We develop the theory of p-Lie algebras of finite Morley rank. In particular, we obtain a quite complete characterization in the soluble case

Edge-AI deployment is bottlenecked by data-movement energy; pairing event-driven vision sensors with in-memory analog compute could lift that ceiling by orders of magnitude. Both technologies are individually mature; the framework distinguishing fabricated demonstrations from projected systems is missing. Of six application domains surveyed (robotics, autonomous vehicles, AR/VR, surveillance, medical imaging, IoT), half rest entirely on projection, and existing hardware sits at Technology Readiness Levels 2-5. This evidence-graded review applies a three-paradigm architectural taxonomy and benchmarks the gap against current digital neuromorphic alternatives. It identifies an end-to-end integrated DVS-memristor system as the field's open challenge, with testable accuracy and power targets.

The rapid expansion of the Internet of Things (IoT) has introduced millions of resource-constrained devices into critical infrastructures, consumer environments, and industrial systems. These devices rely on lightweight communication protocols such as MQTT to support low-power, intermittent, and bandwidth-limited operation. However, common TLS algorithms used to secure MQTT communications are vulnerable to quantum attacks made feasible by Shor's algorithm. As a result, IoT infrastructures must evaluate and adopt post-quantum cryptographic (PQC) methods capable of providing long-term resilience. This report investigates the implementation of PQC algorithms within an MQTT-based IoT networks using three Raspberry Pis. Specifically, it integrates the FALCON digital signature scheme, one of NIST's selected post-quantum signature algorithms, to maintain message authenticity and integrity across resource-constrained MQTT clients and brokers. By measuring system performance, the research characterizes the practical trade-offs of deploying lattice-based PQC on lightweight hardware.

Guitar nebula is a prime example of a class of bow-shock pulsar wind nebulae (PWNe), powered by a wind of a supersonically moving neutron star. Bow-shock PWNe can probe particle acceleration processes in relativistic pulsar winds, as well as the structure of the interstellar medium (ISM). We demonstrate that the Guitar is an exceptional object in a number of ways. First, particles escaping the PWN and forming the X-ray ``kinetic jet'' need to be accelerated to the energies corresponding to the maximal electric potential of the neutron star $η_\text{acc}\gtrsim 3/4$ : it is another example of the class of extreme accelerators. Second, exceptionally bright H$_α$ emission requires that the central pulsar PSR J2225+6535 passes through a dense, low ionization ISM region. Bright X-ray emission of the ``kinetic jet'' then also requires exceptionally high magnetic field, $\sim 100~μ$G. We hypothesize that Guitar passes through the one of long-predicted, narrow dense shells of an old supernova remnant, currently in the ``pressure-driven snowplow'' regime.

Spectral shape differences between photons produced in $π^0\toγ+γ$ and $π^0\toγ+A_D$ may provide a new avenue for dark photon searches. Assuming 70 $μ$m thick tungsten foils separated by 200 $μ$m and a 1 GeV proton beam, we developed a GEANT4 model to estimate photon production and detection including background. Our results demonstrate that multiple campaign runs with a 10-50 $μ$A beam could probe previously unexplored regions of parameter space in models where the dark photon has predominantly invisible decays. The results are highly model independent.

Tweezer arrays of polarizable objects are a promising platform for assembling quantum matter and building next-generation quantum sensors. Light-induced dipolar interactions have emerged as a method to couple their motion, thereby establishing a new paradigm for controlling collective mechanical degrees of freedom. Here, we extend these into the regime of Floquet-driven interactions, combined with the intrinsic nonreciprocity of optical forces. We demonstrate beamsplitter, single-, and two-mode squeezing operations, as well as signatures of a negative-mass-like oscillator arising from the nonreciprocity. Moreover, we show that a programmable combination of these operations enables continuous tuning of complex eigenfrequencies. These results establish a toolbox of quantum operations of nonreciprocal interactions that are essential for investigating non-Hermitian many-body physics and collective quantum optomechanics.

Idle animations are essential for virtual characters, as they convey realistic behaviour during inactive states. While automatic animation generation has been widely studied, limited attention has been given to idle motion due to the absence of dedicated training datasets. We introduce StayStill, a large-scale dataset of 3D idle animations comprising diverse motion types from 50 subjects, totalling approximately 6 hours of data. We also propose a standardised evaluation protocol for both numerical and user-based metrics as a first step towards a standardised evaluation process for future systems. To facilitate future research, we publicly release StayStill along with the evaluation code and a pre-trained baseline model that generates idle animations via transition concatenation. We believe that these contributions will enable future research on idle motion generation.

