arXiv subjects

Yun-Feng Lo

Publications and source records attributed to Yun-Feng Lo.

11 recordsLinked to original sources

arXiv2026

Covert Bayesian Quickest Change Detection

We investigate the problem of covert quickest change detection in a Bayesian and infinite-horizon setting. A legitimate entity seeks to detect a change in the state of a discrete memoryless channel as quickly as possible by actively probing it. Simultaneously, the entity must ensure its probing remains covert from an adversary monitoring the channel for active sensing. We introduce the expected covertness budget (ECB) as an analytically tractable covertness metric that bounds from above the relative entropy between the observation sequences induced by active and passive sensing. Under constraints on both the probability of false alarm (PFA) and the ECB, we establish a second-order asymptotic converse bound on the average detection delay as the PFA constraint approaches zero, for any positive ECB constraint, explicitly quantifying the maximum square-root-order covert sensing gain possible. Furthermore, we propose an achievability scheme utilizing a constant-sensing-probability Shiryaev-type policy and show that it matches the second-order asymptotic converse. We illustrate our result with a numerical example.

cs.IT↗

arXiv2025

Synchronization Relations in the Hybrid Kuramoto Flow: Equivalence and a High-Coherence Criterion

We study four synchronization notions for the all-to-all hybrid Kuramoto model containing both first- and second-order oscillators with heterogeneous inertias and damping coefficients. We prove that full phase locking, bounded phase locking, and frequency synchronization are equivalent for arbitrary hybrid ensembles, and that each of these properties implies convergence of the complex order parameter. Conversely, if an order-parameter synchronized trajectory has limiting order parameter $Z^*$ satisfying $|Z^*|>\max\left\{\frac{\omega_M}{\lambda},\,1-\frac{2}{N}\right\}$, then the trajectory is frequency synchronized and hence fully phase locked. The converse proof is entirely real-dynamical. The omega-limit set is internally chain transitive and, because the order parameter is constant on that set, the dynamics reduce there to a product of frozen scalar equations. A tilted-energy argument shows that every nonstationary scalar factor of an internally chain transitive frozen set must cover the whole phase circle. Evaluating the constant mean field at an antipodal phase then forces $|Z^*|\le 1-2/N$, a contradiction. For zero natural frequencies, convergence follows from the analytic periodic gradient structure with degenerate inertia.

math.DS↗

arXiv2025

Spatiotemporal First-Arrival Modeling and Parameter Estimation in Drift-Diffusion Molecular Channels

We derive a closed-form joint distribution of the first arrival time (FAT) and first arrival position (FAP) in drift-diffusion molecular communication (MC) channels. In contrast to prior studies that analyze FAT or FAP in isolation, our framework explicitly captures the spatiotemporal coupling inherent in multidimensional transport. Building on this derivation, we compute the Fisher information matrix (FIM) and demonstrate that estimation accuracy for diffusivity scales proportionally with the spatial dimension, enabling increased sensitivity in higher-dimensional environments. Furthermore, we show that lateral drift -- which is unobservable from timing data alone -- can be recovered via a closed-form Maximum Likelihood Estimator (MLE) with a simple physical interpretation. Leveraging this spatial degree of freedom, we propose Drift Shift Keying (DSK), proving that joint receivers can reliably detect signals that are undetectable to timing-only receivers due to identical marginal FAT distributions. These results highlight the significant potential of spatiotemporal processing for future nanoscale communication and sensing.

cs.IT↗

arXiv2025

Three-Dimensional Channel Modeling for Molecular Communications in Tubular Environments with Heterogeneous Boundary Conditions

