=p^k$, from [A. Rai, R. Gupta, {\it Further results on a class of permutation trinomials}, Cryptogr. Commun. 15 (2023), 811--820].

This study focuses on the optimization of a single-cell multi-user multiple-input multiple-output (MIMO) system with multiple large-size reconfigurable intelligent surfaces (RISs). The overall transmit power is minimized by optimizing the precoding coefficients and the RIS configuration, with constraints on users' signal-to-interference-plus-noise ratios (SINRs). The minimization problem is divided into two sub-problems and solved by means of an iterative alternating optimization (AO) approach. The first sub-problem focuses on finding the best precoder design. The second sub-problem optimizes the configuration of the RISs by partitioning them into smaller tiles. Each tile is then configured as a combination of pre-defined configurations. This allows the efficient optimization of RISs, especially in scenarios where the computational complexity would be prohibitive using traditional approaches. Simulation results show the good performance and limited complexity of the proposed method in comparison to benchmark schemes.

The International Muon Collider Collaboration (IMCC) [1] was established in 2020 following the recommendations of the European Strategy for Particle Physics (ESPP) and the implementation of the European Strategy for Particle Physics-Accelerator R&D Roadmap by the Laboratory Directors Group [2], hereinafter referred to as the the European LDG roadmap. The Muon Collider Study (MuC) covers the accelerator complex, detectors and physics for a future muon collider. In 2023, European Commission support was obtained for a design study of a muon collider (MuCol) [3]. This project started on 1st March 2023, with work-packages aligned with the overall muon collider studies. In preparation of and during the 2021-22 U.S. Snowmass process, the muon collider project parameters, technical studies and physics performance studies were performed and presented in great detail. Recently, the P5 panel [4] in the U.S. recommended a muon collider R&D, proposed to join the IMCC and envisages that the U.S. should prepare to host a muon collider, calling this their "muon shot". In the past, the U.S. Muon Accelerator Programme (MAP) [5] has been instrumental in studies of concepts and technologies for a muon collider., Comment: This document summarises the International Muon Collider Collaboration (IMCC) progress and status of the Muon Collider R&D programme

In this paper we propose a novel macroscopic (fluid dynamics) model for describing pedestrian flow in low and high density regimes. The model is characterized by the fact that the maximal density reachable by the crowd - usually a fixed model parameter - is instead a state variable. To do that, the model couples a conservation law, devised as usual for tracking the evolution of the crowd density, with a Burgers-like PDE with a nonlocal term describing the evolution of the maximal density. The variable maximal density is used here to describe the effects of the psychological/physical pushing forces which are observed in crowds during competitive or emergency situations. Specific attention is also dedicated to the fundamental diagram, i.e., the function which expresses the relationship between crowd density and flux. Although the model needs a well defined fundamental diagram as known input parameter, it is not evident a priori which relationship between density and flux will be actually observed, due to the time-varying maximal density. An a posteriori analysis shows that the observed fundamental diagram has an elongated "tail" in the congested region, thus resulting similar to the concave/concave fundamental diagram with a "double hump" observed in real crowds. The main features of the model are investigated through 1D and 2D numerical simulations. The numerical code for the 1D simulation is freely available at https://gitlab.com/cristiani77/code_arxiv_2406.14649

The exploration of linear subspaces, particularly scattered subspaces, has garnered considerable attention across diverse mathematical disciplines in recent years, notably within finite geometries and coding theory. Scattered subspaces play a pivotal role in analyzing various geometric structures such as blocking sets, two-intersection sets, complete arcs, caps in affine and projective spaces over finite fields and rank metric codes. This paper introduces a new infinite family of $h$-subspaces, along with their associated MRD codes. Additionally, it addresses the task of determining the generalized weights of these codes. Notably, we demonstrate that these MRD codes exhibit some larger generalized weights compared to those previously identified.

In this work we present results on the classification of $\mathbb{F}_{q^n}$-linear MRD codes of dimension three. In particular, using connections with certain algebraic varieties over finite fields, we provide non-existence results for MRD codes $\mathcal{C}=\langle x^{q^t}, F(x), G(x) \rangle \subseteq \mathcal{L}_{n,q}$ of exceptional type, i.e. such that $\mathcal{C}$ is MRD over infinite many extensions of the field $\mathbb{F}_{q^n}$. These results partially address a conjecture of Bartoli, Zini and Zullo in 2023.

Scattered subspaces and $h$-scattered subspaces have been extensively studied in recent decades for both theoretical purposes and their connections to various applications. While numerous constructions of scattered subspaces exist, relatively few are known about $h$-scattered subspaces with $h\geq2$. In this paper, we establish the existence of maximum $2$-scattered $\F_q$-subspaces in $V(r,q^6)$ whenever $r\geq 3$, $r\ne 5$, and $q$ is an odd power of $2$. Additionally, we explore the corresponding MRD codes.

Over the past few decades, there has been extensive research on scattered subspaces, partly because of their link to MRD codes. These subspaces can be characterized using linearized polynomials over finite fields. Within this context, scattered sequences extend the concept of scattered polynomials and can be viewed as geometric equivalents of exceptional MRD codes. Up to now, only scattered sequences of orders one and two have been developed. However, this paper presents an infinite series of exceptional scattered sequences of any order beyond two which correspond to scattered subspaces that cannot be obtained as direct sum of scattered subspaces in smaller dimensions. The paper also addresses equivalence concerns within this framework., Comment: arXiv admin note: substantial text overlap with arXiv:2306.03448

Augmented reality for laparoscopic liver resection is a visualisation mode that allows a surgeon to localise tumours and vessels embedded within the liver by projecting them on top of a laparoscopic image. Preoperative 3D models extracted from CT or MRI data are registered to the intraoperative laparoscopic images during this process. In terms of 3D-2D fusion, most of the algorithms make use of anatomical landmarks to guide registration. These landmarks include the liver's inferior ridge, the falciform ligament, and the occluding contours. They are usually marked by hand in both the laparoscopic image and the 3D model, which is time-consuming and may contain errors if done by a non-experienced user. Therefore, there is a need to automate this process so that augmented reality can be used effectively in the operating room. We present the Preoperative-to-Intraoperative Laparoscopic Fusion Challenge (P2ILF), held during the Medical Imaging and Computer Assisted Interventions (MICCAI 2022) conference, which investigates the possibilities of detecting these landmarks automatically and using them in registration. The challenge was divided into two tasks: 1) A 2D and 3D landmark detection task and 2) a 3D-2D registration task. The teams were provided with training data consisting of 167 laparoscopic images and 9 preoperative 3D models from 9 patients, with the corresponding 2D and 3D landmark annotations. A total of 6 teams from 4 countries participated, whose proposed methods were evaluated on 16 images and two preoperative 3D models from two patients. All the teams proposed deep learning-based methods for the 2D and 3D landmark segmentation tasks and differentiable rendering-based methods for the registration task. Based on the experimental outcomes, we propose three key hypotheses that determine current limitations and future directions for research in this domain., Comment: 24 pages