Search Results (69)

The physics of systems of quantum emitters in waveguide quantum electrodynamics is significantly influenced by the relation between their spatial separation and the wavelength of the emitted photons. If the distance that separates a pair of emitters meets specific resonance conditions, the photon amplitudes produced from decay may destructively interfere. In an infinite-waveguide setting, this effect gives rise to bound states in the continuum, where a photon remains confined between the emitters. In the case of a finite-length waveguide with periodic boundary conditions, there exist two such relevant distances for a given arrangement of the quantum emitters, leading to states in which a photon is confined to either the shorter or the longer path that connects the emitters. If the ratio of the shorter and the longer path is a rational number, these two kinds of resonant eigenstates are allowed to co-exist for the same Hamiltonian. In this paper, we investigate the existence of quasi-degenerate resonant doublets of a pair of identical emitters coupled to a linear waveguide mode. The states that form the doublet are searched among the ones in which a single excitation tends to remain bound to the emitters. We investigate the spectrum in a finite range around degeneracy points to check whether the doublet remains well separated from the closest eigenvalues in the spectrum. The identification of quasi-degenerate doublets opens the possibility to manipulate the emitters-waveguide system as an effectively two-level system in specific energy ranges, providing an innovative tool for quantum technology tasks. Full article

Reversible data hiding in encrypted point clouds presents unique challenges due to their unstructured geometry, absence of mesh connectivity, and high sensitivity to spatial perturbations. In this paper, we propose an efficient and secure reversible data hiding framework for encrypted point clouds, incorporating KD tree-based path planning, adaptive multi-MSB prediction, and a dual-model design. To establish a consistent spatial traversal order, a Hamiltonian path is constructed using a KD tree-accelerated nearest-neighbor algorithm. Guided by this path, a prediction-driven embedding strategy dynamically adjusts the number of most significant bits (MSBs) embedded per point, balancing capacity and reversibility while generating a label map that reflects local predictability. The label map is then compressed using Huffman coding to reduce the auxiliary overhead. For enhanced security and lossless recovery, the encrypted point cloud is divided into two complementary shares through a lightweight XOR-based (2, 2) secret sharing scheme. The Huffman tree and compressed label map are distributed across both encrypted shares, ensuring that neither share alone can reveal the original point cloud or the embedded message. Experimental evaluations on diverse 3D models demonstrate that the proposed method achieves near-optimal embedding rates, perfect reconstruction of the original model, and significant obfuscation of the geometric structure. These results confirm the practicality and robustness of the proposed framework for scenarios involving secure 3D point cloud transmission, storage, and sharing. Full article

We propose Observer-Linked Branching (OLB), a mathematically rigorous extension of quantum theory in which an observer’s cognitive commitment actively modulates collapse dynamics at macroscopic scales. The OLB framework rests on four axioms, employing a norm-preserving nonlinear Schrödinger evolution and Lüders-type projection triggered by crossing a cognitive commitment threshold. Our expanded formalism provides five main contributions: (1) deriving Lie symmetries of the observer–environment interaction Hamiltonian; (2) embedding OLB into the Consistent Histories and path-integral formalisms; (3) multi-agent network simulations demonstrating intentional synchronisation toward shared macroscopic outcomes; (4) detailed statistical power analyses predicting measurable biases (up to ~5%) in practical experiments involving traffic delays, quantum random number generators, and financial market sentiment; and (5) examining the conceptual, ethical, and neuromorphic implications of intent-driven reality selection. Full reproducibility is ensured via the provided code notebooks and raw data tables in the appendices. While the theoretical predictions are precisely formulated, empirical validation is ongoing, and no definitive field results are claimed at this stage. OLB thus offers a rigorous, norm-preserving and falsifiable framework to empirically test whether cognitive engagement modulates macroscopic quantum outcomes in ways consistent with—but extending—standard quantum predictions. Full article

