Search Results (97)

Symmetry plays a fundamental role in the structural analysis of lattice-based systems, particularly in graphene-like molecular structures. In chemical graph theory, counting independent sets is equivalent to computing the Merrifield–Simmons (M–S) index, a key descriptor of molecular stability in conjugated systems. Most existing exact counting methods rely on regular lattice symmetry, where structural uniformity simplifies computation; however, these approaches are difficult to extend to irregular graphs, where symmetry breaking introduces non-local dependencies and increases computational complexity. This paper proposes an asymmetry-aware algorithmic framework based on Hamiltonian traversals and a traversal-induced pathwidth parameter $w\left(G\right)$, defined through backward dependencies. Our method organizes non-local adjacencies into a bounded set of structured constraints, enabling a dynamic programming scheme over a reduced state space. The resulting algorithm runs in time $\mathcal{O}\left(2^{w\left(G\right)}·\mathrm{poly}\left(n\right)\right)$ and is fixed-parameter tractable with respect to $w\left(G\right)$. The results demonstrate that asymmetry-aware traversal strategies enable efficient exact enumeration in irregular mesh graph families, providing a robust computational framework for analyzing molecular descriptors in graphene-based structures with topological defects such as Stone–Wales transformations. Full article

This study evaluates structure-preserving neural network architectures for learning holonomically constrained mechanical dynamics in Cartesian coordinates. In contrast to methods using reduced coordinates, the full ambient phase space ${\mathbb{R}}^{2n}$ is retained with explicit algebraic constraints $C_i\left(\mathbf{q}\right)=0$ to provide a test bed for constraint-aware learning. The Constraint-Aware Hamiltonian Neural Network (CA-HNN) is proposed, which augments the standard HNN with a dedicated multiplier network ${\lambda }_{\varphi }(\mathbf{q},\mathbf{p})$ for Lagrange multipliers and a composite loss function evaluated on predicted rollouts. The theoretical framework is grounded in the geometry of constrained Hamiltonian systems: the extended phase space ${\mathbb{R}}^{2n+m}$ carries a degenerate antisymmetric structure where an m-dimensional kernel encodes constraint directions, while the symplectic structure emerges on the $2(n-m)$-dimensional reduced manifold $\Sigma$. It is proven that the physical Hamiltonian is conserved on the constraint surface under augmented flow. Benchmarks on a pendulum ($C=x^2+y^2-l^2$), double pendulum, and bead on a parabola ($C=y-x^2$) demonstrate that CA-HNN reduces constraint violations $\parallel C\left(\mathbf{q}\right)\parallel$ by $5\times$ to $2400\times$ compared to standard HNNs. While the best energy conservation is achieved by PINNs, these findings clarify the roles of architectural inductive bias, constraint augmentation, and soft physics regularization. Full article

Real-world autonomous agents learn under nonstationarity, safety constraints, and finite energetic budgets. We develop a framework for perennial learning—agents that continuously refine their models while provably controlling the cost of forgetting—by unifying three classical pillars: Kolmogorov complexity, which equates scientific discovery with algorithmic compression; Landauer’s principle, which assigns a minimal thermodynamic cost of $k_{\mathrm{B}}Tln2$ per erased bit to every irreversible model update; and port-Hamiltonian (PH) dynamics, whose $(J-R)\nabla H$ decomposition separates zero-cost reversible inference from costly irreversible forgetting by construction. The Maxwell demon analogy is formalized: each learning episode is a Szilard cycle in which information acquisition, belief transport, and memory erasure must balance thermodynamically. The information-distance framework, comprising the normalized information distance (NID) and normalized compression distance (NCD), provides a computable geometry for measuring learning progress and guiding curriculum design. We separate theideal uncomputable regularizer based on prefix complexity from the practical compressor/MDL (minimum description length) surrogate that appears in optimization and prove a calibration lemma linking the two under a mild uniform-accuracy assumption. Under explicit regularity, compact-sublevel, and non-energy-extracting assumptions, we prove a passivity speed limit for curriculum-induced contractions of the effective feasible set. Under local asymptotic normality, we reprove that Fisher information is a local posterior codelength proxy rather than an exact theorem about algorithmic entropy. A conditional sequential information-budget proposition shows that the per-stage sample requirement scales as $\tilde{O}(\Delta k_t/{\lambda }_{\star })$, where $\Delta k_t$ is the number of materially changed model coordinates (not the total model complexity $k_t$); the $k^3\to \Delta k$ improvement is conditional on a warm-start assumption and a chosen cold-start baseline. A double-integrator running example with a moving obstacle illustrates the architecture. Full article

