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Ovoids of the Klein quadric $Q^+(5,q)$ of $\mathrm{PG}(5,q)$ have been studied in the last 40 year, also because of their connection with spreads of $\mathrm{PG}(3,q)$ and hence translation planes. Beside the classical example given by a three dimensional elliptic quadric (corresponding to the regular spread of $\mathrm{PG}(3,q)$) many other classes of examples are known. First of all the other examples (beside the elliptic quadric) of ovoids of $Q(4,q)$ give also examples of ovoids of $Q^+(5,q)$. Another important class of ovoids of $Q^+(5,q)$ is given by the ones associated to a flock of a three dimensional quadratic cone. To every ovoid of $Q^+(5,q)$ two bivariate polynomials $f_1(x,y)$ and $f_2(x,y)$ can be associated. In this paper, we classify ovoids of $Q^+(5,q)$ such that $f_1(x,y)=y+g(x)$ and $\max\{deg(f_1),deg(f_2)\}<(\frac{1}{6.3}q)^{\frac{3}{13}}-1$, that is $f_1(x,y)$ and $f_2(x,y)$ have "low degree" compared with $q$., Comment: Submitted to Journal of Algebraic Combinatorics. arXiv admin note: substantial text overlap with arXiv:2203.14687

The Indy Autonomous Challenge (IAC) brought together for the first time in history nine autonomous racing teams competing at unprecedented speed and in head-to-head scenario, using independently developed software on open-wheel racecars. This paper presents the complete software architecture used by team TII EuroRacing (TII-ER), covering all the modules needed to avoid static obstacles, perform active overtakes and reach speeds above 75 m/s (270 km/h). In addition to the most common modules related to perception, planning, and control, we discuss the approaches used for vehicle dynamics modelling, simulation, telemetry, and safety. Overall results and the performance of each module are described, as well as the lessons learned during the first two events of the competition on oval tracks, where the team placed respectively second and third., Comment: Preprint: Accepted to Field Robotics "Opportunities and Challenges with Autonomous Racing" Special Issue

In recent years, several families of scattered polynomials have been investigated in the literature. However, most of them only exist in odd characteristic. In [B. Csajb\'ok, G. Marino and F. Zullo: New maximum scattered linear sets of the projective line, Finite Fields Appl. 54 (2018), 133-150; G. Marino, M. Montanucci and F. Zullo: MRD-codes arising from the trinomial $x^q+x^{q^3}+cx^{q^5}\in\mathbb{F}_{q^6}[x]$, Linear Algebra Appl. 591 (2020), 99-114], the authors proved that the trinomial $f_c(X)=X^{q}+X^{q^{3}}+cX^{q^{5}}$ of $\mathbb{F}_{q^6}[X]$ is scattered under the assumptions that $q$ is odd and $c^2+c=1$. They also explicitly observed that this is false when $q$ is even. In this paper, we provide a different set of conditions on $c$ for which this trinomial is scattered in the case of even $q$. Using tools of algebraic geometry in positive characteristic, we show that when $q$ is even and sufficiently large, there are roughly $q^3$ elements $c \in \mathbb{F}_{q^6}$ such that $f_{c}(X)$ is scattered. Also, we prove that the corresponding MRD-codes and $\mathbb{F}_q$-linear sets of $\mathrm{PG}(1,q^6)$ are not equivalent to the previously known ones.

Saturating sets are combinatorial objects in projective spaces over finite fields that have been intensively investigated in the last three decades. They are related to the so-called covering problem of codes in the Hamming metric. In this paper, we consider the recently introduced linear version of such sets, which is, in turn, related to the covering problem in the rank metric. The main questions in this context are how small the rank of a saturating linear set can be and how to construct saturating linear sets of small rank. Recently, Bonini, Borello, and Byrne provided a lower bound on the rank of saturating linear sets in a given projective space, which is shown to be tight in some cases. In this paper, we provide construction of saturating linear sets meeting the lower bound and we develop a link between the saturating property and the scatteredness of linear sets. The last part of the paper is devoted to show some parameters for which the bound is not tight., Comment: 26 pages

Necessary and sufficient conditions on $A,B\in \mathbb{F}_{q^3}^*$ for $f(X)=X^{q^2-q+1}+AX^{q^2}+BX$ being a permutation polynomial of $\mathbb{F}_{q^3}$ are investigated via a connection with algebraic varieties over finite fields.