The Bayesian network is a directed, acyclic graphical model that can offer a structured description for probabilistic dependencies among random variables. As powerful tools for classification tasks, Bayesian classifiers often require computing joint probability distributions, which can be computationally intractable due to potential full dependencies among feature variables. On the other hand, Naïve Bayes, which presumes zero dependencies among features, trades accuracy for efficiency and often comes with underperformance. As a result, non-zero dependency structures, such as trees, are often used as more feasible probabilistic graph approximations; in particular, Tree Augmented Naïve Bayes (TAN) has been demonstrated to outperform Naïve Bayes and has become a popular choice. For applications where a variable is strongly influenced by multiple other features, TAN has been further extended to the k-dependency Bayesian classifier (KDB), where one feature can depend on up to k other features (for a given $k\ge 2$). In such cases, however, the selection of the k parent features for each variable is often made through heuristic search methods (such as sorting), which do not guarantee an optimal approximation of network topology. In this paper, the novel notion of k-tree Augmented Naïve Bayes (k-TAN) is introduced to augment Naïve Bayesian classifiers with k-tree topology as an approximation of Bayesian networks. It is proved that, under the Kullback–Leibler divergence measurement, k-tree topology approximation of Bayesian classifiers loses the minimum information with the topology of a maximum spanning k-tree, where the edge weights of the graph are mutual information between random variables conditional upon the class label. In addition, while in general finding a maximum spanning k-tree is NP-hard for fixed $k\ge 2$, this work shows that the approximation problem can be solved in time $O\left(n^{k+1}\right)$ if the spanning k-tree also desires to retain a given Hamiltonian path in the graph. Therefore, this algorithm can be employed to ensure efficient approximation of Bayesian networks with k-tree augmented Naïve Bayesian classifiers of the guaranteed minimum loss of information. Full article

The path-integral re-formulation due to E. Gozzi, M. Regini, M. Reuter, and W. D. Thacker of Koopman and von Neumann’s original operator formulation of a classical Hamiltonian system on a symplectic manifold M is identified as a gauge slice of a one-dimensional Alexandrov–Kontsevich–Schwarz–Zaboronsky sigma model with target $T^{*}(T\left[1\right]M\times \mathbb{R}\left[1\right])$. Full article

This paper addresses the challenge of coordinating task allocation and generating collision-free trajectories for a fleet of mobile robots in dynamic environments. Our approach introduces an integrated framework comprising a centralized task allocation system and a distributed trajectory planner. The centralized task allocation system, employing a heuristic approach, aims to minimize the maximum spatial cost among the slowest robots. Tasks and trajectories are continuously refined using a distributed version of CHOMP (Covariant Hamiltonian Optimization for Motion Planning), tailored for multiple-wheeled mobile robots where the spatial costs are derived from a high-level global path planner. By employing this combined methodology, we are able to achieve near-optimal solutions and collision-free trajectories with computational performance for up to 50 robots within seconds. Full article

This study concerns Riemannian manifolds with two types of tangent vectors. Let it be given that there are two subspaces of a tangent space with the property that each tangent vector has a unique decomposition as the sum of a vector in one subspace and a vector in the other subspace. Then, these tangent spaces can be complexified in such a way that the theory of the modular operator applies and that the complexified subspaces are invariant for the modular automorphism group. Notions coming from Kubo–Mori theory are introduced. In particular, the admittance function and the inner product of the Kubo–Mori theory can be generalized to the present context. The parallel transport operators are complexified as well. Suitable basis vectors are introduced. The real and imaginary contributions to the connection coefficients are identified. A version of the fluctuation–dissipation theorem links the admittance function to the path dependence of the eigenvalues and eigenvectors of the Hamiltonian generator of the modular automorphism group. Full article