With the increasing penetration of renewable energy, power systems are facing stronger frequency fluctuations, which make fast and flexible frequency support increasingly important. Although vehicle-to-grid (V2G) technology provides a promising source of distributed regulation capacity, many existing studies do not explicitly consider EV owners’ participation, which may lead to a mismatch between theoretical regulation potential and practically available V2G support. To address this issue, this paper proposes a distributed Grid–Aggregator–EV frequency-regulation (FR) framework that incorporates EV participation factor into the control design. A three-layer architecture and a dynamic participation-aware model are established to describe the coordination of distributed V2G resources, and a Hamiltonian-based robust control law is developed under V2G power constraints. An integral reinforcement learning scheme is then adopted to realize the optimal regulation policy online, where the controller does not require explicit online knowledge of the system drift matrix, while preserving the physical control structure. In this way, the proposed method explicitly links the EV participation factor, dispatchable V2G regulation capacity, and coordinated FR, thereby improving robustness, adaptability, and practical relevance. Simulation studies on the IEEE 14-bus and IEEE 39-bus systems, together with an evening-period, time-varying participation case, demonstrate that the proposed method provides more effective frequency-deviation suppression, better overall regulation performance, and stable operation under dynamic EV participation. Full article

The Effective Mode Approximation (EMA) is a verification-oriented framework for characterizing collective Hamiltonian dynamics in large continuous-variable (CV) quantum systems from experimentally accessible collective measurements. Rather than reconstructing a full mode-resolved Hamiltonian, EMA maps the observed dynamics onto a canonically normalized collective mode and tests whether summed quadrature trajectories are consistent with an effective harmonic description. We validate EMA using time-resolved homodyne sampling in Gaussian simulations of ring-coupled multi-qu-mode optical systems with $N=8,16,32,$ and 64 modes. One-tone and two-tone sinusoidal models, selected using the Akaike Information Criterion (AIC), recover a stable dominant collective frequency across system size and produce residuals that remain centred near zero. The results show that EMA can verify dominant collective behaviour with a fixed number of effective parameters even when full microscopic reconstruction is impractical. EMA is therefore best understood not as a full-state ansatz, but as a low-overhead tool for validating collective dynamics under realistic measurement constraints in scalable CV hardware. Full article

As modern power systems grow increasingly complex, there is a pressing need for stability analysis methods capable of handling nonlinear dynamics while providing physically meaningful and reliable stability indices. Port-Hamiltonian (PH) frameworks have emerged as strong candidates in this regard, offering inherently stable formulations, energy-consistent representations, and modular plug-and-play scalability. However, the practical deployment of PH-based stability analysis remains hindered by the absence of reliable, high-fidelity parameter identification methods that rely on sensor measurements to capture system dynamics while remaining compatible with PH model structures. This paper addresses that gap by proposing a comprehensive three-stage data-driven identification framework for PH modeling of synchronous generators—the central dynamic component of any power system. While the IEEE Standard 115 provides established procedures for transient parameter identification, it exhibits fundamental limitations when applied to PH modeling, including single-scenario identifiability constraints, noise-sensitive derivative-based formulations that amplify sensor measurement errors, and the inability to decouple generator-internal damping from grid contributions. The proposed framework resolves these limitations through multi-scenario excitation using sensor-acquired voltage and current signals, derivative-free state consistency optimization, and physics-based regularization that enforces PH structure preservation. Complete identification of eight key parameters (H, D, $X_d$, $X_q$, $X_d^{\prime }$, $X_q^{\prime }$, $T_{do}^{\prime }$, $T_{qo}^{\prime }$) is achieved with errors ranging from 1.26% to 9.10%, and validation confirms RMS rotor angle errors below 1.2° and speed errors below 0.15%, demonstrating suitability for transient stability analysis, passivity-based control design, and oscillation damping assessment. Full article

