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Modern vehicles have evolved from mechanical systems to complex and connected ones controlled by numerous digital computers interconnected through internal networks. While this development has improved their efficiency and safety, it also brings new potential risks, particularly cyber-attacks. Several studies have explored the security of vehicle dynamics against such threats. Among these dynamics, the vehicle's lateral dynamics are crucial for maintaining stability and control during turns and maneuvers, making them a key focus of research. However, only a few recent studies have specifically investigated the security of lateral dynamics. This paper explores the potential for zero dynamics attacks on the vehicle's lateral dynamics, where the attacker can remain undetected by leaving no trace on the system's outputs. Three scenarios are studied: when the output includes yaw rate, lateral acceleration, and their combination. These two critical measurements of a vehicle's lateral motion are accessible through the inertial measurement units (IMU) in every vehicle. For each scenario, the impact of zero dynamics attacks on system performance is analyzed and illustrated through simulations. Finally, the paper provides recommendations for securing vehicles' lateral dynamics against such attacks., Comment: Submitted to the 23rd European Control Conference (ECC)

We study matrix integrals of the form $$\int_{\mathrm{USp(2n)}}\prod_{j=1}^k\mathrm{tr}(U^j)^{a_j}\mathrm d U,$$ where $a_1,\ldots,a_r$ are natural numbers and integration is with respect to the Haar probability measure. We obtain a compact formula (the number of terms depends only on $\sum a_j$ and not on $n,k$) for the above integral in the non-Gaussian range $\sum_{j=1}^kja_j\le 4n+1$. This extends results of Diaconis-Shahshahani and Hughes-Rudnick who obtained a formula for the integral valid in the (Gaussian) range $\sum_{j=1}^kja_j\le n$ and $\sum_{j=1}^kja_j\le 2n+1$ respectively. We derive our formula using the connection between random symplectic matrices and hyperelliptic $L$-functions over finite fields, given by an equidistribution result of Katz and Sarnak, and an evaluation of a certain multiple character sum over the function field $\mathbb F_q(x)$. We apply our formula to study the linear statistics of eigenvalues of random unitary symplectic matrices in a narrow bandwidth sampling regime.

Let $M$ be chosen uniformly at random w.r.t. the Haar measure on the unitary group $U_n$, the unitary symplectic group $USp_{2n}$ or the orthogonal group $O_n$. Diaconis and Shashahani proved that the traces $\mathrm{tr}(M),\mathrm{tr}(M^2),\ldots,\mathrm{tr}(M^k)$ converge in distribution to independent normal random variables as $k$ is fixed and $n\to\infty$. Recently, Gorodetsky and Rodgers proved analogs for these results for matrices chosen from certain finite matrix groups. For example, let $M$ be chosen uniformly at random from $U_n(\mathbb{F}_q)$. They show that $\{\mathrm{tr}(M^i)\}_{i=1,p\nmid i}^{k}$ converge in distribution to independent uniform random variables in $\mathbb{F}_{q^2}$ as $k$ is fixed and $n\to\infty$. We prove analogs for these results over local fields. Let $\mathcal{F}$ be a local field with a ring of integers $\mathcal{O}$, a uniformizer $\pi$, and a residue field of odd characteristic. Let $\mathcal{K}/\mathcal{F}$ be an unramified extension of degree $2$ with a ring of integers $\mathcal{R}$. Let $M$ be chosen uniformly at random w.r.t. the Haar measure on the unitary group $U_n(\mathcal{O})$, and fix $k$. We prove that the traces of powers $\{\mathrm{tr}(M^i)\}_{i=1,p\nmid i}^k$ converge to independent uniform random variables on $\mathcal{R}$, as $n\to\infty$. We also consider the case where $k$ may tend to infinity with $n$. We show that for some constant $c$ (coming from the mod $\pi$ distribution), the total variation distance from independent uniform random variables on $\mathcal{R}$ is $o(1)$ as $n\to\infty$, as long as $k