In this paper, we explore the connection between sensor networks and graph theory. Sensor networks represent distributed systems of interconnected devices that collect and transmit data, while graph theory provides a robust framework for modeling and analyzing complex networks. Specifically, we focus on vertex coloring, Eulerian paths, and Hamiltonian paths within the Delaunay graph associated with a sensor network. These concepts have critical applications in sensor networks, including connectivity analysis, efficient data collection, route optimization, task scheduling, and resource management. We derive theoretical results related to the chromatic number and the existence of Eulerian and Hamiltonian trails in the graph linked to the sensor network. Additionally, we complement this theoretical study with the implementation of several algorithmic procedures. A case study involving the monitoring of a sugarcane field, coupled with a computational analysis, demonstrates the performance and practical applicability of these algorithms in real-world scenarios. Full article

Let $G=(V,E)$ be a graph. The first Zagreb index of a graph G is defined as ${\sum }_{u\in V}{d}_G^2\left(u\right)$, where $d_G\left(u\right)$ is the degree of vertex u in G. A graph G is called Hamiltonian (resp. traceable) if G has a cycle (resp. path) containing all the vertices of G. Using two established inequalities, in this paper, we present sufficient conditions involving the first Zagreb index for Hamiltonian graphs and traceable graphs. We also present upper bounds for the first Zagreb index of a graph and characterize the graphs achieving the upper bounds. Full article

In a recent contribution, we identified possible points of contact between the asymptotically safe and canonical approaches to quantum gravity. The idea is to start from the reduced phase space (often called relational) formulation of canonical quantum gravity, which provides a reduced (or physical) Hamiltonian for the true (observable) degrees of freedom. The resulting reduced phase space is then canonically quantized, and one can construct the generating functional of time-ordered Wightman (i.e., Feynman) or Schwinger distributions, respectively, from the corresponding time-translation unitary group or contraction semigroup, respectively, as a path integral. For the unitary choice, that path integral can be rewritten in terms of the Lorentzian Einstein–Hilbert action plus observable matter action and a ghost action. The ghost action depends on the Hilbert space representation chosen for the canonical quantization and a reduction term that encodes the reduction of the full phase space to the phase space of observables. This path integral can then be treated with the methods of asymptotically safe quantum gravity in its Lorentzian version. We also exemplified the procedure using a concrete, minimalistic example, namely Einstein–Klein–Gordon theory, with as many neutral and massless scalar fields as there are spacetime dimensions. However, no explicit calculations were performed. In this paper, we fill in the missing steps. Particular care is needed due to the necessary switch to Lorentzian signature, which has a strong impact on the convergence of “heat” kernel time integrals in the heat kernel expansion of the trace involved in the Wetterich equation and which requires different cut-off functions than in the Euclidian version. As usual we truncate at relatively low order and derive and solve the resulting flow equations in that approximation. Full article

In this review work, we outline a conceptual path that, starting from the numerical investigation of the transition between weak chaos and strong chaos in Hamiltonian systems with many degrees of freedom, comes to highlight how, at the basis of equilibrium phase transitions, there must be major changes in the topology of submanifolds of the phase space of Hamiltonian systems that describe systems that exhibit phase transitions. In fact, the numerical investigation of Hamiltonian flows of a large number of degrees of freedom that undergo a thermodynamic phase transition has revealed peculiar dynamical signatures detected through the energy dependence of the largest Lyapunov exponent, that is, of the degree of chaoticity of the dynamics at the phase transition point. The geometrization of Hamiltonian flows in terms of geodesic flows on suitably defined Riemannian manifolds, used to explain the origin of deterministic chaos, combined with the investigation of the dynamical counterpart of phase transitions unveils peculiar geometrical changes of the mechanical manifolds in correspondence to the peculiar dynamical changes at the phase transition point. Then, it turns out that these peculiar geometrical changes are the effect of deeper topological changes of the configuration space hypersurfaces ${\sum }_v=V_N^{-1}\left(v\right)$ as well as of the manifolds ${\{M_v=V_N^{-1}((-\infty ,v]\left)\right\}}_v\in \mathbb{R}$ bounded by the ∑_v. In other words, denoting by vc the critical value of the average potential energy density at which the phase transition takes place, the members of the family ${\left\{{\sum }_v\right\}}_{v<v_c}$ are not diffeomorphic to those of the family ${\left\{{\sum }_v\right\}}_{v>v_c}$; additionally, the members of the family ${\left\{M_v\right\}}_{v>v_c}$ are not diffeomorphic to those of ${\left\{M_v\right\}}_{v>v_c}$. The topological theory of the deep origin of phase transitions allows a unifying framework to tackle phase transitions that may or may not be due to a symmetry-breaking phenomenon (that is, with or without an order parameter) and to finite/small N systems. Full article

