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This paper studies a multi-task control problem where multiple linear systems are to be regulated by a single non-linear controller. In particular, motivated by recent advances in multi-task learning and the design of brain-inspired architectures, we consider a neural controller with (smooth) ReLU activation function. The parameters of the controller are a connectivity matrix and a bias vector: although both parameters can be designed, the connectivity matrix is constant while the bias vector can be varied and is used to adapt the controller across different control tasks. The bias vector determines the equilibrium of the neural controller and, consequently, of its linearized dynamics. Our multi-task control strategy consists of designing the connectivity matrix and a set of bias vectors in a way that the linearized dynamics of the neural controller for the different bias vectors provide a good approximation of a set of desired controllers. We show that, by properly choosing the bias vector, the linearized dynamics of the neural controller can replicate the dynamics of any single, linear controller. Further, we design gradient-based algorithms to train the parameters of the neural controller, and we provide upper and lower bounds for the performance of our neural controller. Finally, we validate our results using different numerical examples., Comment: submitted to ECC25

We investigated magnetization, muon spin rotation ($\mu$SR), and $^{119}Sn$ M\"{o}ssbauer spectroscopy on Sn substituted $CuCr_{2-x}Sn_xS_4$ (x=0.03 and 0.08) spinel compounds. The magnetization and $\mu$SR results reveal similar additional low-temperature magnetic transitions around 80 K and 40 K as found for the undoped material, indicating a magnetic ground state deviating from a simple collinear ferromagnet. The observed changes in the M\"{o}ssbauer hyperfine spectra are less pronounced and are discussed in view of the different positions of the local probes $\mu^+$ and $^{119}Sn$ and their different magnetic coupling to the magnetic Cr lattice. Above 80 K, both $\mu$SR and M\"{o}ssbauer spectra show temperature-dependent inhomogeneous broadening either due to structural or charge disorder and changing spin dynamics that can be related to a precursor magnetic phase above the well-defined static low-temperature phase., Comment: 15 pages, 13 figures

Firing rate models are dynamical systems widely used in applied and theoretical neuroscience to describe local cortical dynamics in neuronal populations. By providing a macroscopic perspective of neuronal activity, these models are essential for investigating oscillatory phenomena, chaotic behavior, and associative memory processes. Despite their widespread use, the application of firing rate models to associative memory networks has received limited mathematical exploration, and most existing studies are focused on specific models. Conversely, well-established associative memory designs, such as Hopfield networks, lack key biologically-relevant features intrinsic to firing rate models, including positivity and interpretable synaptic matrices that reflect excitatory and inhibitory interactions. To address this gap, we propose a general framework that ensures the emergence of re-scaled memory patterns as stable equilibria in the firing rate dynamics. Furthermore, we analyze the conditions under which the memories are locally and globally asymptotically stable, providing insights into constructing biologically-plausible and robust systems for associative memory retrieval., Comment: 20 pages, 7 figures

The Hopfield model provides a mathematically idealized yet insightful framework for understanding the mechanisms of memory storage and retrieval in the human brain. This model has inspired four decades of extensive research on learning and retrieval dynamics, capacity estimates, and sequential transitions among memories. Notably, the role and impact of external inputs has been largely underexplored, from their effects on neural dynamics to how they facilitate effective memory retrieval. To bridge this gap, we propose a novel dynamical system framework in which the external input directly influences the neural synapses and shapes the energy landscape of the Hopfield model. This plasticity-based mechanism provides a clear energetic interpretation of the memory retrieval process and proves effective at correctly classifying highly mixed inputs. Furthermore, we integrate this model within the framework of modern Hopfield architectures, using this connection to elucidate how current and past information are combined during the retrieval process. Finally, we embed both the classic and the new model in an environment disrupted by noise and compare their robustness during memory retrieval., Comment: 24 pages, 15 figures

This paper investigates the existence of a separation principle between model identification and control design in the context of model predictive control. First, we elucidate that the separation principle holds asymptotically in the number of data in a Fisherian setting, and universally in a Bayesian setting. Then, by formulating model predictive control within a Gaussian regression framework, we describe how the Bayesian separation principle can be used to derive explicit, uncertainty-aware expressions for the control cost and optimal input sequence, thereby bridging direct and indirect data-driven approaches., Comment: 13 pages, 1 figure

