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We investigate the global hypoellipticity and global solvability of systems of left-invariant differential operators on compact Lie groups. Focusing on diagonal systems, we establish necessary and sufficient conditions for these global properties. Specifically, we show that global solvability is characterized by a Diophantine condition on the symbol of the system, while global hypoellipticity further requires that a set depending on the symbol to be finite. As an application, we provide a complete characterization of these properties for systems of vector fields defined on products of tori and spheres. Additionally, we present illustrative examples, including systems involving higher-order differential operators. Finally, we extend our analysis to triangular systems on compact Lie groups, introducing an additional condition related to the boundedness of the dimensions of the representations in these Lie groups.

A lattice implementation of the recently introduced center-symmetric Landau gauge is discussed and its predictions confronted with numerical Monte Carlo simulations. It is shown that the link average and the link correlators computed in that gauge are order parameters of the confinement-deconfinement transition at nonzero temperature. Strictly speaking, this requires a specific treatment of the Gribov copies that we discuss in detail. The numerical simulations comply with the theoretical predictions for the link average computed below and above the deconfinement temperature. Our results show that, within appropriately chosen gauges, one can construct local order parameters for center symmetry, as proxies for the non-local Polyakov loop., Comment: 28 pages, 8 figures

The lattice computation of the one-particle irreducible ghost-gluon Green function in the Landau gauge is revisited with a set of large gauge ensembles. The large statistical ensembles enable a precise determination of this Green function over a wide range of momenta, accessing its IR and UV properties with a control on the lattice effects., Comment: Contribution to the 41st International Symposium on Lattice Field Theory (LATTICE2024), 28 July - 3 August 2024, Liverpool, UK

This paper addresses the design and analysis of a multivariable gradient-based stochastic extremum-seeking control method for multi-input systems with arbitrary input delays. The approach accommodates systems with distinct time delays across input channels and achieves local exponential stability of the closed-loop system, guaranteeing convergence to a small neighborhood around the extremum point. By incorporating phase compensation for dither signals and a novel predictor-feedback mechanism with averaging-based estimates of the unknown gradient and Hessian, the proposed method overcomes traditional challenges associated with arbitrary, distinct input delays. Unlike previous work on deterministic multiparameter extremum-seeking with distinct input delays, this stability analysis is achieved without using backstepping transformations, simplifying the predictor design and enabling a more straightforward implementation. Specifically, the direct application of Artstein's reduction approach results in delay- and system-dimension-independent convergence rates, enhancing practical applicability. A numerical example illustrates the robust performance and advantages of the proposed delay-compensated stochastic extremum-seeking method., Comment: 8 pages, 8 figures

The problem of encoded quantum gate generation is studied in this paper. The idea is to consider a quantum system of higher dimension $n$ than the dimension $\bar n$ of the quantum gate to be synthesized. Given two orthonormal subsets $\mathbb{E} = \{e_1, e_2, \ldots, e_{\bar n}\}$ and $\mathbb F = \{f_1, f_2, \ldots, f_{\bar n}\}$ of $\mathbb{C}^n$, the problem of encoded quantum gate generation consists in obtaining an open loop control law defined in an interval $[0, T_f]$ in a way that all initial states $e_i$ are steered to $\exp(\jmath \phi) f_i, i=1,2, \ldots ,\bar n$ up to some desired precision and to some global phase $\phi \in \mathbb{R}$. This problem includes the classical (full) quantum gate generation problem, when $\bar n = n$, the state preparation problem, when $\bar n = 1$, and finally the encoded gate generation when $ 1 < \bar n < n$. Hence, three problems are unified here within a unique common approach. The \emph{Reference Input Generation Algorithm (RIGA)} is generalized in this work for considering the encoded gate generation problem for closed quantum systems. A suitable Lyapunov function is derived from the orthogonal projector on the support of the encoded gate. Three case-studies of physical interest indicate the potential interest of such numerical algorithm: two coupled transmon-qubits, a cavity mode coupled to a transmon-qubit, and a chain of $N$ qubits, including a large dimensional case for which $N=10$., Comment: unpublished

