arXiv subjects

Ting Gao

Publications and source records attributed to Ting Gao.

At least 19 recordsLinked to original sources

arXiv2026

Geometric Methods for Stochastic Dynamical Systems

Geometric methods are indispensable for analyzing, predicting, and mitigating the complex behaviors inherent in nonlinear systems. In this regime, the most probable transition path minimizes the Onsager-Machlup action functional, marking the likeliest route across an energy barrier. Lifting the analysis from individual sample paths to the infinite-dimensional space of probability densities, the book recasts these transitions as Schr\"odinger bridges - optimal paths between boundary distributions defined by minimizing relative entropy - and shows that the Onsager-Machlup path emerges as a special case when metastable states are idealized as Dirac masses. Generalizing further through {\alpha}-divergences, which connect to entropies and the thermodynamic cost of nonequilibrium transitions, it introduces information geodesics as the resulting optimal density paths, offering a unified geometric account of how complex systems move between metastable regimes under uncertainty.

math.DS↗

arXiv2026

The fidelity of controlled quantum teleportation in a noisy environment

In this work, we investigate controlled quantum teleportation in the presence of noisy channels acting on the three-qubit resource state. We employ a series of generalized noisy channels that bridge the dephasing channels and amplitude damping channels while encompassing extensive intermediate scenarios. We provide an in-depth analysis of the degradation of the maximal average fidelity and the optimal average fidelity in controlled quantum teleportation induced by such noisy channels by deriving the analytical expression and examining several special cases. The analytical expression shows that attaining the optimal average fidelity requires Charlie's cooperation in performing a measurement at suitably chosen angles, and is also related to the initial state and the channel parameters. Our analysis reveals that the optimal average fidelity does not always decrease monotonically with the evolution parameter, instead, it first decreases and then increases. This non-monotonic behavior depends on the entanglement of the initial resource state, as well as on the parameters of the channel traversed by the first qubit.

quant-ph↗

arXiv2026

Joint Discovery of Graph Structure and Dynamics in Stochastic Interacting Particle Systems

We study the joint identification of network structure and governing dynamics in stochastic interacting particle systems, which consist of an unknown directed weighted interaction graph with unknown local and non-local interaction components. We formulate the problem as a coupled inverse problem for the graph and the associated basis coefficients, and develop two alternating least-squares-type estimators: a three-block scheme (TALS) and an integrated diagonal-augmented scheme (IALS). The IALS formulation combines the updates of the local and interaction coefficients into a single least-squares subproblem, and is particularly well suited to settings in which the nodewise local dynamics share a common functional template up to node-dependent scaling. We further establish an identifiability result under a rank-2 joint coercivity condition together with an appropriate normalization convention. Synthetic experiments show that the proposed estimators accurately recover both the interaction graph and the dynamical components, and remain robust under stochastic forcing, observation noise, and basis mismatch. We also provide an illustrative real-data application on ictal SEEG recordings, where the learned models produce stable and interpretable dynamical summaries across multiple basis configurations. This work advances a theoretically guaranteed scalable framework for learning stochastic interacting particle systems, with broad potential for data-driven identification in computational biology, neuroscience, and beyond.

cs.SI↗

arXiv2026

Topological Kalman Filtering on Cell Complexes

Inferring latent dynamics from multivariate time-series defined over topological cell complexes is crucial for capturing the complex, higher-order interactions inherent in real-world systems such as in water, sensor, and transportation networks. However, reconstructing these latent states is challenging because the signals are coupled across higher-order topologies, while high dimensionality, nonlinear observations, and unknown structures increase the difficulty. To address this, we propose a topology-aware state space framework derived from stochastic partial differential equations on cell complexes. State evolution follows heat-like topological diffusion, with perturbations propagating along boundary operators. Under partial observability, we model observations using a cell complex convolution of latent states coupled with a nonlinear mapping. We perform recursive state estimation via an Extended Kalman Filter, simultaneously learning model parameters and uncertainties through an online Expectation-Maximization algorithm. Finally, for scenarios where only lower-order topological structure is known, e.g., nodes and edges, as in critical infrastructure networks, we introduce a heuristic cell identification algorithm to explicitly infer the second-order cell structures. Validations on synthetic and real datasets from water, sensor and transportation networks demonstrate that our approach yields reliable estimates under partial observability and successfully recovers the underlying topological structures.