In a recent paper, Mandelkern & Linzen (2024) - henceforth M&L - address the question of whether language models' (LMs) words refer. Their argument draws from the externalist tradition in philosophical semantics, which views reference as the capacity of words to "achieve 'word-to-world' connections". In the externalist framework, causally uninterrupted chains of usage, tracing every occurrence of a name back to its bearer, guarantee that, for example, 'Peano' refers to the individual Peano (Kripke 1980). This account is externalist both because words pick out referents 'out there' in the world, and because what determines reference are coordinated linguistic actions by members of a community, and not individual mental states. The "central question to ask", for M&L, is whether LMs too belong to human linguistic communities, such that words by LMs may also trace back causally to their bearers. Their answer is a cautious "yes": inputs to LMs are linguistic "forms with particular histories of referential use"; "those histories ground the referents of those forms"; any occurrence of 'Peano' in LM outputs is as causally connected to the individual Peano as any other occurrence of the same proper name in human speech or text; therefore, occurrences of 'Peano' in LM outputs refer to Peano. In this commentary, we first qualify M&L's claim as applying to a narrow class of natural language expressions. Thus qualified, their claim is valid, and we emphasise an additional motivation for that in Section 2. Next, we discuss the actual scope of their claim, and we suggest that the way they formulate it may lead to unwarranted generalisations about reference in LMs. Our critique is likewise applicable to other externalist accounts of LMs (e.g., Lederman & Mahowald 2024; Mollo & Milliere 2023). Lastly, we conclude with a comment on the status of LMs as members of human linguistic communities.

In this paper, we address the finite time synchronization of a network of dynamical systems with time-varying interactions modeled using temporal networks. We synchronize a few nodes initially using external control inputs. These nodes are termed as pinning nodes. The other nodes are synchronized by interacting with the pinning nodes and with each other. We first provide sufficient conditions for the network to be synchronized. Then we formulate an optimization problem to minimize the number of pinning nodes for synchronizing the entire network. Finally, we address the problem of maximizing the number of synchronized nodes when there are constraints on the number of nodes that could be pinned. We show that this problem belongs to the class of NP-hard problems and propose a greedy heuristic. We illustrate the results using numerical simulations., Comment: 7 pages and 3 figures. Submitted for American Control Conference 2024

The present study contributes to an increased understanding of pyro-convection phenomena by using a fire-atmosphere coupled simulation, and investigates in detail the large-scale meteorological conditions affecting Portugal during the occurrence of multiple mega-fires events on 15 October 2017. Two numerical simulations were performed using the MesoNH atmospheric model. The first simulation, was run for a large single domain (300 x 250 grid points) with a 15 km resolution. In the second one, the MesoNH was coupled to a fire propagation model (ForeFire) to study in detail the Quiaios's fire. To optimize both high resolution in the proximity of the fire region and computational efficiency, the simulation is set up using 3 nested domains (300 x 300 grid points) with horizontal resolution of 2000 m, 400 m, and 80 m respectively. The emission into the atmosphere of the heat and the water vapour fluxes caused by the evolving fire is managed by the ForeFire code. The fire spatio-temporal evolution is based on an assigned map, which follows what reported by public authorities. At the large scale, the simulation shows the evolution of the hurricane Ophelia, pointing out the influence of south/southwest winds on the rapid spread of active fires, as well as the subtropical moisture transport toward mainland Portugal in the early evening, when violent pyro-convective activity was observed in Central Portugal. The coupled simulation allowed to reproduce the formation of a PyroCu cloud inside the smoke plume. The convective updraughts caused by the fire led to the vertical transport of water vapour to higher levels and enhanced the development of a high-based cloud over a dry atmospheric layer within the smoke plume.

We consider the problem of short-term forecasting of surface wind speed probability distribution. Our approach consists in predicting the parameters of a given probability density function by training a neural network model whose loss function is the corresponding log-likelihood. We compare different possibilities among a set of distributions that have been previously considered in the context of modeling wind fluctuations. Our results rely on two wind datasets recorded respectively by M\'et\'eo-France in Corsica (South France) and by KNMI over the Netherlands. A first part of our work globally unveils the superiority of the so-called "Multifractal Rice" (M-Rice) distribution over alternative parametric models, showcasing its potential as a reliable tool for wind speed forecasting. This family ofdistributions relies on a random cascade model model for wind speeds along the same picture as fully developed turbulence. For all stations in both regions, it consistently provides better results regardless of the considered scoring rule or forecasting horizon. Our second findings demonstrate significant enhancements in forecasting accuracy when one incorporates wind speed data from proximate weather stations, in full agreement with former results for point-wise wind speed prediction. Moreover, we reveal that the incorporation of ERA5 reanalysis of 10 m wind data from neighboring grid points contributes to a substantial improvement mostly at longest time horizons ($h=6$ h). It turns out that accounting for pertinent explanatory factors, notably those related the spatial distribution and wind speed and direction, emerges as a more critical factor in enhancing accuracy than the choice of the "optimal" parametric distribution. We also find out that such explanatory factors mainly increases the resolution performances while it does not change the reliability contribution to the CRPS score., Comment: 31 pages, 10 figures, 15 tables, to appear in "Applied Energy" (Elsevier)