Scattered sequences are a generalization of scattered polynomials. So far, only scattered sequences of order one and two have been constructed. In this paper an infinite family of scattered sequences of order three is obtained. Equivalence issues are also considered.

We prove that, if $q$ is large enough, the set of the $\mathbb{F}_{q^6}$-rational points of the Hermitian curve is a complete $(q+1)$-arc in $\mathrm{PG}(2,\mathbb{F}_{q^6})$, addressing an open case from a recent paper by Korchm\'aros, Sz\H{o}nyi and Nagy. An algebraic approach based on the investigation of some algebraic varieties attached to the arc is used.

The Surrogate Modeling Toolbox (SMT) is an open-source Python package that offers a collection of surrogate modeling methods, sampling techniques, and a set of sample problems. This paper presents SMT 2.0, a major new release of SMT that introduces significant upgrades and new features to the toolbox. This release adds the capability to handle mixed-variable surrogate models and hierarchical variables. These types of variables are becoming increasingly important in several surrogate modeling applications. SMT 2.0 also improves SMT by extending sampling methods, adding new surrogate models, and computing variance and kernel derivatives for Kriging. This release also includes new functions to handle noisy and use multifidelity data. To the best of our knowledge, SMT 2.0 is the first open-source surrogate library to propose surrogate models for hierarchical and mixed inputs. This open-source software is distributed under the New BSD license., Comment: 10.1016/j.advengsoft.2023.103571

In this paper we investigate the relationships between a multipreferential semantics for defeasible reasoning in knowledge representation and a multilayer neural network model. Weighted knowledge bases for a simple description logic with typicality are considered under a (many-valued) ``concept-wise" multipreference semantics. The semantics is used to provide a preferential interpretation of MultiLayer Perceptrons (MLPs). A model checking and an entailment based approach are exploited in the verification of conditional properties of MLPs., Comment: arXiv admin note: text overlap with arXiv:2106.00390

In this paper, the Ni Schottky barrier on GaN epilayer grown on free standing substrates has been characterized. First, transmission electrical microscopy (TEM) images and nanoscale electrical analysis by conductive atomic force microscopy (C-AFM) of the bare material allowed visualizing structural defects in the crystal, as well as local inhomogeneities of the current conduction. The forward current-voltage (I-V) characteristics of Ni/GaN vertical Schottky diodes fabricated on the epilayer gave average values of the Schottky barrier height of 0.79 eV and ideality factor of 1.14. A statistical analysis over a set of diodes, combined with temperature dependence measurements, confirmed the formation of an inhomogeneous Schottky barrier in this material. From a plot of FB versus n, an ideal homogeneous barrier close to 0.9 eV was estimated, similar to that extrapolated by capacitance-voltage (C-V) analysis. Local I-V curves, acquired by means of C-AFM, displayed the inhomogeneous distribution of the onset of current conduction, which in turn resembles the one observed in the macroscopic Schottky diodes. Finally, the reverse characteristic of the diodes fabricated in the defects-free region have been acquired at different temperature and its behaviour has been described by the thermionic field emission (TFE) model.

The Schwinger limit could be approached by focusing to its diffraction limit the light reflected by a plasma mirror irradiated by a multi-petawatt laser. We explore numerically the interaction between such intense light and matter. We find that the interaction with a relativistic counterpropagative electron beam would enable the exploration of the fully nonperturbative regime of strong-field quantum electrodynamics (SF-QED), while the interaction with an initially solid target leads to a profusion of SF-QED effects that retroact on the laser-plasma interaction. We observe in both scenarios the formation of relativistic attosecond electron-positron jets with very high densities., Comment: 7 pages, 3 figures

The aim of this work is to implement a simple freehand ultrasound (US) probe calibration technique. This will enable us to visualize US image data during surgical procedures using augmented reality. The performance of the system was evaluated with different experiments using two different pose estimation techniques. A near-millimeter accuracy can be achieved with the proposed approach. The developed system is cost-effective, simple and rapid with low calibration error

In Human-Robot Interaction (HRI) systems, a challenging task is sharing the representation of the operational environment, fusing symbolic knowledge and perceptions, between users and robots. With the existing HRI pipelines, users can teach the robots some concepts to increase their knowledge base. Unfortunately, the data coming from the users are usually not enough dense for building a consistent representation. Furthermore, the existing approaches are not able to incrementally build up their knowledge base, which is very important when robots have to deal with dynamic contexts. To this end, we propose an architecture to gather data from users and environments in long-runs of continual learning. We adopt Knowledge Graph Embedding techniques to generalize the acquired information with the goal of incrementally extending the robot's inner representation of the environment. We evaluate the performance of the overall continual learning architecture by measuring the capabilities of the robot of learning entities and relations coming from unknown contexts through a series of incremental learning sessions.