eess.SP↗

arXiv2026

Efficient Encrypted Computation in Convolutional Spiking Neural Networks with TFHE

With the rapid advancement of AI technology, we have seen more and more concerns on data privacy, leading to some cutting-edge research on machine learning with encrypted computation. Fully Homomorphic Encryption (FHE) is a crucial technology for privacy-preserving computation, while it struggles with continuous non-polynomial functions, as it operates on discrete integers and supports only addition and multiplication. Spiking Neural Networks (SNNs), which use discrete spike signals, naturally complement FHE's characteristics. In this paper, we introduce FHE-DiCSNN, a framework built on the TFHE scheme, utilizing the discrete nature of SNNs for secure and efficient computations. By leveraging bootstrapping techniques, we successfully implement Leaky Integrate-and-Fire (LIF) neuron models on ciphertexts, allowing SNNs of arbitrary depth. Our framework is adaptable to other spiking neuron models, offering a novel approach to homomorphic evaluation of SNNs. Additionally, we integrate convolutional methods inspired by CNNs to enhance accuracy and reduce the simulation time associated with random encoding. Parallel computation techniques further accelerate bootstrapping operations. Experimental results on the MNIST and FashionMNIST datasets validate the effectiveness of FHE-DiCSNN, with a loss of less than 3\% compared to plaintext, respectively, and computation times of under 1 second per prediction. We also apply the model into real medical image classification problems and analyze the parameter optimization and selection.

cs.CR↗

arXiv2026

Teleporting an unknown qutrit state via a 2-qudit entangled channel

We propose a quantum teleportation scheme for transmitting a single qutrit state by adopting a 2-qudit entangled state as the quantum channel. The measurement basis for Alice has been carefully and systematically constructed, which is essential for the successful implementation of the teleportation protocol. Based on Alice's measurement outcomes, we design the corresponding collective unitary transformations to be performed by Bob on an auxiliary qubit and information particle. After implementing the collective unitary transformation, Bob performs a von Neumann measurement on the auxiliary qubit. The single qutrit state is then teleported to the distant receiver Bob with a finite success probability. We obtain the achievable success probabilities of the proposed teleportation scheme for different quantum channels. The obtained results not only enrich the theory of quantum teleportation over high-dimensional entangled channels but also provide a novel and feasible approach to implementing qutrit teleportation.

quant-ph↗

arXiv2026

Flow Matching Policy Optimization with Mirror Descent and Entropy Constraints

Balancing policy expressiveness with the exploration-exploitation trade-off is a core challenge in online Reinforcement Learning (RL). While Stochastic Differential Equation (SDE)-based diffusion policies can represent complex, multimodal action distributions, they suffer from two critical limitations: their stochastic reverse processes render entropy intractable (necessitating heuristic exploration), and computing policy gradients through long denoising chains is expensive and unstable. In this work, we show that ODE-based flow matching inherently resolves these issues by enabling both simulation-free policy optimization and tractable entropy computation. Building on this, we introduce Flow Matching Policy Optimization with Mirror Descent and Entropy Constraints (FMER). Our framework exploits this insight in three ways. First, we theoretically establish that minimizing an advantage-weighted conditional flow matching loss acts as a simulation-free surrogate for policy mirror descent. This steers the velocity field toward high-value regions while entirely avoiding backpropagation through the ODE solver. Second, we derive an analytic entropy objective that corrects for the density distortion caused by the $\tanh$ transformation (mapping an unbounded latent space to bounded actions), thereby facilitating principled maximum-entropy optimization. Finally, we dynamically tune the mirror descent temperature based on the effective sample size to enforce a robust trust region during training. Empirical evaluations demonstrate that FMER achieves superior performance on the challenging sparse-reward FrankaKitchen environment, while maintaining competitive results across standard dense-reward MuJoCo benchmarks.

cs.LG↗

arXiv2026

A Jacobi Field Approach to Splitting Detection in Schr\"{o}dinger Bridge

We study the problem of detecting the onset of path splitting in stochastic interpolation between probability distributions. This question is especially subtle when the target distribution is nonconvex or supported on disconnected components, where interpolating trajectories may separate into distinct branches. Motivated by the stochastic control and Schr\"odinger bridge viewpoint, we propose a Jacobi field based indicator for identifying candidate splitting times and locations. Our approach is based on the Jacobi field associated with the linearization of an induced interpolating flow. Starting from a stochastic interpolation ansatz, we construct an Eulerian velocity field by conditional averaging and derive its spatial Jacobian in terms of the local posterior geometry of the target sample cloud. This allows us to interpret the symmetric part of the Jacobian as a local strain tensor and to use its spectral structure to quantify the amplification of infinitesimal perturbations along reference trajectories. Numerical experiments on non-convex and disconnected target distributions show that the proposed indicator consistently localizes the emergence of branching regions and captures the temporal development of splitting. These results suggest that Jacobi field analysis provides a natural mathematical framework for studying local instability and splitting phenomena in stochastic interpolation.