With the growing application of spatial predictive modeling in ecology, the question of how to appropriately evaluate the resulting maps has gained increasing attention. While there is consensus that map accuracy is ideally estimated using an independent probability sample of the prediction area, there is still no agreement on the most appropriate way to conduct an evaluation for the common case when such a sample is not available. Cross-validation, which involves multiple train-test splits, is commonly applied not only to estimate final model accuracy but also to guide model tuning and selection. Many different spatial and non-spatial approaches to cross-validation have been proposed, and approaches in both groups have faced substantial criticism. It has been shown that random cross-validation methods are suitable when the training points are randomly distributed in the prediction area, while spatial cross-validation is better suited towards extrapolation situations. In practice, however, there is a continuum and most cases are between those two extremes. To address this gap, we advocate for a new category of cross-validation methods to account for this: prediction-domain adaptive evaluation. Methods in this category flexibly adapt to the prediction situation, yielding most reliable estimates of map accuracy across different scenarios. To ground this perspective empirically, we reproduce a simulation study that was used in earlier research and systematically compare different evaluation methods and discuss their purpose.

Geometric phases are foundational to isolated quantum systems, yet their thermodynamic role in open systems remains unrevealed Developing a dissipative adiabatic perturbation expansion, we discover a Berry-phase-induced chiral work difference that survives decoherence. This chirality evolves from an interferometric thermodynamic Aharonov-Bohm effect in the unitary regime to a fringe-free signal in the dissipative regime. We illustrate this framework in a two-level system and assess its experimental feasibility. Our findings clarify the role of quantum geometry in the geometric formulation of thermodynamics.

Given a structure $\mathcal{M}$ with a definable topology, its open core is a structure defined on the same universe whose language consists of all open sets of all arities definable in $\mathcal{M}$. In response to questions raised by Dolich, Miller, and Steinhorn in their early work on open core, we prove that having an o-minimal open core is not an elementary property. In particular, we construct an expansion of the structure $(\mathbb{Q},<)$ that has an o-minimal open core, but some of its elementary superstructures do not.

Crack initiation and propagation are fundamental problems in materials science, often leading to catastrophic failure. While fracture in elastic solids occurs instantaneously above a critical load, viscoelastic materials may sustain high loads for a finite time before cracks start to propagate. This phenomenon, known as delayed fracture, has been widely observed experimentally but is still only partially understood theoretically. In this study, we present a rigorous framework based on the Lagrange--d'Alembert principle of virtual work (PVW) to predict both the viscoelastic delay time and the subsequent crack evolution under arbitrary loading histories. We derive how the delay time depends on the applied remote load and validate the theory through quantitative comparison with experiments, using directly measured delay times together with DMA-based viscoelastic characterization of the material. Very good agreement is obtained over a broad range of loading and delay times. Our results also show that crack propagation starts at finite speed and that load-dependent steady-state conditions are soon established. Finite element analyses further support the proposed framework and clarify the role of finite-ranged adhesion forces at fixed adhesion energy, showing that shorter interaction ranges yield results in quantitative agreement with theory. We also present, for the first time, a rigorous J-integral formulation valid for linear viscoelastic solids under arbitrary, time-varying loading histories. The result restores path independence and yields a generalized Griffith criterion that naturally predicts delayed fracture initiation in non-conservative materials. Remarkably, fracture initiation can be described without specifying the detailed stress distribution within the process zone, as long as it remains small relative to the crack length.

High-purity germanium (Ge) has re-emerged as a versatile semiconductor platform for spin-based quantum information processing because it combines mature materials processing, access to spin-free isotopes, high mobilities, small effective masses, and strong but engineerable spin--orbit coupling. However, ``Ge qubits'' are not a single technology. Donor spin qubits, acceptor spin qubits, gate-defined hole spin qubits, and gate-defined electron spin qubits exploit different parts of the Ge band structure and therefore make distinct trade-offs among coherence, controllability, fabrication complexity, and scalability. Here we compare these four Ge-based spin-qubit modalities on a common physical and architectural footing. We review the shared Ge materials physics, including isotopic purification, the multivalley \(L\)-point conduction band, the spin-\(3/2\) valence band, heavy-hole/light-hole mixing, strain, interfaces, disorder, and phonons. We also introduce a common framework for estimating phononic-crystal-modified \(T_1\) using a calibrated reference relaxation rate, a geometry-dependent strain-density-of-states suppression factor, and parasitic relaxation channels. The comparison shows that gate-defined Ge hole-spin qubits currently offer the strongest combination of all-electrical control, demonstrated multiqubit operation, and scalability. Donor, acceptor, and gate-defined electron qubits remain important complementary directions for memory, hybrid, and exploratory architectures. Overall, Ge supports a diverse qubit ecosystem, with gate-defined hole-spin qubits presently providing the clearest path toward scalable Ge-based quantum processors.