Tracking the 3D shape of a deforming object using only monocular 2D vision is a challenging problem. This is because one should (i) infer the 3D shape from a 2D image, which is a severely underconstrained problem, and (ii) implement the whole solution pipeline in real-time. The pipeline typically requires feature detection and matching, mismatch filtering, 3D shape inference and feature tracking algorithms. We propose ROBUSfT, a conventional pipeline based on a template containing the object's rest shape, texturemap and deformation law. ROBUSfT is ready-to-use, wide-baseline, capable of handling large deformations, fast up to 30 fps, free of training, and robust against partial occlusions and discontinuity in video frames. It outperforms the state-of-the-art methods in challenging datasets. ROBUSfT is implemented as a publicly available C++ library and we provide a tutorial on how to use it in https://github.com/mrshetab/ROBUSfT, Comment: This is the arXiv version of an article published in Image and Vision Computing. Please cite the accepted version: M. Shetab-Bushehri, M. Aranda, E. Ozgur, Y. Mezouar and Adrien Bartoli "ROBUSfT: Robust Real-Time Shape-from-Template, a C++ Library," in Image and Vision Computing, doi: 10.1016/j.imavis.2023.104867

We consider a multiple-input multiple-output (MIMO) channel in the presence of a reconfigurable intelligent surface (RIS). Specifically, our focus is on analyzing the spatial multiplexing gains in line-of-sight and low-scattering MIMO channels in the near field. We prove that the channel capacity is achieved by diagonalizing the end-to-end transmitter-RIS-receiver channel, and applying the water-filling power allocation to the ordered product of the singular values of the transmitter-RIS and RIS-receiver channels. The obtained capacity-achieving solution requires an RIS with a non-diagonal matrix of reflection coefficients. Under the assumption of nearly-passive RIS, i.e., no power amplification is needed at the RIS, the water-filling power allocation is necessary only at the transmitter. We refer to this design of RIS as a linear, nearly-passive, reconfigurable electromagnetic object (EMO). In addition, we introduce a closed-form and low-complexity design for RIS, whose matrix of reflection coefficients is diagonal with unit-modulus entries. The reflection coefficients are given by the product of two focusing functions: one steering the RIS-aided signal towards the mid-point of the MIMO transmitter and one steering the RIS-aided signal towards the mid-point of the MIMO receiver. We prove that this solution is exact in line-of-sight channels under the paraxial setup. With the aid of extensive numerical simulations in line-of-sight (free-space) channels, we show that the proposed approach offers performance (rate and degrees of freedom) close to that obtained by numerically solving non-convex optimization problems at a high computational complexity. Also, we show that it provides performance close to that achieved by the EMO (non-diagonal RIS) in most of the considered case studies., Comment: Submitted for publication

Extensible objects form a challenging case for NRSfM, owing to the lack of a sufficiently constrained extensible model of the point-cloud. We tackle the challenge by proposing 1) convex relaxations of the isometric model up to quasi-isometry, and 2) convex relaxations involving the equiareal deformation model, which preserves local area and has not been used in NRSfM. The equiareal model is appealing because it is physically plausible and widely applicable. However, it has two main difficulties: first, when used on its own, it is ambiguous, and second, it involves quartic, hence highly nonconvex, constraints. Our approach handles the first difficulty by mixing the equiareal with the isometric model and the second difficulty by new convex relaxations. We validate our methods on multiple real and synthetic data, including well-known benchmarks.

The concept of scattered polynomials is generalized to those of exceptional scattered sequences which are shown to be the natural algebraic counterpart of $\mathbb{F}_{q^n}$-linear MRD codes. The first infinite family in the first nontrivial case is also provided and equivalence issues are considered. As a byproduct, a new infinite family of MRD codes is obtained., Comment: 32 pages

Recently, there has been a growing interest for mixed-categorical meta-models based on Gaussian process (GP) surrogates. In this setting, several existing approaches use different strategies either by using continuous kernels (e.g., continuous relaxation and Gower distance based GP) or by using a direct estimation of the correlation matrix. In this paper, we present a kernel-based approach that extends continuous exponential kernels to handle mixed-categorical variables. The proposed kernel leads to a new GP surrogate that generalizes both the continuous relaxation and the Gower distance based GP models. We demonstrate, on both analytical and engineering problems, that our proposed GP model gives a higher likelihood and a smaller residual error than the other kernel-based state-of-the-art models. Our method is available in the open-source software SMT., Comment: Published in Neurocomputing. 10.1016/j.neucom.2023.126472