Molecular communication (MC), one of the emerging techniques in the field of communication, is entering a new phase following several decades of foundational research. Recently, attention has shifted toward MC in liquid media, particularly within tubular environments, due to novel application scenarios. The spatial constraints of such environments make accurate modeling of molecular movement in tubes more challenging than in traditional free-space channels. In this paper, we propose a three-dimensional channel model for molecular communications with an absorbing ring-shaped receiver in a tubular environment. To the best of our knowledge, this is the first theoretical study to model the impact of an absorbing ring-shaped receiver on the channel response in tube-based MC systems. The problem is formulated as a partial differential equation with heterogeneous boundary conditions, and an approximate solution is derived under flow-dominated conditions. The accuracy of the proposed model is validated through particle-based simulations. We anticipate that the results of this study will contribute to the design of practical MC systems in real-world tubular environments.

cs.IT↗

arXiv2025

On the Equivalence of Synchronization Definitions in the Kuramoto Flow: A Unified Approach

We present a rigorous mathematical framework establishing the equivalence of four classical notions of synchronization full phase-locking, phase-locking, frequency synchronization, and order parameter synchronization in generalized Kuramoto models, via a non-perturbative, finite-dimensional analysis. Our approach avoids linearization, mean-field limits, and restrictions on initial conditions, relying instead on global phase-space geometry, periodic vector field structure, and compactness arguments based on contradiction. These results clarify the foundational role of the order parameter and provide a unified understanding of synchronization across a broad class of heterogeneous oscillator networks.

math.DS↗

arXiv2025

Synchronization in the complexified Kuramoto model

In this paper, we consider an $N$-oscillators complexified Kuramoto model. We first observe that there are solutions exhibiting finite-time blow-up behavior in all coupling regimes. When the coupling strength $\lambda>\lambda_c$, sufficient conditions for various types of synchronization are established for general $N \geq 2$. On the other hand, we analyze the case when the coupling strength is weak. For $N=2$ with coupling below $\lambda_c$, our complex-analytic approach not only recovers the periodic orbits reported by Th\"umler--Srinivas--Schr\"oder--Timme but also provides, for the first time, their exact period $T_{\omega,\lambda}=2\pi/\sqrt{\omega^{2}-\lambda^{2}}$, confirming full phase locking. Furthermore, for the critical case $\lambda = \lambda_c$, we find that the complexified Kuramoto system admits homoclinic orbits. These phenomena significantly differentiate the complexified Kuramoto model from the real Kuramoto system, as synchronization never occurs when $\lambda<\lambda_c$ in the latter. For $N=3$, we demonstrate that if the natural frequencies are in arithmetic progression, non-trivial synchronization states can be achieved for certain initial conditions even when the coupling strength is weak. In particular, we characterize the critical coupling strength ($\lambda/\lambda_c = 0.85218915...$) such that a semistable equilibrium point in the real Kuramoto model bifurcates into a pair of stable and unstable equilibria, marking a new phenomenon in complexified Kuramoto models.

math.DS↗

arXiv2025

Active Hypothesis Testing for Quantum Detection of Phase-Shift Keying Coherent States

This paper explores the quantum detection of Phase-Shift Keying (PSK)-coded coherent states through the lens of active hypothesis testing, focusing on a Dolinar-like receiver with constraints on displacement amplitude and energy. With coherent state slicing, we formulate the problem as a controlled sensing task in which observation kernels have parameters shrinking with sample size. The constrained open-loop error exponent and a corresponding upper bound on the Bayesian error probability are proven. Surprisingly, the exponent-optimal open-loop policy for binary PSK with high dark counts is not simply time-sharing. This work serves as a first step towards obtaining analytical insights through the active hypothesis testing framework for designing resource-constrained quantum communication receivers.

quant-ph↗

arXiv2024

Characterizing First Arrival Position Channels: Noise Distribution and Capacity Analysis

This paper introduces a novel mathematical model for Molecular Communication (MC) systems, utilizing First Arrival Position (FAP) as a fundamental mode of information transmission. We address two critical challenges: the characterization of FAP density and the establishment of capacity bounds for channels with vertically-drifted FAP. Our method relate macroscopic Partial Differential Equation (PDE) models to microscopic Stochastic Differential Equation (SDE) models, resulting in a precise expression that links FAP density with elliptic-type Green's function. This formula is distinguished by its wide applicability across any spatial dimensions, any drift directions, and various receiver geometries. We demonstrate the practicality of our model through case studies: 2D and 3D planar receivers. The accuracy of our formula is also validated by particle-based simulations. Advancing further, the explicit FAP density forms enable us to establish closed-form upper and lower bounds for the capacity of vertically-drifted FAP channels under a second-moment constraint, significantly advancing the understanding of FAP channels in MC systems.