This paper presents a stochastic framework for the inverse identification of structural material degradation (SMD) in cantilever beams. The method combines the Karhunen–Loéve (KL) expansion for the efficient parameterisation of spatially varying material decay with experimental Frequency Response Function (FRF) data within a Bayesian inference scheme. This approach employs a low-dimensional spectral parameterisation via the KL expansion, which mitigates the curse of dimensionality inherent in element-wise model updating, and provides a full-field probabilistic description of SMD. A two-phase constraint strategy was developed to address the fundamental tension between physical plausibility and algorithmic stability of the inverse identification algorithm: (1) physical regularisation during identification stabilises the ill-posed inverse problem, and (2) post-convergence selective regularisation eliminates physically impossible stiffness enhancements (exceeding 1.1 × baseline) that arise from measurement and modelling uncertainties. This phased approach prevents the algorithm distortion that occurs when constraints are applied too stringently during iteration, while ensuring final results respect fundamental physical principles. The framework is experimentally validated on a steel cantilever beam with a symmetric open-edge cut. Laser vibrometry measurements under swept-sine excitation demonstrate successful localisation and quantification of SMD, with the 95% credible interval accurately capturing the damaged region after physical constraint application. The adaptive constraint strategy resolves the delicate balance between mathematical stability and physical plausibility in inverse identification. Full article

The Profitable Tour Problem is a well-known NP-hard optimization challenge central to tourism planning, aiming to maximize collected profit while minimizing travel costs. While classical heuristics provide approximate solutions, they often struggle with finding globally optimal routes. This paper explores the application of near-term quantum computing to this problem. We propose a framework based on the Variational Quantum Eigensolver to find high-quality solutions for the Profitable Tour Problem. The core of our contribution is a novel methodology for constructing a constraint-aware variational ansatz that directly encodes the problem’s hard constraints. This approach circumvents the need for large penalty terms in the Hamiltonian problem, which are often a source of optimization challenges. We validate our method through numerical simulations on a representative tourism scenario of up to 25 qubits. The results demonstrate the viability of the approach, achieving high solution accuracy consistent with brute-force enumeration for smaller instances. This work serves as a proof-of-concept for applying Variational Quantum Eigensolver to complex tourism optimization problems and provides a basis for future exploration on real quantum hardware. Full article

Establishing precise and reliable quadrotor dynamics model is crucial for safe and stable tracking control in obstacle environments. However, obtaining such models is challenging, as it requires precise inertia identification and accounting for complex aerodynamic effects, which handcrafted models struggle to do. To address this, this paper proposes a safety-critical control framework built on a Hamiltonian neural differential model (HDM). The HDM formulates the quadrotor dynamics under a Hamiltonian structure over the $\mathit{SE}\left(3\right)$ manifold, with explicitly optimizable inertia parameters and a neural network-approximated control input matrix. This yields a neural ordinary differential equation (ODE) that is solved numerically for state prediction, while all parameters are trained jointly from data via gradient descent. Unlike black-box models, the HDM incorporates physical priors—such as $\mathit{SE}\left(3\right)$ constraints and energy conservation—ensuring a physically plausible and interpretable dynamics representation. Furthermore, the HDM is reformulated into a control-affine form, enabling controller synthesis via control Lyapunov functions (CLFs) for stability and exponential control barrier functions (ECBFs) for rigorous safety guarantees. Simulations validate the framework’s effectiveness in achieving safe and stable tracking control. Full article

We compare three modern Bayesian approaches, Hamiltonian Monte Carlo (HMC), Variational Bayes (VB), and Integrated Nested Laplace Approximation (INLA), for two classic spatial econometric specifications: the spatial lag model and spatial error model. Our Monte Carlo experiments span a range of sample sizes and spatial neighborhood structures to assess accuracy and computational efficiency. Overall, posterior means exhibit minimal bias for most parameters, with precision improving as sample size grows. VB and INLA deliver substantial computational gains over HMC, with VB typically fastest at small and moderate samples and INLA showing excellent scalability at larger samples. However, INLA can be sensitive to dense spatial weight matrices, showing elevated bias and error dispersion for variance and some regression parameters. Two empirical illustrations underscore these findings: a municipal expenditure reaction function for Île-de-France and a hedonic price for housing in Ames, Iowa. Our results yield actionable guidance. HMC remains a gold standard for accuracy when computation permits; VB is a strong, scalable default; and INLA is attractive for large samples provided the weight matrix is not overly dense. These insights help practitioners select Bayesian tools aligned with data size, spatial neighborhood structure, and time constraints. Full article