Embedding cycles into a network topology is crucial for a network simulation. In particular, embedding Hamiltonian cycles is a major requirement for designing good interconnection networks. A graph G is called r-spanning cyclable if, for any r distinct vertices $v_1,v_2,\dots ,v_r$ of G, there exist r cycles $C_1,C_2,\dots ,C_r$ in G such that $v_i$ is on $C_i$ for every i, and every vertex of G is on exactly one cycle $C_i$. If $r=1$, this is the classical Hamiltonian problem. In this paper, we focus on the problem of embedding spanning disjoint cycles in bipartite k-ary n-cubes. Let $k\ge 4$ be even and $n\ge 2$. It is shown that the n-dimensional bipartite k-ary n-cube $Q_n^k$ is m-spanning cyclable with $m\le 2n-1$. Considering the degree of $Q_n^k$, the result is optimal. Full article

The meaning of the quantum minimum effective length that should distinguish the quantum nature of a gravitational field is investigated in the context of manifestly covariant quantum gravity theory (CQG-theory). In such a framework, the possible occurrence of a non-vanishing minimum length requires one to identify it necessarily with a 4-scalar proper length s.It is shown that the latter must be treated in a statistical way and associated with a lower bound in the error measurement of distance, namely to be identified with a standard deviation. In this reference, the existence of a minimum length is proven based on a canonical form of Heisenberg inequality that is peculiar to CQG-theory in predicting massive quantum gravitons with finite path-length trajectories. As a notable outcome, it is found that, apart from a numerical factor of $O\left(1\right)$, the invariant minimum length is realized by the Planck length, which, therefore, arises as a constitutive element of quantum gravity phenomenology. This theoretical result permits one to establish the intrinsic minimum-length character of CQG-theory, which emerges consistently with manifest covariance as one of its foundational properties and is rooted both on the mathematical structure of canonical Hamiltonian quantization, as well as on the logic underlying the Heisenberg uncertainty principle. Full article

In this work, we derived a new type model for spatial Hill’s system considering the created perturbation by the parameter effect of the continuation fractional potential. The new model is considered a reduced system from the restricted three-body problem under the same effect for describing Hill’s problem. We identified the associated Lagrangian and Hamiltonian functions of the new system, and used them to verify the existence of the new equations of motion. We also proved that the new model has different six valid solutions under different six symmetries transformations as well as the original solution, where the new model is an invariant under these transformations. The several symmetries of Hill’s model can extremely simplify the calculation and analysis of preparatory studies for the dynamical behavior of the system. Finally, we confirm that these symmetries also authorize us to explore the similarities and differences among many classes of paths that otherwise differ from the obtained trajectories by restricted three-body problem. Full article

The Sustainable Time-Dependent Cheapest Path Problem (STDCPP) entails locating a Hamiltonian path that covers all of the graph’s vertices at the lowest possible total sustainability cost. The issue is inspired by actual city logistics, where it is important to consider the opinions of diverse stakeholders in the light of sustainable urban mobility plans and service viability. To address this issue, this paper suggests a twofold contribution. First, we describe the Sustainable Time-Dependent Cheapest Path Problem and define the complex cost function, which, based on the multi-criteria decision-making approach, integrates the views of different stakeholders and sustainability elements into the route cost calculation. Second, we show that the modified problem satisfies the FIFO (First-In First-Out) property and demonstrate the applicability of the suggested approach on a real-life scenario where route sustainability is extracted from the traffic sign information system available in Flanders, Belgium. Full article