We show that for a plane imaged by an endoscope the specular isophotes are concentric circles on the scene plane, which appear as nested ellipses in the image. We show that these ellipses can be detected and used to estimate the plane's normal direction, forming a normal reconstruction method, which we validate on simulated data. In practice, the anatomical surfaces visible in endoscopic images are locally planar. We use our method to show that the surface normal can thus be reconstructed for each of the numerous specularities typically visible on moist tissues. We show results on laparoscopic and colonoscopic images., Comment: Paper accepted for publication in the IEEE International Symposium on Biomedical Imaging (ISBI)

In this paper, we consider the affine variety codes obtained evaluating the polynomials $by=a_kx^k+\dots+a_1x+a_0$, $b,a_i\in\mathbb{F}_{q^r}$, at the affine $\F_{q^r}$-rational points of the Norm-Trace curve. In particular, we investigate the weight distribution and the set of minimal codewords. Our approach, which uses tools of algebraic geometry, is based on the study of the absolutely irreducibility of certain algebraic varieties.

Minimal rank-metric codes or, equivalently, linear cutting blocking sets are characterized in terms of the second generalized rank weight, via their connection with evasiveness properties of the associated $q$-system. Using this result, we provide the first construction of a family of $\mathbb{F}_{q^m}$-linear MRD codes of length $2m$ that are not obtained as a direct sum of two smaller MRD codes. In addition, such a family has better parameters, since its codes possess generalized rank weights strictly larger than those of the previously known MRD codes. This shows that not all the MRD codes have the same generalized rank weights, in contrast to what happens in the Hamming metric setting., Comment: 31 pages; published in Annali di Matematica Pura ed Applicata

We give an effective solution to the regularized optimization problem $g (\boldsymbol{x}) + h (\boldsymbol{x})$, where $\boldsymbol{x}$ is constrained on the unit sphere $\Vert \boldsymbol{x} \Vert_2 = 1$. Here $g (\cdot)$ is a smooth cost with Lipschitz continuous gradient within the unit ball $\{\boldsymbol{x} : \Vert \boldsymbol{x} \Vert_2 \le 1 \}$ whereas $h (\cdot)$ is typically non-smooth but convex and absolutely homogeneous, \textit{e.g.,}~norm regularizers and their combinations. Our solution is based on the Riemannian proximal gradient, using an idea we call \textit{proxy step-size} -- a scalar variable which we prove is monotone with respect to the actual step-size within an interval. The proxy step-size exists ubiquitously for convex and absolutely homogeneous $h(\cdot)$, and decides the actual step-size and the tangent update in closed-form, thus the complete proximal gradient iteration. Based on these insights, we design a Riemannian proximal gradient method using the proxy step-size. We prove that our method converges to a critical point, guided by a line-search technique based on the $g(\cdot)$ cost only. The proposed method can be implemented in a couple of lines of code. We show its usefulness by applying nuclear norm, $\ell_1$ norm, and nuclear-spectral norm regularization to three classical computer vision problems. The improvements are consistent and backed by numerical experiments., Comment: 19 pages

Differential cryptanalysis famously uses statistical biases in the propagation of differences in a block cipher to attack the cipher. In this paper, we investigate the existence of more general statistical biases in the differences. To this end, we discuss the $c$-differential uniformity of S-boxes, which is a concept that was recently introduced in Ellingsen et. al. to measure certain statistical biases that could potentially be used in attacks similar to differential attacks. Firstly, we prove that a large class of potential candidates for S-boxes necessarily has large $c$-differential uniformity for all but at most $B$ choices of $c$, where $B$ is a constant independent of the size of the finite field $q$. This result implies that for a large class of functions, certain statistical differential biases are inevitable. In a second part, we discuss the practical possibility of designing a differential attack based on weaknesses of S-boxes related to their $c$-differential uniformity., Comment: 14 pages, 2 figures