In loop quantum gravity (LQG), states of the gravitational field are represented by labeled graphs called spin networks. Their dynamics can be described by a Hamiltonian constraint, which acts on the spin network states, modifying both spins and graphs. Fixed-graph approximations of the dynamics have been extensively studied, but its full graph-changing action so far remains elusive. The latter, alongside the solutions of its constraint, are arguably the missing features in canonical LQG to access phenomenology in all its richness. Here, we discuss a recently developed numerical tool that, for the first time, implements graph-changing dynamics via the Hamiltonian constraint. We explain how it is used to find new solutions to that constraint and to show that some quantum geometric observables behave differently than in the graph-preserving truncation. We also point out that these new numerical methods can find applications in other domains. Full article

Quantum energy teleportation (QET) has been proposed to overcome the restrictions of strong local passivity (SLP) and to facilitate energy transfer in quantum systems. Traditionally, QET has only been considered under strict constraints, including the requirements that the initial state be the ground state of an interacting Hamiltonian, that Alice’s measurement commute with the interaction terms, and that entanglement be present. These constraints have significantly limited the broader applicability of QET protocols. In this work, we demonstrate that SLP can arise beyond these conventional constraints, establishing the necessity of QET in a wider range of scenarios for local energy extraction. This leads to a more flexible and generalized framework for QET. Furthermore, we introduce the concept of a “local effective Hamiltonian,” which eliminates the need for optimization techniques in determining Bob’s optimal energy extraction in QET protocols. As an additional advantage, the amount of energy that can be extracted using our new protocol is amplified to be 7.2 times higher than that of the original protocol. These advancements enhance our understanding of QET and extend its broader applications to quantum technologies. To support our findings, we implement the protocol on quantum hardware, confirming its theoretical validity and experimental feasibility. Full article

We construct a family of self-adjoint operators on the prime numbers whose entries depend on pairwise arithmetic divergences, replacing geometric distance with number-theoretic dissimilarity. The resulting spectra encode how coherence propagates through the prime sequence and define an emergent arithmetic geometry. From these spectra we extract observables such as the heat trace, entropy, and eigenvalue growth, which reveal persistent spectral compression): eigenvalues grow sublinearly, entropy scales slowly, and the inferred dimension remains strictly below one. This rigidity appears across logarithmic, entropic, and fractal-type kernels, reflecting intrinsic arithmetic constraints. Analytically, we show that for the unnormalized Laplacian, the continuum limit of its squared Hamiltonian corresponds to the one-dimensional bi-Laplacian, whose heat trace follows a short-time scaling proportional to $t^{-1/4}$. Under the spectral dimension convention $d_s=-2d\log \Theta /d\log t$, this result produces $d_s=1/2$ directly from first principles, without fitting or external hypotheses. This value signifies maximal spectral compression and the absence of classical diffusion, indicating that arithmetic sparsity enforces a coherence-limited, non-Euclidean geometry linking spectral and number-theoretic structure. Full article

This work introduces non-Hermitian position-dependent mass Hamiltonians characterized by complex ladder operators and real, equidistant spectra. By imposing the Heisenberg–Weyl algebraic structure as a constraint, we derive the corresponding potentials, ladder operators, and eigenfunctions. The method provides a systematic procedure for constructing exactly solvable models for arbitrary mass profiles. Specific cases are illustrated for quadratic, cosinusoidal, and exponential mass functions. Full article

Aperiodic tessellations of polykite unitiles, such as hats and turtles, and the recently introduced hares, red squirrels, and gray squirrels, have attracted significant interest due to their structural and combinatorial properties. Our primary objective here is to learn how we could build a self-assembling polyhedron that would have an aperiodic tessellation of its surface using only a single type of polykite unitile. Such a structure would be analogous to some viral capsids that have been reported to have a quasicrystal configuration of capsomeres. We report on our use of a graph–theoretic approach to examine the adjacency and symmetry constraints of these unitiles in tessellations because by using graph theory rather than the usual geometric description of polykite unitiles, we are able (1) to identify which particular vertices and/or edges join one another in aperiodic tessellations; (2) to take advantage of being scale invariant; and (3) to use the deformability of shapes in moving from the plane to the sphere. We systematically classify their connectivity patterns and structural characteristics by utilizing Hamiltonian cycles of vertex degrees along the perimeters of the unitiles. In addition, we applied Blumeyer’s 2 × 2 classification framework to investigate the influence of chirality and periodicity, while Heesch numbers of corona structures provide further insights into tiling patterns. Furthermore, we analyzed the distribution of polykite unitiles with Voronoi tessellations and their Delaunay triangulations. The results of this study contribute to a better understanding of self-assembling structures with potential applications in biomimetic materials, nanotechnology, and synthetic biology. Full article