Despite being used for decades as stabilizers, amino acids (AAs) remain mysterious components of many medical and biological formulations. Hypotheses on their role vary ranging from hydrotropic to protein-specific effects (stabilization against misfolding). Here, we deduce that AAs possess a new and broad colloidal property by finding that stabilizing effect of the AAs is comparable on dispersion of various proteins, plasmid DNA, and non-biological nanoparticles. The interactions among colloidal particles in dispersion are carefully evaluated by the second osmotic virial coefficient (B_22) and the potential of mean force. We propose a theoretical framework that explains the stabilization as the effect of weakly interacting small molecules with patchy nanoscale colloids. We validate it through quantitative comparison with experimental data by comparing equilibrium dissociation constants for AA/proteins obtained either by fitting the B22 data with this theory or experimentally. We find excellent quantitative agreement (e.g. proline/lysozyme 1.18 and 2.28 M, respectively) and indeed that the interactions are very weak. The theory presented implies that (i) charged AAs will be effective only for proteins of opposite charge; (ii) short peptides composed of n AAs will be as or more effective than n separate AAs; (iii) any small molecule weakly interacting with nanoscale colloids that increases the solvation of the surface will have a stabilizing effect. The experimental evidences corroborate all three predictions. Much like the ionic strength of the solution is commonly reported, our results imply that the same should be done for the small molecules, as they also affect fundamentally colloidal properties. As an example, we show that AAs vary the cloud point of a lysozyme solution by as much as 4 K.

We present a monotonic numerical algorithm including time optimization for generating quantum gates for open systems. Such systems are assumed to be governed by Lindblad master equations for the density operators on a large Hilbert-space whereas the quantum gates are relative to a sub-space of small dimension. Starting from an initial seed of the control input, this algorithm consists in the repetition of the following two steps producing a new control input: (A) backwards integration of adjoint Lindblad-Master equations (in the Heisenberg-picture) from a set of final conditions encoding the quantum gate to generate; (B) forward integration of Lindblad-Master equations in closed-loop where a Lyapunov based control produced the new control input. The numerical stability is ensured by the stability of both the open-loop adjoint backward system and the forward closed-loop system. A clock-control input can be added to the usual control input. The obtained monotonic algorithm allows then to optimise not only the shape of the control imput, but also the gate time. Preliminary numerical implementations indicate that this algorithm is well suited for cat-qubit gates, where Hilbert-space dimensions (2 for the Z-gate and 4 for the CNOT-gate) are much smaller than the dimension of the physical Hilbert-space involving mainly Fock-states (typically 20 or larger for a single cat-qubit). This monotonic algorithm, based on Lyapunov control techniques, is shown to have a straightforward interpretation in terms of optimal control: its stationary conditions coincides with the first-order optimality conditions for a cost depending linearly on the final values of the quantum states., Comment: Submitted, 4 figures

Modern big data workflows are characterized by computationally intensive kernels. The simulated results are often combined with knowledge extracted from AI models to ultimately support decision-making. These energy-hungry workflows are increasingly executed in data centers with energy-efficient hardware accelerators since FPGAs are well-suited for this task due to their inherent parallelism. We present the H2020 project EVEREST, which has developed a system development kit (SDK) to simplify the creation of FPGA-accelerated kernels and manage the execution at runtime through a virtualization environment. This paper describes the main components of the EVEREST SDK and the benefits that can be achieved in our use cases., Comment: Accepted for presentation at DATE 2024 (multi-partner project session)

A lattice QCD calculation for the four gluon one-particle irreducible Green function in the Landau gauge is discussed. Results for some of the associated form factors are reported for kinematical configurations with a single momentum scale. Our results show that the computation of this Green function requires large statistical ensembles with 10K or larger number of gauge configurations. The simulations considered herein have a clear Monte Carlo signal for momenta up to $\sim 1$ GeV. The form factors show an hierarchy, with the form factor associated with the tree level Feynman rule being dominant and essentially constant for the range of momenta accessed. The remaining form factors seem to increase as the momentum decreases, suggesting that a possible $\log$ divergence may occur. The computed form factors are, at least, in qualitative agreement with the results obtained with continuum approaches to this vertex, when available.