There has long been an apparent consensus in the literature on intra-household allocation and fertility that greater paternal involvement in childcare relaxes maternal time constraints, enabling mothers to increase their labor supply or leisure. Recent evidence, particularly from South Korea, challenges this view: increases in fathers' childcare time have coincided with a further increase in mothers' time dedicated to child-rearing. This paper develops an Overlapping Generations (OLG) growth model to address such a puzzle. The central mechanism and our main innovation hinge on the functional form of the childcare technology. When maternal and paternal time are substitutes, the conventional result holds. However, when they are complements, greater paternal involvement necessarily raises maternal childcare time, depressing fertility and redirecting household resources toward child quality. We further argue that the elasticity of substitution should not be interpreted as a pure preference parameter, as it also reflects the social and institutional norms, the skills each parent brings to child-rearing and their intergenerational transmission. The model is extended to study the effectiveness of pro-natalist subsidies, suggesting that such policies may generate an unintended anti-fertility bias. Numerical simulations calibrated loosely to South Korean data confirm that the model is consistent with the observed quantity-quality trade-off and the persistence of low fertility despite active pro-natalist policy.

Container runtimes provide a stable operational interface for deploying, monitoring, and controlling modern workloads, while trusted execution environments (TEEs) provide hardware-enforced isolation for sensitive computation. Existing confidential-container systems often rely on VM-backed deployment stacks or TEE-specific execution substrates, which can separate confidential execution from the conventional OCI runtime lifecycle. This paper presents EBCC (Enclave-Backed Confidential Containers), an OCI-compatible runtime architecture for managing composite confidential-computing workloads. EBCC treats the REE-side anchor and TEE-side confidential stages as a single containerized confidential-computing composite, preserves standard OCI lifecycle operations, and keeps TEE-specific execution behind a backend adapter. It also maintains persistent per-instance state and per-stage artifacts for request handling, response generation, logging, and evidence binding. We implement EBCC on a Keystone backend and evaluate its correctness, performance, footprint, and concurrent execution behavior. The results show that EBCC introduces additional latency over native Keystone execution, mainly due to lifecycle mediation, request validation, EID allocation, backend dispatch, and artifact persistence, while keeping the added footprint concentrated on host-side management state. Cross-TEE case studies on SGX, TDX, and OP-TEE show that the same lifecycle and stage abstraction can be mapped to enclave-style, VM-style, and embedded-style TEEs. These results indicate that EBCC can make TEE-backed execution manageable through an OCI-style lifecycle without materially enlarging the protected-side TCB.

Modeling turbulent flows by a random Fourier decomposition is a classical procedure in order to use simplified models of turbulence in heat transport and other applications. We carefully investigate the Fourier time series of two-dimensional turbulent flows forced at intermediate scales and identify significant statistical structures. In particular, we find the existence of a typical time correlation length, and propose a stochastic model for the Fourier components. Finally, we compute the transport of a passive tracer under purely convective dynamics by means of direct numerical simulation of the turbulent flow and compare it with the effective diffusion produced by the stochastic model.

Runtime verification enables checking temporal logic specifications over individual execution traces and offers a scalable alternative to exhaustive formal verification. In practice, systems must satisfy dozens to hundreds of temporal properties simultaneously; however, existing approaches monitor each property in isolation, resulting in redundant computation and limited scalability. In this work, we present an online multi-property monitoring framework that compiles past-time LTL and MTL specifications into a shared directed acyclic graph of subformulas with one output per property. Unlike prior approaches that construct monitors independently, our method extends compositional sequential network-based temporal logic monitor construction to a shared setting, enabling reuse of intermediate results across properties while preserving their individual structure. Central to our approach is a data-oriented execution model based on an arena-allocated, double-buffered layout that stores intermediate results for each subformula in compact, contiguous memory. This design favors spatial locality and enables incremental updates with minimal overhead. Experimental results demonstrate per-property throughput improvements of 2x to 4.5x and 6x to 12x in multi-property configurations compared to conventional single-property monitoring, enabling scalability to large specification sets and deployment in high-performance and resource-constrained systems.