Methyl cyanide is one of the simplest interstellar complex organic molecules, widely detected in young solar analogues, shocked regions, protoplanetary disks and comets. CH3CN can be considered a key species to explore the chemical connections between planet forming disks and comets. For such comparison to be meaningful kinetics data for the reactions leading to CH3CN formation and destruction must be updated. We focus on the destruction of methyl cyanide through collisions with He+. A combined experimental and theoretical methodology is employed to obtain cross sections (CSs) and branching ratios (BRs) as a function of collision energy, from which reaction rate coefficients $k(T)$ are calculated in the temperature range from 10 to 300 K. CSs and BRs are measured using a guided ion beam set-up. A theoretical treatment based on an analytical formulation of the potential energy surfaces (PESs) for the charge exchange process is developed. The method employs a Landau Zener model to obtain reaction probabilities at crossings between the entrance and exit PESs, and an adiabatic centrifugal sudden approximation to calculate CSs and k(T). Rates and BRs differ from those predicted from widely-used capture models. In particular, the rate coefficient at 10 K is estimated to be almost one order of magnitude smaller than what reported in the KIDA database. As for BRs, the charge exchange is completely dissociative and the most abundant fragments are HCCN+/CCNH+, HCNH+ and CH2+. Our results, combined with a revised chemical network for formation of CH3CN, support the hypothesis that methyl cyanide in protoplanetary disks could be mostly the product of gas-phase processes rather than grain chemistry, as currently proposed. These findings are expected to have implications in the comparison of the abundance ratios of N-bearing molecules observed in disks with cometary abundance ratios, Comment: 19 pages, 7 figures, full article

Since 2019, GRAVITY has provided direct observations of giant planets and brown dwarfs at separations of down to 95 mas from the host star. Some of these observations have provided the first direct confirmation of companions previously detected by indirect techniques (astrometry and radial velocities). We want to improve the observing strategy and data reduction in order to lower the inner working angle of GRAVITY in dual-field on-axis mode. We also want to determine the current limitations of the instrument when observing faint companions with separations in the 30-150 mas range. To improve the inner working angle, we propose a fiber off-pointing strategy during the observations to maximize the ratio of companion-light-to-star-light coupling in the science fiber. We also tested a lower-order model for speckles to decouple the companion light from the star light. We then evaluated the detection limits of GRAVITY using planet injection and retrieval in representative archival data. We compare our results to theoretical expectations. We validate our observing and data-reduction strategy with on-sky observations; first in the context of brown dwarf follow-up on the auxiliary telescopes with HD 984 B, and second with the first confirmation of a substellar candidate around the star Gaia DR3 2728129004119806464. With synthetic companion injection, we demonstrate that the instrument can detect companions down to a contrast of $8\times 10^{-4}$ ($\Delta \mathrm{K}= 7.7$ mag) at a separation of 35 mas, and a contrast of $3\times 10^{-5}$ ($\Delta \mathrm{K}= 11$ mag) at 100 mas from a bright primary (K<6.5), for 30 min exposure time. With its inner working angle and astrometric precision, GRAVITY has a unique reach in direct observation parameter space. This study demonstrates the promising synergies between GRAVITY and Gaia for the confirmation and characterization of substellar companions., Comment: 16 pages, 14 figures. Submitted to A&A

Flasque resolutions play an important role in understanding birational properties of algebraic tori. For instance, Colliot-Th\'{e}l\`{e}ne and Sansuc have used them to compute $R$-equivalence classes of algebraic tori. We extend this notion to a larger class of algebraic varieties, including homogeneous spaces. This leads to a lower bound on the number of $R$-equivalence classes of homogeneous spaces, which is a slightly stronger version of a theorem of Colliot-Th\'el\`ene and Kunyavskii., Comment: Comments are very welcome :)

Resource allocation and scheduling in multi-agent systems present challenges due to complex interactions and decentralization. This survey paper provides a comprehensive analysis of distributed algorithms for addressing the distributed resource allocation (DRA) problem over multi-agent systems. It covers a significant area of research at the intersection of optimization, multi-agent systems, and distributed consensus-based computing. The paper begins by presenting a mathematical formulation of the DRA problem, establishing a solid foundation for further exploration. Real-world applications of DRA in various domains are examined to underscore the importance of efficient resource allocation, and relevant distributed optimization formulations are presented. The survey then delves into existing solutions for DRA, encompassing linear, nonlinear, primal-based, and dual-formulation-based approaches. Furthermore, this paper evaluates the features and properties of DRA algorithms, addressing key aspects such as feasibility, convergence rate, and network reliability. The analysis of mathematical foundations, diverse applications, existing solutions, and algorithmic properties contributes to a broader comprehension of the challenges and potential solutions for this domain., Comment: Submitted to annual reviews in control

