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In the present work, we analyzed theoretically and experimentally the nonlinear dynamics of a magnetic pendulum excited through the interactions of a strong neodymium magnet and two coils placed symmetrically around the zero angular position. The forces between the magnet and coils and generated torques acting on the pendulum are derived using the magnetic charges interaction model and an experimentally fitted model. System equilibrium points are obtained, and their stability is investigated. It is found that when the currents in two coils are negative, the shape of the mechanical potential is bistable. The bistable potential might be symmetric if the currents have the same values and asymmetric when they are different. Asymmetric bistable potential is observed when coil currents have different signs. However, in the case of positive coil currents, a symmetric tristable potential is detected when the currents are the same, and an asymmetric tristable potential takes place when the positive currents have different values. Considering the sinusoidal coil current signals, analytical calculations using the harmonic balance method and numerical simulations are carried out for this elect

RISC-V is emerging as a viable platform for automotive-grade embedded computing, with recent ISO 26262 ASIL-D certifications demonstrating readiness for safety-critical deployment in autonomous driving systems. However, functional safety in automotive systems is fundamentally a certification problem rather than a processor problem. The dominant costs arise from diagnostic coverage analysis, toolchain qualification, fault injection campaigns, safety-case generation, and compliance with ISO 26262, ISO 21448 (SOTIF), and ISO/SAE 21434. This paper analyzes the role of RISC-V in automotive functional safety, focusing on ISA openness, formal verifiability, custom extension control, debug transparency, and vendor-independent qualification. We examine autonomous driving safety requirements and map them to RISC-V architectural challenges such as lockstep execution, safety islands, mixed-criticality isolation, and secure debug. Rather than proposing a single algorithmic breakthrough, we present an analytical framework and research roadmap centered on certification economics as the primary optimization objective. We also discuss how selected ML methods, including LLM-assisted FMEDA generation

Biomedical applications of plasmonic nanoparticle conjugates need control over their optical properties modulated by surface coating with stabilizing or targeting molecules often attached to or embedded in the secondary functionalization shell, such as silica. Although current numerical techniques can simulate the plasmonic response of such structures, it is desirable in practice to have analytical models based on simple physical ideas that can be implemented without considerable computer resources. Here, we present two efficient analytical methods based on improved electrostatic approximation (IEA) and modal expansion method (MEM) combined with the dipole equivalence method (DEM). The last approach avoids additional electromagnetic simulations and provides a direct bridge between analytical IEA and MEM models for bare particles and those with multilayer shells. As simple as the original IEA and MEM, the developed analytical extensions provide accurate extinction and scattering spectra for coated particles compared to exact calculations by separation of variable method and COMSOL. The possibility and accuracy of analytical models are illustrated by extensive simulations for prolate

Scattering-type scanning near-field optical microscopy (s-SNOM) is a versatile technique in nanooptics, enabling local probing of optical responses beyond the diffraction limit from vis to THz frequencies. Its theoretical modeling based on tip-sample interactions typically relies on computationally intensive numerical methods or phenomenological models with empiric fitting parameters, complicating spectral analysis and interpretation. Developing a rigorous quantitative analytical model remains a significant challenge in near-field microscopy. Here, we introduce an accurate analytical solution for the prolate spheroid model of s-SNOM in the quasi-electrostatic limit. We validate our solution through comparisons with numerical simulations and experimental spectra. Due to its higher computational efficiency compared to numerical simulation and higher accuracy compared to phenomenological solutions, our solution for spheroid model facilitates spectrum prediction and interpretation for homogeneous bulk samples, enables systematic exploration of parameter effects, and supports data generation for machine learning applications. Furthermore, the generality of our approach allows straightfo

Nanomechanical sensors and their arrays have attracted significant attention for detecting, distinguishing, and identifying target analytes, especially complex mixtures of odors. In the static mode operation, sensing signals are obtained by a concen-tration-dependent sorption-induced mechanical strain/stress. Understanding of the dynamic responses is crucial for develop-ing practical artificial olfaction; however, the analytical formulations are still limited to single-component analytes. Here, we derive an analytical model of viscoelastic material-based static mode nanomechanical sensing for multi-component analytes by extending the theoretical model via solving differential equations. The present model can reduce the dynamic responses to the multi-component target analytes observed in the experimental signal responses. Moreover, the use of optimized fitting parameters extracted from pure vapors with viscoelastic parameters allows us to predict the concentration of each analyte in the multi-component system.