In this paper, we consider stable stochastic linear systems modeling whole-brain resting-state dynamics. We parametrize the state matrix of the system (effective connectivity) in terms of its steady-state covariance matrix (functional connectivity) and a skew-symmetric matrix $S$. We examine how the matrix $S$ influences some relevant dynamic properties of the system. Specifically, we show that a large $S$ enhances the degree of stability and excitability of the system, and makes the latter more responsive to high-frequency inputs., Comment: 6 pages, 5 figures, to appear in the proceedings of IEEE CDC 2023

This paper presents a novel approach for solving the pole placement and eigenstructure assignment problems through data-driven methods. By using open-loop data alone, the paper shows that it is possible to characterize the allowable eigenvector subspaces, as well as the set of feedback gains that solve the pole placement problem. Additionally, the paper proposes a closed-form expression for the feedback gain that solves the eigenstructure assignment problem. Finally, the paper discusses a series of optimization problems aimed at finding sparse feedback gains for the pole placement problem., Comment: 6 pages, submitted to CDC2023

Tellurium is a gyrotropic, p-type Weyl semiconductor with remarkable electronic, optical, and transport properties. It has been argued that some of these properties might stem from Weyl nodes at crossing points in the band structure, and their nontrivial topological textures. However, Weyl nodes in time-reversal invariant semiconductors are split up in energy, rather than in momentum, and located deep below (far above) the top (bottom) of the valence (conduction) band, challenging such an interpretation. Here, instead, we use a 4-band kp Hamiltonian for $p-$type tellurium to show how the k-dependent spin-orbit interaction mixes up the top two (Weyl node free) and bottom two (Weyl node containing) valence bands, generating a 3D hedgehog orbital magnetic texture at the uppermost valence band, accessible to transport already at the lowest doping. Hedgehog textures are important signatures of Weyl fermion physics in general and in the context of condensed matter physics arise form the carriers' wave packet rotation being locked to their propagation wavevector. For spatially dispersive media, such an induced hedgehog texture/carrier rotation stabilizes two novel, nonreciprocal and antisymmetric components to the Hall transport within different weak-localization (antilocalization) relaxation regimes: the anomalous and planar Hall effects, usually forbidden by time reversal symmetry. Our AC magnetotransport measurements on Sn-doped tellurium confirm the theoretical predictions and our work demonstrates how Weyl signatures generally appear in transport on enantiomorphic materials with natural optical activity., Comment: 12 pages and 8 figures

Dislocation nucleation in homogeneous crystals initially unfolds as a linear symmetry-breaking elastic instability. In the absence of explicit nucleation centers, such instability develops simultaneously all over the crystal and due to the dominance of long range elastic interactions it advances into the nonlinear stage as a collective phenomenon through pattern formation. In this paper we use a novel mesoscopic tensorial model (MTM) of crystal plasticity to study the delicate role of crystallographic symmetry in the development of the dislocation nucleation patterns in defect free crystals loaded in a hard device. The model is formulated in 2D and we systematically compare lattices with square and triangular symmetry. To avoid the prevalence of the conventional plastic mechanisms, we consider the loading paths represented by pure shears applied on the boundary of the otherwise unloaded body. These loading protocols can be qualified as exploiting the 'softest' and the 'hardest' directions and we show that the associated dislocation patterns are strikingly different.

Mie theory is a powerful method to model electromagnetic scattering from a multilayered sphere. Usually, the incident beam is expanded to its vector spherical harmonic representation defined by beam shape coefficients, and the multilayer sphere scattering is obtained by the T-matrix method. However, obtaining the beam shape coefficients for arbitrarily shaped incident beams has limitations on source locations and requires different methods when the incident beam is defined inside or outside the computational domain or at the scatterer surface. We propose a 3D angular spectrum method for defining beam shape coefficients from arbitrary source field distributions. This method enables the placement of the sources freely within the computational domain without singularities, allowing flexibility in beam design. We demonstrate incident field synthesis and spherical scattering by comparing morphology-dependent resonances to known values, achieving excellent matching and high accuracy. Additionally, we present mathematical proof to support our proposal. The proposed method has significant benefits for optical systems and inverse beam design. It allows for the analysis of electromagnetic forward/backward propagation between optical elements and spherical targets using a single method. It is also valuable for optical force beam design and analysis.