Methyl cyanide (CH$_3$CN) is one of the most abundant and widely spread interstellar complex organic molecules (iCOMs). Several studies found that, in hot corinos, methyl cyanide and methanol abundances are correlated suggesting a chemical link, often interpreted as a synthesis of them on the interstellar grain surfaces. In this article, we present a revised network of the reactions forming methyl cyanide in the gas-phase. We carried out an exhaustive review of the gas-phase CH$_3$CN formation routes, propose two new reactions and performed new quantum mechanics computations of several reactions. We found that 13 of the 15 reactions reported in the databases KIDA and UDfA have incorrect products and/or rate constants. The new corrected reaction network contains 10 reactions leading to methyl cyanide. We tested the relative importance of those reactions in forming CH$_3$CN using our astrochemical model. We confirm that the radiative association of CH${_3}{^+}$ and HCN, forming CH$_{3}$CNH$^{+}$, followed by the electron recombination of CH$_{3}$CNH$^{+}$, is the most important CH$_3$CN formation route in both cold and warm environments, notwithstanding that we significantly corrected the rate constants and products of both reactions. The two newly proposed reactions play an important role in warm environments. Finally, we found a very good agreement between the CH$_3$CN predicted abundances with those measured in cold ($\sim$10 K) and warm ($\sim$90 K) objects. Unexpectedly, we also found a chemical link between methanol and methyl cyanide via the CH$_{3}^{+}$ ion, which can explain the observed correlation between the CH$_3$OH and CH$_3$CN abundances measured in hot corinos., Comment: 24 pages, 19 figures, accepted in MNRAS

There is an existing exact algorithm that solves DC programming problems if one component of the DC function is polyhedral convex (Loehne, Wagner, 2017). Motivated by this, first, we consider two cutting-plane algorithms for generating an $\epsilon$-polyhedral underestimator of a convex function g. The algorithms start with a polyhedral underestimator of g and the epigraph of the current underestimator is intersected with either a single halfspace (Algorithm 1) or with possibly multiple halfspaces (Algorithm 2) in each iteration to obtain a better approximation. We prove the correctness and finiteness of both algorithms, establish the convergence rate of Algorithm 1, and show that after obtaining an $\epsilon$-polyhedral underestimator of the first component of a DC function, the algorithm from (Loehne, Wagner, 2017) can be applied to compute an $\epsilon$ solution of the DC programming problem without further computational effort. We then propose an algorithm (Algorithm 3) for solving DC programming problems by iteratively generating a (not necessarily $\epsilon$-) polyhedral underestimator of g. We prove that Algorithm 3 stops after finitely many iterations and it returns an $\epsilon$-solution to the DC programming problem. Moreover, the sequence $\{x_k\}_{k\geq 0} outputted by Algorithm 3 converges to a global minimizer of the DC problem when $\epsilon$ is set to zero. Computational results based on some test instances from the literature are provided.

We propose a distributed (single) target tracking scheme based on networked estimation and consensus algorithms over static sensor networks. The tracking part is based on linear time-difference-of-arrival (TDOA) measurement proposed in our previous works. This paper, in particular, develops delay-tolerant distributed filtering solutions over sparse data-transmission networks. We assume general arbitrary heterogeneous delays at different links. This may occur in many realistic large-scale applications where the data-sharing between different nodes is subject to latency due to communication-resource constraints or large spatially distributed sensor networks. The solution we propose in this work shows improved performance (verified by both theory and simulations) in such scenarios. Another privilege of such distributed schemes is the possibility to add localized fault-detection and isolation (FDI) strategies along with survivable graph-theoretic design, which opens many follow-up venues to this research. To our best knowledge no such delay-tolerant distributed linear algorithm is given in the existing distributed tracking literature., Comment: ICRoM22

The paper presents the algorithm of a code written for computing the cross section for a charge transfer process involving a neutral molecule and a monatomic ion. The entrance and exit potential energy surfaces, driving the collision dynamics, are computed employing the Improved Lennard-Jones function that accounts for the role of non-electrostatic forces, due to size repulsion plus dispersion and induction attraction. In addition, electrostatic components, affecting the entrance channels, are evaluated as sum of Coulomb contributions, determined by the He$^+$ ion interacting with the charge distribution on the molecular frame. The cross section is estimated by employing the Landau-Zener-St\"uckelberg approach. The code implemented has been employed in systems involving helium cation and a small organic molecule, such as methanol, dimethyl ether and methyl formate., Comment: 16 pages, 5 figures. Preprint version submitted to LNCS (Springer) ICCSA2022. The final authenticated version is available online at https://doi.org/10.1007/978-3-031-10592-0_24

In this work we characterize an initial van der Waals adduct in the potential energy surface of reaction between cyanoacetylene HC3N and the cyano radical. The geometry of the CN-HC3N adduct has been optimized through calculations employing ab initio methods. Results show that the energy of the adduct lays below the reactants. Additionally, a saddle point that connects the adduct to an important intermediate of the PES has been localized, with energy below the reactants. Calculations of the intermolecular potential have been performed and results show that the energy of the van der Waals adduct is higher than estimated with the ab initio methods., Comment: 13 pages, 5 figures. Preprint version submitted to LNCS (Springer) ICCSA2021