A unified analytical solution is presented for constructing the phase space near collinear libration points in the Circular Restricted Three-body Problem (CRTBP), encompassing Lissajous orbits and quasihalo orbits, their invariant manifolds, as well as transit and non-transit orbits. Traditional methods could only derive separate analytical solutions for the invariant manifolds of Lissajous orbits and halo orbits, falling short for the invariant manifolds of quasihalo orbits. By introducing a coupling coefficient η and a bifurcation equation, a unified series solution for these orbits is systematically developed using a coupling-induced bifurcation mechanism and Lindstedt-Poincaré method. Analyzing the third-order bifurcation equation reveals bifurcation conditions for halo orbits, quasihalo orbits, and their invariant manifolds. Furthermore, new families of periodic orbits similar to halo orbits are discovered, and non-periodic/quasi-periodic orbits, such as transit orbits and non-transit orbits, are found to undergo bifurcations. When η = 0, the series solution describes Lissajous orbits and their invariant manifolds, transit, and non-transit orbits. As η varies from zero to non-

Trusted Execution Environments (TEEs), such as Intel's Software Guard Extensions (SGX), are increasingly being adopted to address trust and compliance issues in the public cloud. Intel SGX's second generation (SGXv2) addresses many limitations of its predecessor (SGXv1), offering the potential for secure and efficient analytical cloud DBMSs. We assess this potential and conduct the first in-depth evaluation study of analytical query processing algorithms inside SGXv2. Our study reveals that, unlike SGXv1, state-of-the-art algorithms like radix joins and SIMD-based scans are a good starting point for achieving high-performance query processing inside SGXv2. However, subtle hardware and software differences still influence code execution inside SGX enclaves and cause substantial overheads. We investigate these differences and propose new optimizations to bring the performance inside enclaves on par with native code execution outside enclaves.

The purpose of this paper is to contribute towards the near-future privacy-preserving big data analytical healthcare platforms, capable of processing streamed or uploaded timeseries data or videos from patients. The experimental work includes a real-life knee rehabilitation video dataset capturing a set of exercises from simple and personalised to more general and challenging movements aimed for returning to sport. To convert video from mobile into privacy-preserving diagnostic timeseries data, we employed Google MediaPipe pose estimation. The developed proof-of-concept algorithms can augment knee exercise videos by overlaying the patient with stick figure elements while updating generated timeseries plot with knee angle estimation streamed as CSV file format. For patients and physiotherapists, video with side-to-side timeseries visually indicating potential issues such as excessive knee flexion or unstable knee movements or stick figure overlay errors is possible by setting a-priori knee-angle parameters. To address adherence to rehabilitation programme and quantify exercise sets and repetitions, our adaptive algorithm can correctly identify (91.67%-100%) of all exercises from sid

We develop an analytical synthesis that bridges data-driven Distributionally Robust Optimization (DRO) and Economic Decision Theory under Ambiguity (DTA). By reinterpreting standard regularization and DRO techniques as data-driven counterparts of ambiguity-averse decision models, we provide a unified framework that clarifies their intrinsic connections. Building on this synthesis, we propose a novel DRO approach that leverages a popular DTA model of smooth ambiguity-averse preferences together with tools from Bayesian nonparametric statistics. Our baseline framework employs Dirichlet Process (DP) posteriors, which naturally extend to heterogeneous data sources via Hierarchical Dirichlet Processes (HDPs), and can be further refined to induce outlier robustness through a procedure that selectively filters poorly-fitting observations during training. Theoretical performance guarantees and convergence results, together with extensive simulations and real-data experiments, illustrate the method's favorable performance in terms of prediction accuracy and stability.

In concentrated macromolecular dispersions, far-from-ideal intermolecular interactions determine the dispersion behaviors including phase transition, crystallization, and liquid-liquid phase separation. Here, we present a novel versatile capillary-cell design for analytical ultracentrifugation-sedimentation equilibrium (AUC-SE), ideal for studying samples at high concentrations. Current setups for such studies are difficult and unreliable to handle, leading to a low experimental success rate. The design presented here is easy to use, robust, and reusable for samples in both aqueous and organic solvents while requiring no special tools or chemical modification of AUC cells. The key and unique feature is the fabrication of liquid reservoirs directly on the bottom window of AUC cells, which can be easily realized by laser ablation or mechanical drilling. The channel length and optical path length are therefore tunable. The success rate for assembling this new cell is close to 100%. We demonstrate the practicality of this cell by studying: 1) the equation of state and second virial coefficients of concentrated gold nanoparticle dispersions in water and bovine serum albumin (BSA) as wel

Investigation of the mathematical requirements for a three dimensional geometrical object to qualify as a Gomboc (mono-monostatic) has resulted in the discovery of two specific, analytical Gomboc shapes. Analytical in that the function describing the Gomboc surface is infinitely differentiable. In this brief note, the analysis undertaken is summarized and the formulae for the two specific shapes provided.