Given a (possibly infinite) subset $A$ of the natural numbers, we ask how many times a fair six-sided die must be rolled until the rolled numbers add up to an element of $A$. Using a one-dimensional dynamic programming recursion together with truncation and rigorous error bounds, we compute the expected number of rolls efficiently and with very high accuracy. When $A$ is the set of prime numbers, the irregular distribution of primes makes it difficult to obtain explicit error estimates. Nevertheless, the density of primes implies that the associated survival probability decays exponentially fast, which enables highly accurate truncation estimates. As a result, our calculations yield significantly sharper estimates for this expectation and its higher moments than the original results of Conroy, Alon, and Malinovsky. In particular, we determine the expectation to more than $1000$ decimal places.

The distance-reduction property for a generating set, i.e., a Markov basis, of a toric ideal is a condition that ensures tight connectivity of its fibres. In this paper, we study the distance-reduction property for toric ideals of graphs and move on to explore the relationship between the distance-reduction property and the bouquet structure of homogeneous toric ideals, which includes the class of toric ideals of graphs. For toric ideals of graphs which are complete intersection, we show that the minimal Markov bases are distance-reducing if and only if they distance-reduce the circuits of the ideal. We then consider how the distance-reduction properties interact with the bouquet structure of the toric ideal. Bouquets are a combinatorial structure that capture the essential combinatorial information of the toric ideal. Under the condition of homogeneity, we show that, for toric ideals with the same bouquet structure and signature, the distance-reduction properties are preserved. For homogeneous toric ideals whose bouquet matrix is a monomial curve in $\mathbb{A}^3$, we give necessary and sufficient conditions for when the minimal Markov bases are distance-reducing.

Air-sea surface interactions play a critical role in underwater-to-air optical wireless communication (OWC) links, particularly in vertical autonomous underwater vehicle (AUV) to unmanned aerial vehicle (UAV) scenarios, where the stochastic nature of the sea surface introduces optical distortions that impair link reliability. This work investigates the impact of air-sea surface roughness on AUV-to-UAV OWC systems using two experimentally validated models: the classical Cox-Munk and the Elfouhaily-Chapron-Katsaros-Vandemark (ECKV). A tractable analytical representation of the ECKV model is derived and validated against measured sea-state data. Using both analytical and Monte Carlo approaches, the link ergodic capacity is evaluated with particular emphasis on operating range, pointing errors, receiver field-of-view, and solar noise level, providing practical system design insights.

Camera traps have become a core tool in ecological research, enabling large-scale, noninvasive monitoring of wildlife populations and behavior. By automatically recording animals as they pass within view, these devices generate massive image datasets with minimal field effort. Yet this data richness introduces a new bottleneck when translating the images into usable information due to time and effort required for human annotation. Recently, artificial intelligent (AI) has been integrated into the workflow to improve this efficiency. However, the data procured from AI approaches are of a different nature, necessitating new statistical methods in order to obtain inference, make predictions, and quantify uncertainty. We propose a new Bayesian hierarchical data-fusion model which combines the strengths of human annotations and AI predictions. The benefits of our approach are an ability to provide uncertainty quantification as well as improved inference and prediction power, which we demonstrate using a simulation study. We apply our model to an AI analysis of the body condition of white-tailed deer (Odocoileus virginianus) from camera trap images from North Carolina to study the relationship between health and their environment. We find that bucks in rut have higher body condition than other deer and that green, open habitats are correlated with high body condition. Our new model derived novel ecological inference compared to a traditional approach using the same data.

We present the first paleo-detector dark matter sensitivity analysis based on a calorimetric readout, in which the number of stable lattice vacancies produced by each nuclear recoil is used as a per-event observable complementary to the track length. Using full-cascade SRIM simulations in olivine, we compute the expected sensitivity for a 100 gGyr exposure. We find that a vacancy-only readout reaches a sensitivity envelope very similar to that of state-of-the-art track-only analyses. The combination of the two observables provides an event-by-event proxy for |dE/dx| and hence for the recoiling nuclear species. Since the neutron-nucleus cross section is approximately flat in nuclear mass while the dark-matter--nucleus cross section scales as $A^2$, this discrimination suppresses the dominant neutron background by more than an order of magnitude at moderate dark matter masses. The combined-analysis sensitivity reaches spin-independent dark-matter--nucleon cross sections of order $10^{-48}\,\mathrm{cm}^2$ at WIMP masses of a few tens of GeV, comparable to future direct detection experiments. A two-stage readout combining selective-plane illumination microscopy with scanning electron microscopy is identified as a path to making a 100 g-scale analysis plausible.