Generalized Procrustes Analysis (GPA) is the problem of bringing multiple shapes into a common reference by estimating transformations. GPA has been extensively studied for the Euclidean and affine transformations. We introduce GPA with deformable transformations, which forms a much wider and difficult problem. We specifically study a class of transformations called the Linear Basis Warps (LBWs), which contains the affine transformation and most of the usual deformation models, such as the Thin-Plate Spline (TPS). GPA with deformations is a nonconvex underconstrained problem. We resolve the fundamental ambiguities of deformable GPA using two shape constraints requiring the eigenvalues of the shape covariance. These eigenvalues can be computed independently as a prior or posterior. We give a closed-form and optimal solution to deformable GPA based on an eigenvalue decomposition. This solution handles regularization, favoring smooth deformation fields. It requires the transformation model to satisfy a fundamental property of free-translations, which asserts that the model can implement any translation. We show that this property fortunately holds true for most common transformation models, including the affine and TPS models. For the other models, we give another closed-form solution to GPA, which agrees exactly with the first solution for models with free-translation. We give pseudo-code for computing our solution, leading to the proposed DefGPA method, which is fast, globally optimal and widely applicable. We validate our method and compare it to previous work on six diverse 2D and 3D datasets, with special care taken to choose the hyperparameters from cross-validation., Comment: Published on International journal of computer vision (IJCV) 2022

Scattered polynomials over finite fields attracted an increasing attention in the last years. One of the reasons is their deep connection with Maximum Rank Distance (MRD) codes. Known classification results for exceptional scattered polynomials, i.e. polynomials which are scattered over infinite field extensions, are limited to the cases where their index $\ell$ is small, or a prime number larger than the $q$-degree $k$ of the polynomial, or an integer smaller than the $k$ in the case where $k$ is a prime. In this paper we completely classify exceptional scattered polynomials when the maximum between $\ell$ and $k$ is odd, and give partial results when it is even, extending a result of Ferraguti and Micheli in 2021.

Ionic gating is a powerful technique for tuning the physical properties of a material via electric field-induced charge doping, but is prone to introduce extrinsic disorder and undesired electrochemical modifications in the gated material beyond pure electrostatics. Conversely, reversible, volatile and electrostatic modulation is pivotal in the reliable design and operation of novel device concepts enabled by the ultrahigh induced charge densities attainable via ionic gating. Here we demonstrate a simple and effective method to achieve reversible and volatile gating of surface-sensitive ultrathin niobium nitride films via controlled oxidation of their surface. The resulting niobium oxide encapsulation layer exhibits a capacitance comparable to that of non-encapsulated ionic transistors, withstands gate voltages beyond the electrochemical stability window of the gate electrolyte, and enables a fully-reversible tunability of both the normal-state resistivity and the superconducting transition temperature of the encapsulated films. Our approach should be transferable to other materials and device geometries where more standard encapsulation techniques are not readily applicable., Comment: Main text: 11 pages, 6 figures; Supplementary: 8 pages, 6 figures

Ovoids of the non-degenerate quadric Q(4,q) of PG(4,q) have been studied since the end of the '80s. They are rare objects and, beside the classical example given by an elliptic quadric, only three classes are known for q odd, one class for $q$ even, and a sporadic example for $\`iq=3^5. It is well known that to any ovoid of Q(4,q) a bivariate polynomial f(x,y) can be associated. In this paper we classify ovoids of Q(4,q) whose corresponding polynomial f(x,y) has 'low degree' compared with q, in particular deg(f)<(q/6.3)^(3/13)-1. Finally, as an application, {two classes} of permutation polynomials in characteristic 3 are obtained., Comment: Submitted to Combinatorica

The tensor rank of some Gabidulin codes of small dimension is investigated. In particular, we determine the tensor rank of any rank metric code equivalent to an $8$-dimensional $\mathbb{F}_q$-linear generalized Gabidulin code in $\mathbb{F}_{q}^{4\times4}$. This shows that such a code is never minimum tensor rank. In this way, we detect the first infinite family of Gabidulin codes which are not minimum tensor rank.

In this paper, we construct some piecewise defined functions, and study their $c$-differential uniformity. As a by-product, we improve upon several prior results. Further, we look at concatenations of functions with low differential uniformity and show several results. For example, we prove that given $\beta_i$ (a basis of $\mathbb{F}_{q^n}$ over $\mathbb{F}_q$), some functions $f_i$ of $c$-differential uniformities $\delta_i$, and $L_i$ (specific linearized polynomials defined in terms of $\beta_i$), $1\leq i\leq n$, then $F(x)=\sum_{i=1}^n\beta_i f_i(L_i(x))$ has $c$-differential uniformity equal to $\prod_{i=1}^n \delta_i$.