Abstract Synchronization phenomena in rhythmic systems are commonly modeled using phase oscillator frameworks in which interactions are represented as sums of pairwise coupling functions. Accurate estimation of these coupling functions from observed data remains a fundamental challenge, particularly when observations are sparse or biased due to synchronization. In this paper, we propose a nonparametric Bayesian approach based on Gaussian process regression for estimating coupling functions in phase oscillator models. We model each pairwise interaction function as a periodic Gaussian process and represent the total interaction as their sum. To incorporate this structure, we introduce an additive periodic kernel that reflects both the periodicity of phase interactions and their pairwise-additive form. The proposed method is validated using coupled van der Pol oscillators, coupled FitzHugh–Nagumo oscillators, and networks of Hodgkin–Huxley-type neurons. Numerical experiments demonstrate that the proposed method provides more accurate estimates than a conventional Fourier-based Bayesian approach under sparse-data and synchronization-biased conditions. These improvements also lead to more accurate reconstruction of neuronal oscillator networks. The results illustrate how additive Gaussian process models can incorporate prior knowledge about interaction structure through kernel design and provide a flexible framework for estimating pairwise interaction functions from oscillatory data.
Abstract We study semileptonic B meson decays $B^+ \rightarrow D_1^{(\prime )}\ell ^+\nu _\ell$ and $B_s^0 \rightarrow D_{s1}^{-(\prime )}\ell ^+\nu _\ell$, where ℓ = μ, τ. The final state axial vector mesons are treated as mixtures of the heavy quark basis states with light degree of freedom angular momenta jℓ = 1/2 and jℓ = 3/2, parametrized by the mixing angle $\theta _{D_1}$. Using form factors obtained in the covariant light front quark model, we analyze the dependence of various observables on $\theta _{D_1}$ such as polarized and unpolarized branching ratios, the lepton forward-backward asymmetry, the longitudinal polarization fraction, and the lepton flavor universality ratios. In addition, we also discuss correlations among different observables. We study these observables in the experimentally motivated mixing angle regions as well as over a wider range of $\theta _{D_1}$. Our results show that branching ratios and other observables are sensitive to the axial-vector mixing structure. These predictions provide useful Standard Model benchmarks for future measurements of semileptonic B(s) decays into orbitally excited mesons and may help to clarify the long standing 1/2 vs. 3/2 puzzle through semileptonic B decays.
Abstract We revisit the species scale in quantum gravity from the viewpoint of effective field theory (EFT). Two common parametric characterizations relate it to the breakdown of perturbative gravity and to the suppression scale of higher-derivative gravitational operators. We examine their correspondence through local threshold corrections from infinite Kaluza–Klein (KK) towers. In four dimensions, we compute the four-derivative one-loop action of minimally coupled scalar and Dirac towers with KK spectra in graviton, radion, and photon backgrounds. Feynman diagrams determine the single-mode coefficients, while analytic summation with full threshold functions tests the logarithmic coefficient inferred from renormalization-group evolution. The leading contribution scales with the effective number of KK levels, reproducing the standard species-scale relation under the stated matching assumptions, but its coefficient depends on the cutoff profile and belongs to EFT matching data. In contrast, the subleading curvature-squared thresholds contain logarithms of the KK mass gap whose spin-dependent coefficients remain stable under changes of the cutoff profile within the class studied here.
Abstract We study the one-dimensional generalized Dirac oscillator with a complex Morse interaction, f(x) = D − qe−αx, in the Magueijo–Smolin (MS) and Amelino-Camelia (AC) realizations of doubly special relativity (DSR). The spatial problem factorizes into supersymmetric partners. For D > 0 and Re q > 0, the positive metric η = exp ( − θp/ℏ), $\theta =2\arg q/\alpha$, defines, on analytic bound states, a similarity transformation ρ = η1/2 to a Hermitian Morse representative. Direct Kummer analysis on the complex ray gives the real spectrum εn = D2 − (D − nℏα)2, independent of the phase of q, with 0 ≤ n < D/(ℏα) following from square integrability on the whole line. We relate the Morse parameters to the DSR scale k. Both DSR equations preserve the spatial spectrum but deform energy reconstruction and spinor amplitudes. On admissible branches, $E^{\rm MS}_{n,\sigma }=\sigma \Omega _n-m^2/k$ and $E^{\rm AC}_{n,\sigma }=\sigma \Omega _n+\epsilon _n/(2k)$ to first order, with $\Omega _n=\sqrt{m^2+\epsilon _n}$. On nonzero SUSY doublets, the AC generalized-eigenvalue weight is positive exactly for εn < 4k2. At this boundary the positive branch diverges while the negative branch remains finite, yielding a Morse excitation threshold. Quantitative use requires |E|/k ≪ 1. The model provides an exactly solvable testbed linking pseudo-Hermiticity, supersymmetry, and DSR kinematics.
Abstract We discuss the AdS/CFT correspondence from the viewpoint of gravity as a broken phase of conformal gauge symmetry. In AdS$_2$/CFT$_1$, the Schwarzian structure is related to the boundary extrinsic curvature. In AdS$_4$/CFT$_3$, the gauge-theoretic formulation of four-dimensional gravity contains a boundary-sensitive Euler sector whose descent structure leads to the Cotton tensor characterizing the three-dimensional boundary conformal geometry. At the structural and kinematical level considered here, these results suggest a unified geometrical interpretation of holography in terms of boundary remnants of broken bulk conformal gauge symmetry.