High-pressure X-ray diffraction experiments were performed on Ti-Al-V alloys to investigate the effect of composition on structural stability, focusing on Ti-3Al-2.5V and comparing with pure Titanium and Ti-6Al-4V. Measurements using different pressure-transmitting media show a phase transition in Ti-3Al-2.5V at 17-19 GPa, intermediate between pure Ti (5-10 GPa) and Ti-6Al-4V (~30 GPa). Despite variations arising from the choice of pressure medium, the transition pressure shows a clear and systematic increase with higher Al and V content. Equation-of-state analysis indicates that the bulk modulus remains nearly unchanged across compositions. This suggests a decoupling between elastic properties and phase stability, with alloying primarily affecting the transition pressure rather than compressibility. These results highlight the role of composition in tuning high-pressure phase transformations in Ti-Al-V based alloys.

For an arbitrary reductive group $G$, we compute the infinitesimal automorphisms of $L$-valued principal $G$-Higgs bundles over a compact Kähler manifold $X$, extending known results for $Ω_X^{1}$-valued $G$-Higgs bundles. Using this computation, when $G$ is semisimple and $X$ is a smooth projective variety, we show that the moduli stack of stable $L$-valued $G$-Higgs bundles is a Deligne-Mumford (DM) stack. Furthermore, when $X$ is a smooth projective surface and $L=K_X$, we construct a symmetric perfect obstruction theory on this stable locus. We expect this will provide a foundation for defining Vafa-Witten invariants for reductive groups $G$.

Topological superconductivity hosts protected quasiparticles and is central to topological quantum computation, yet its realization in intrinsic materials remains challenging and often relies on engineered platforms. Here we uncover a symmetry-constrained mechanism for nodal topological superconductivity in altermagnets. Focusing on fourfold rotational collinear altermagnets, we show that the native crystalline antiunitary symmetry $\mathcal{T}C_{4z}$ generically forbids pure spin-singlet pairing and selects pairing structures that admit Bogoliubov-de Gennes (BdG) Hamiltonians with emergent chiral symmetries. These symmetries further give rise to robust nodal topological phases over broad parameter regimes, including a nodal-point phase hosting Majorana flat bands (MFBs) and two distinct nodal-loop phases with chiral Majorana edge states. Notably, the nodal structure persists even after spontaneous breaking of the antiunitary symmetry, indicating that the topology originates from symmetry-constrained pairing rather than direct symmetry protection. Finally, we propose tunneling signatures that can distinguish these nodal phases and probe symmetry breaking experimentally.

We study the Hardy spaces $\mathcal{H}^p$, $0<p<\infty$ of quasiregular mappings on the unit ball $\mathbb{B}^n$ in ${\mathbb{R}}^n$ under the appropriate growth and multiplicity conditions. Our focus is on the averaged derivatives of maps and their Harnack and quantitative Harnack estimates. The averaged derivatives are employed to study the non-tangential limit functions and non-tangential maximal functions of quasiregular mappings and to characterize $\mathcal{H}^p$ in the case of finite multiplicity of $f$. Moreover, we study relations between quasiregular mappings, averaged derivatives, BMO spaces and Carleson measures on $\mathbb{B}^n$ and the role of the multiplicity of a map. We also apply our results to the second order elliptic PDEs and $\mathcal{A}$-harmonic equations. Our paper extends results by Astala and Koskela [AK] and Nolder [No1] to the setting of quasiregular maps.

We report the experimental characterization of free-surface deformations generated by three-dimensional homogeneous and isotropic turbulence. Using Fourier transform profilometry in a jet-forced turbulent tank, we perform spatiotemporal measurements of the surface elevation field over a wide range of turbulence intensities. The standard deviation of surface deformations scales linearly with subsurface velocity fluctuations. The spectra of surface deformations highlight the coexistence of two mechanisms: transient coherent structures (e.g., upwelling) contributing to the low-frequency, large-scale spectral components, and a passive response to subsurface turbulent pressure fluctuations responsible for the power-law spectral scaling. The wavenumber and frequency spectra of surface deformations exhibit similar power-law exponents (-2.5), suggesting the advection of turbulent structures at the free surface. We develop a linear response model based on the transfer function from the free surface to turbulent pressure fluctuations, incorporating wave-turbulent damping. The model successfully predicts the main features of the turbulent surface: spatiotemporal spectrum shape, similar spectrum power-law exponents (-7/3), and dominance of passive response over wave generation. These findings provide new insights into free-surface turbulence in regimes where turbulent velocities remain below the surface-breaking threshold.