cs.IT↗

arXiv2024

Symmetry-Enforced Quadratic Degradability Beyond Low Dimensions

Approximate degradability provides a powerful framework for bounding the quantum and private capacities of noisy quantum channels in regimes where exact degradability fails. While generic low-noise channels exhibit a non-degradability parameter that decays as a fractional power of the noise strength, certain symmetric channels are known to display an enhanced quadratic suppression. In this work, we investigate the structural origin of this phenomenon through a family of high-dimensional, rotationally symmetric noise models constructed from angular momentum operators. We first establish that the pure noise component of these channels is maximally distinguishable from the identity channel in diamond norm, revealing a geometric orthogonality between signal and noise. Building on this structure, we construct an explicit symmetric degrading map and prove that the approximate degradability parameter scales quadratically with the noise parameter for all system dimensions. To clarify the mechanism behind this behavior, we identify algebraic conditions on the noise operators that guarantee the cancellation of leading-order non-degradability terms. These conditions apply not only to the rotationally symmetric model studied here, but also to a distinct family of high-dimensional depolarizing channels based on discrete unitary operator bases. Numerical evaluations of capacity lower bounds further illustrate the practical impact of the quadratic suppression. Together, these results demonstrate that enhanced approximate degradability arises from symmetry-induced orthogonality and invariance properties, rather than from low-dimensional or model-specific effects.

cs.IT↗

arXiv2024

Synchronization in the quaternionic Kuramoto model

In this paper, we propose an $N$ oscillators Kuramoto model with quaternions $\mathbb{H}$. In case the coupling strength is strong, a sufficient condition of synchronization is established for general $N\geqslant 2$. On the other hand, we analyze the case when the coupling strength is weak. For $N=2$, when coupling strength is weak (below the critical coupling strength $λ_c$), we show that new periodic orbits emerge near each equilibrium point, and hence phase-locking state exists. This phenomenon is different from the real Kuramoto system since it is impossible to arrive at any synchronization when $λ<λ_c$. We prove a theorem that states a set of closed and dense contour forms near each equilibrium point, resembling a tree's growth rings. In other words, the trajectory of phase difference lies on a $4D$-torus surface. Therefore, this implies that the phase-locking state is Lyapunov stable but not asymptotically stable. The proof uses a new infinite buffer method (``$δ/n$ criterion") and a Lyapunov function argument. This has been studied both analytically and numerically. For $N=3$, we consider the ``Lion Dance flow", the analog of Cherry flow for our model, to demonstrate that the quaternionic synchronization exists even when the coupling strength is ``super weak" (when $λ/ω<0.85218915...$). Also, numerical evaluation reveals that when $N>3$, the stable manifold of Lion Dance flow exists, and the number of these equilibria is $\lfloor \frac{N-1}{2}\rfloor$. Therefore, we conjecture that Lyapunov stable quaternionic synchronization always exists.

math.DS↗

arXiv2023

Capacity Bounds for Vertically-Drifted First Arrival Position Channels under a Covariance Constraint

In this paper, we delve into the capacity problem of additive vertically-drifted first arrival position noise channel, which models a communication system where the position of molecules is harnessed to convey information. Drawing inspiration from the principles governing vector Gaussian interference channels, we examine this capacity problem within the context of a covariance constraint on input distributions. We offer analytical upper and lower bounds on this capacity for a three-dimensional spatial setting. This is achieved through a meticulous analysis of the characteristic function coupled with an investigation into the stability properties. The results of this study contribute to the ongoing effort to understand the fundamental limits of molecular communication systems.

cs.IT↗