The present report summarizes the main theory and implementation steps associated with SELENA (SEmi-anaLytical intEgrator for a luNar Artificial satellite), i.e. the semi-analytical propagator for lunar satellite orbits developed in the framework of the the R&T R-S20/BS-0005-062 CNES research activity in collaboration between the University of Padova (UniPd), and the Aristotle University of Thessaloniki (AUTH), both acting as contractors with CNES. A detailed account of the method, algorithms and symbolic manipulations employed in the derivation of the final theory are described in detail in this report: they invoke the use of canonical perturbation theory in the form of Lie series computed in `closed form', i.e., without expansions in the satellite's orbital eccentricity. These algorithms are provided in the form of a symbolic package accompanying the present report. The package contains symbolic algebra programs, as well as explicit data files containing the final Hamiltonian, equations of motion and transformations (i.e. the coefficients and exponents of each variable in each term) leading to the averaging of the short-periodic terms in the satellite's equations of motion.

Potential game is an emerging notion and framework for studying N-player games, especially with heterogeneous players. In this paper, we build an analytical framework for dynamic potential games. We prove that a game is a dynamic potential game if and only if each player's value function can be decomposed as a potential function and a residual term which is solely dependent on other players' policies. This decomposition is consistent with the result in the static setting and enables us to identify and analyze an important and new class of dynamic potential games called the distributed game. Moreover, we prove that a game is a dynamic potential game if the value function has a symmetric Jacobian. This generalizes the differential characterization for static potential games by replacing the classical derivative with a new notation of functional derivative with respect to Markov policies. For a general class of continuous-time stochastic games, we explicitly characterize their potential functions. In particular, we show that the potential function of linear-quadratic games can be studied through a system of linear ODEs. Furthermore, under a rank condition on control coefficients, we p

We address a novel method for analytical determinations that combines simplicity, rapidity, low consumption of chemicals, and portability with high analytical performance taking into account parameters such as precision, linearity, robustness, and accuracy. This approach relies on the effect of the analyte content over the Gibbs free energy of dispersions, affecting the thermodynamic stabilization of emulsions or Winsor systems to form microemulsions (MEs). Such phenomenon was expressed by the minimum volume fraction of amphiphile required to form microemulsion, which was the analytical signal of the method. The performed studies were: phase behavior, droplet dimension by dynamic light scattering, analytical curve, and robustness tests. The reliability of the method was evaluated by determining water in ethanol fuels and monoethylene glycol in complex samples of liquefied natural gas. The dispersions were composed of water-chlorobenzene (water analysis) and water-oleic acid (monoethylene glycol analysis) with ethanol as the hydrotrope phase. The experiments to determine water demonstrated that the analytical performance depends on the composition of ME. The linear range was fairly

Analytical tools in business management are understood as a combination of information technologies and quantitative methods used to assist stakeholders to make better decisions. The contemporary business environment is dramatically changing by the massive accumulation of data. Now, as never before, the use of analytical tools must be expanded to take advantage of this growing digital universe. This article will apply the laddering technique to see how personal values (or managerial functions) influence a companys adoption of analytical tools. A set of ten in-depth interviews are conducted with CEOs, analytics consultants, academics and businessmen in order to establish quantitative relations among attributes, consequences and personal values. Two easy-to-read outputs are provided to interpret our results. The most important links are quantitatively associated through an implication matrix, and then visually represented on a hierarchical value map. Guidelines for improving the use of analytical tools are provided in the last section

We investigate the energy spectrum for hybrid mechanical systems described by non-parity-symmetric quantum Rabi models. A set of analytical solutions in terms of the confluent Heun functions and their analytical energy spectrum are obtained. The analytical energy spectrum includes regular and exceptional parts, which are both confirmed by direct numerical simulation. The regular part is determined by the zeros of the Wronskian for a pair of analytical solutions. The exceptional part is relevant to the isolated exact solutions and its energy eigenvalues are obtained by analyzing the truncation conditions for the confluent Heun functions. By analyzing the energy eigenvalues for exceptional points, we obtain the analytical conditions for the energy-level-crossings, which correspond to two-fold energy degeneracy.

The paper analyzes a general case of an equation of state, which is an analytical function at the critical point of the liquid-vapor first order phase transition of pure substance. It is shown that the equality to zero of the first- and second-order partial derivatives of pressure with respect to volume (density) at the critical point is the consequence of the thermodynamic conditions of phase equilibrium. We obtained the relations of critical exponents and amplitudes with parameters of the analytical equation of state. It is shown that the substance with the analytical equation of state can have critical exponents of lattice gas which is equivalent to the two dimensional Ising model. It is shown that the analytical equation of state can take into account the density fluctuations.