A macroscopic mesoscopic, deterministic stochastic coupling strategy is proposed to accelerate the direct simulation Monte Carlo (DSMC) method for chemical reaction. First, a macroscopic synthetic equation is formulated by integrating continuum constitutive relations for diffusion, stress, and heat flux, along with higher order constitutive relations that capture nonequilibrium transport effects. Second, higher order constitutive relations and chemical reaction source terms are sampled from DSMC and embedded into the macroscopic synthetic equation. Third, the macroscopic system is solved to the steady state, whose solution is then employed to correct particle distributions in DSMC intermittently. This coupling features asymptotic preserving, fast converging and noise reduction properties, supporting efficient, accurate simulations with coarse spatiotemporal grids and reduced evolution/sampling steps. Accordingly, it mitigates major computational bottlenecks of DSMC for near continuum flows by several orders of magnitude.

Estimation of the extreme value index under right censoring is a fundamental problem in extreme value theory, with important applications in finance, insurance, and reliability. Classical integral estimators for Pareto-type tails typically require that the asymptotic proportion of uncensored observations in the tail is larger than one half, corresponding to the weak censoring regime. This restriction excludes many practically relevant situations involving strong censoring, where the proportion of uncensored observations is smaller than or equal to one half, and reflects the absence of a uniformly valid Gaussian approximation for the associated tail empirical process. To overcome this limitation, we introduce a weighted and truncated Nelson--Aalen tail empirical process and construct a class of integral estimators indexed by a tuning parameter larger than one. This approach restores a tractable asymptotic structure over the entire censoring range, from very weak to very strong censoring. Under standard regular variation conditions, we establish a uniform Gaussian approximation and derive consistency and asymptotic normality without imposing restrictions on the censoring level. A key ingredient of the analysis is a linearization of the estimator as a functional of the underlying process. Simulation studies and real data applications demonstrate improved stability and accuracy, particularly under moderate and strong censoring. In particular, the analysis of insurance loss data, representing weak censoring, and Australian AIDS survival data, representing strong censoring, illustrates the practical relevance of the proposed methodology across contrasting censoring regimes.

A search is presented for single production of a vector-like top quark T, decaying into the standard model top quark and Higgs boson, in a final state including two opposite-sign leptons (electrons or muons), jets, and missing transverse momentum. The data were recorded by the CMS experiment in proton-proton collisions at a center-of-mass energy of 13 TeV at the CERN LHC in the years 2016$-$2018, and corresponding to an integrated luminosity of up to 138 fb$^{-1}$. No excess in data over the background expectations is observed. Upper limits at 95% confidence level on the product of the T production cross section and its decay branching fraction to tH are set, ranging from 2.0 pb at a T mass of 600 GeV to 0.1 pb at 1000 GeV. This is the first search in the T $\to$ tH channel in opposite-sign dilepton final states.

This paper extends the theory of quantum fractional revival (QFR) on unitary Cayley graphs $X=(V(\mathbb{Z}_n),E(S))$ in several directions that remained unresolved in previous work. First, we investigate QFR with respect to the Laplacian matrix Hamiltonian in addition to the adjacency matrix Hamiltonian. In particular, we prove that for regular graphs the two models differ only by a global phase factor, and we determine the conditions under which the Laplacian framework independently admits QFR. Second, for unitary Cayley graphs of order $n=2p$, where $p$ is an odd prime, we derive an explicit closed-form expression for the minimum revival time, $t^{*}=\frac{2π}{p},$ and show that the associated revival amplitudes are given by \[ α=\cos\!\left(\frac{2π}{p}\right), \qquad β=-i\sin\!\left(\frac{2π}{p}\right). \] Third, we provide a complete characterization of strongly cospectral vertex pairs in $X=(V(\mathbb{Z}_n),E(S))$ through the arithmetic structure of $\mathbb{Z}_n$, establishing that strong cospectrality is equivalent to antipodality whenever $n$ is twice a prime. Finally, we compute the von Neumann entanglement entropy generated by QFR for all admissible graphs, thereby obtaining a collection of quantum information measures and proving that the entropy depends solely on the revival amplitudes $|α|$ and $|β|$.