In addition to its connection with a standard confinement criterion, the Kugo-Ojima function constitutes an indispensable component in a multitude of applications in the gauge sector of QCD. In the present work we report on preliminary results of an ongoing large-volume lattice simulation of this special function. In particular, the volume-dependence of the data is studied in detail, and a comparison with results obtained from Schwinger-Dyson equations is carried out., Comment: 7 pages, 5 figures, Lattice 2023 proceedings

In this paper we are concerned with determining lower bounds of the number of limit cycles for piecewise polynomial holomorphic systems with a straight line of discontinuity. We approach this problem with different points of view: study of the number of zeros of the first and second order averaging functions, or with the control of the limit cycles appearing from a monodromic equilibrium point via a degenerated Andronov-Hoph type bifurcation, adding at the very end the sliding effects. We also use the Poincar\'e-Miranda theorem for obtaining an explicit piecewise linear holomorphic systems with 3 limit cycles, result that improves the known examples in the literature that had a single limit cycle.

The temperature dependence of the Landau gauge ghost propagator is investigated in pure SU(3) Yang-Mills theory with lattice QCD simulations. Its behavior around the confined-deconfined phase transition temperature, $T_c \sim 270$ MeV, is investigated. The simulations show that in the deconfined phase, the ghost propagator is enhanced for small momenta, $\lesssim 1$ GeV. Furthermore, the analysis of the spontaneous breaking of center symmetry on the ghost propagator is studied. Similarly as observed for the gluon propagator, the simulations result in a decoupling of the sectors where the phase of the Polyakov loop is either 0 or $\pm 2\pi/3$ sectors, with the latter remaining indistinguishable. The results point to the possible use of the ghost propagator as an "order parameter" for the confined-deconfined phase transition.

The current amount of IoT devices and their limitations has come to serve as a motivation for malicious entities to take advantage of such devices and use them for their own gain. To protect against cyberattacks in IoT devices, Machine Learning techniques can be applied to Intrusion Detection Systems. Moreover, privacy related issues associated with centralized approaches can be mitigated through Federated Learning. This work proposes a Host-based Intrusion Detection Systems that leverages Federated Learning and Multi-Layer Perceptron neural networks to detected cyberattacks on IoT devices with high accuracy and enhancing data privacy protection., Comment: Paper accepted in 2023 IEEE 20th Consumer Communications & Networking Conference (CCNC)

Today digital revolution is having a dramatic impact on the pharmaceutical industry and the entire healthcare system. The implementation of machine learning, extreme-scale computer simulations, and big data analytics in the drug design and development process offers an excellent opportunity to lower the risk of investment and reduce the time to the patient. Within the LIGATE project, we aim to integrate, extend, and co-design best-in-class European components to design Computer-Aided Drug Design (CADD) solutions exploiting today's high-end supercomputers and tomorrow's Exascale resources, fostering European competitiveness in the field. The proposed LIGATE solution is a fully integrated workflow that enables to deliver the result of a virtual screening campaign for drug discovery with the highest speed along with the highest accuracy. The full automation of the solution and the possibility to run it on multiple supercomputing centers at once permit to run an extreme scale in silico drug discovery campaign in few days to respond promptly for example to a worldwide pandemic crisis., Comment: Paper Accepted to the 20th ACM International Conference on Computing Frontiers (CF'23)

In this paper, we are concerned with studying the existence of invariant complex manifolds of two-dimensional holomorphic systems. From the geometric singular perturbation theory we know that if a slow-fast system has associated a normally hyperbolic compact critical manifold, then there exists a smooth locally invariant manifold. However, this smooth manifold does not necessarily have a complex structure. Here, we provide conditions to guarantee the existence of one-dimensional invariant complex manifolds. Consequently, this allows us to establish that the centers, foci, and nodes of the reduced problem are persistent by singular perturbation. The tools used by us are the usual techniques of Fenichel and Briot-Bouquet Theories.