The middle infrared (MIR) channel of the Atmospheric Chemistry Suite (ACS) instrument onboard the ExoMars Trace Gas Orbiter (TGO) ESA-Roscosmos mission has performed Solar occultation measurements of the Martian atmosphere in the 2.3-4.2 $\mu$m spectral range since March 2018, which now covers two Martian Years (MY). We use the methodology previously developed for the study of the MY 34 Global Dust Storm (GDS) (Stcherbinine et al., 2020) to monitor the properties (effective radii, extinction, altitude) of the Martian water ice clouds over the first two Martian years covered by ACS-MIR. The observations encompass the period $L_s$ = 163{\deg} in MY 34 to $L_s$ = 181{\deg} in MY 36. We determine that the typical altitude of the clouds varies by 20 to 40 km between the summer and winter, with a maximum extension up to 80 km during summer in the midlatitudes. Similarly, we also note that for a limited temporal range, the altitude of the clouds also varies by 20 to 40 km between the polar regions and the midlatitudes. We also compare observations acquired during the MY 34 GDS to observations from the same period in MY 35, using that latter as a reference to characterize the effects of this GDS on the clouds' properties. In addition, we compare our retrievals with the predictions of the Mars Planetary Climate Model (PCM), which shows a reasonable agreement overall for the altitude of the clouds, although the model usually predicts lower altitudes for the top of the clouds.

The feasibility of a 220 - 330 GHz zero order axicon generated Bessel beam for corneal water content was explored. Simulation and experimental data from the 25-degree cone angle hyperbolic-axicon lens illuminating metallic spherical targets demonstrate a monotonically decreasing, band integrated, backscatter intensity for increasing radius of curvature from 7 - 11 mm, when lens reflector and optical axis are aligned. Further, for radii >= 9.5 mm, maximum signal was obtained with a 1 mm transverse displacement between lens and reflector optical axes arising from spatial correlation between main lobe and out of phase side lobes. Thickness and permittivity parameter estimation experiments were performed on an 8 mm radius of curvature, 1 mm thick fused quartz dome over a 10 mm axial span. Extracted thickness and permittivity varied by less than ~ 25 $\mu$m and 0.2 respectively after correction for superluminal velocity. Estimated water permittivity and thickness of water backed gelatin phantoms showed significantly more variation due to a time varying radius of curvature., Comment: 11 pages; submitted to IEEE Transactions on Terahertz Science and Technology

In this work, we report the synthesis and investigation of structural, electronic, and magnetic properties of La$_{1.5}$Ca$_{0.5}$(Co$_{0.5}$Fe$_{0.5}$)IrO$_6$. Our polycrystalline sample forms as a single-phase double perovskite in monoclinic $P2_{1}/n$ space group. Co and Ir are most likely in bivalent and tetravalent oxidation states, respectively, while Mossbauer spectroscopy indicates that Fe is in a trivalent state. The ac and dc magnetization data suggest a ferrimagnetic behavior resulting from the presence of two antiferromagnetic sublattices at Co/Fe and Ir sites. The large coercive field H_C $\simeq$ 32 kOe observed at 10 K, comparable to that of other double perovskites of interest for hard magnets, is discussed in terms of the structural distortion and the spin and orbital magnetic moments of the transition metal ions., Comment: 15 pages, 5 figures

Plastic deformations in crystals often produce textures in the form of randomly oriented patches of the unstressed lattice. We use a novel mesoscopic Landau-type model of crystal plasticity to show that in such textures large crystallographic lattice rotations can originate from a highly coordinated inelastic slip at the microscale. Our numerical experiments show that dislocation avalanches, which lead to the formation of such rotations, involve pseudo-turbulent motions with power-law distributed spatial correlations.

Coupling to longitudinal modes of thin spherical shells, under Gaussian-beam illumination, was explored with a theoretical method based on Fourier-optics analysis and vector spherical harmonics. The illumination frequency band was fixed between 100-600 GHz and the outer spherical shell radius of curvature and thickness are 7.5 mm and 0.5 mm, respectively. The shell material was either the lossless cornea or an aqueous effective media representing the cornea. Six different beam-target strategies were introduced being potential candidates for maximum coupling. Two dispersion-tuned beam ensembles with strongly frequency-dependent phase center location have been created with a fixed incident beam 1/e radius and radius of curvature called forward strategies. These computations of different alignments were continued with four beam ensembles of frequency-invariant phase center, constructed from fits to experimental data, oriented at four different axial locations with respect to the spherical shell center of curvature, they are called reverse strategies. Coupling efficiency for all strategies was calculated for different targets including PEC sphere, air-core, and PEC core covered by a cornea loss-free layer and cornea. All scattering strategies contrasted to scattering from equivalent planar targets as a reference with maximum coupling. The results show that, under an ideal calibration, forward strategies are a closer approximation to the plane-wave condition. However, target properties influence the coupling efficiency remarkably for instance the observed difference in cornea scattering is vanishingly small as dielectric loss limits walk-off loss. Furthermore, under perturbed calibration, the forward strategies showed less sensitivity., Comment: 21 pages, 12 figures