math.DS↗

arXiv2026

Beyond Distance: Quantifying Point Cloud Dynamics with Persistent Homology and Dynamic Optimal Transport

We introduce a framework for analyzing topological tipping in time-evolutionary point clouds by extending the recently proposed Topological Optimal Transport (TpOT) distance. While TpOT unifies geometric, homological, and higher-order relations into one metric, its global scalar distance can obscure transient, localized structural reorganizations during dynamic phase transitions. To overcome this limitation, we present a hierarchical dynamic evaluation framework driven by a novel topological and hypergraph reconstruction strategy. Instead of directly interpolating abstract network parameters, our method interpolates the underlying spatial geometry and rigorously recomputes the valid topological structures, ensuring physical fidelity. Along this geodesic, we introduce a set of multi-scale indicators: macroscopic metrics (Topological Distortion and Persistence Entropy) to capture global shifts, and a novel mesoscopic dual-perspective Hypergraph Entropy (node-perspective and edge-perspective) to detect highly sensitive, asynchronous local rewirings. We further propagate the cycle-level entropy change onto individual vertices to form a point-level topological field. Extensive evaluations on physical dynamical systems (Rayleigh-Van der Pol limit cycles, Double-Well cluster fusion), high-dimensional biological aggregation (D'Orsogna model), and longitudinal stroke fMRI data demonstrate the utility of combining transport-based alignment with multi-scale entropy diagnostics for dynamic topological analysis.

stat.ML↗

arXiv2026

Taming Epilepsy: Mean Field Control of Whole-Brain Dynamics

Controlling the high-dimensional neural dynamics during epileptic seizures remains a significant challenge due to the nonlinear characteristics and complex connectivity of the brain. In this paper, we propose a novel framework, namely Graph-Regularized Koopman Mean-Field Game (GK-MFG), which integrates Reservoir Computing (RC) for Koopman operator approximation with Alternating Population and Agent Control Network (APAC-Net) for solving distributional control problems. By embedding Electroencephalogram (EEG) dynamics into a linear latent space and imposing graph Laplacian constraints derived from the Phase Locking Value (PLV), our method achieves robust seizure suppression while respecting the functional topological structure of the brain.

cs.LG↗

arXiv2026

Genuinely entangled subspaces and strongly nonlocal unextendible biseparable bases in four-partite systems

A set of orthogonal pure states is an unextendible biseparable basis (UBB), which means that its complementary subspace contains only genuinely entangled states. UBBs thus serve as an effective tool for constructing genuinely entangled subspaces. If every state within such a subspace exhibits distillable entanglement across all bipartitions, it becomes particularly advantageous for applications in quantum information. In this paper, we mainly conduct research on the 4-qudit quantum systems, where the local dimension $d$ is not less than 3. We present an approach for constructing UBB and prove that the UBB established in this way is strongly nonlocal. We build several genuinely entangled subspaces and demonstrate the distillability of the genuinely entangled subspaces across all bipartitions. In addition, we also describe the specific orthonormal basis for some genuinely entangled subspaces. These results will not only contribute to the development of quantum nonlocality theory, but also provide a crucial theoretical foundation for practical quantum information processing tasks.

quant-ph↗

arXiv2026

Predicting the onset of period-doubling bifurcations via dominant eigenvalue extracted from autocorrelation

Predicting the occurrence of transitions in the qualitative dynamics of many natural systems is crucial, yet it remains a challenging task. Generic early warning signals like variance and lag-1 autocorrelation identify critical slowing down near tipping points but lack practical thresholds for predicting imminent transitions. More recent studies found that the dynamical eigenvalue is rooted in the framework of empirical dynamical modeling and then estimates the dominant eigenvalue of a system from time series, providing a threshold ($|$DEV$|$ = 1) to predict bifurcations and classify their types. However, its application requires careful calibration of the hyperparameters and focuses on reconstructing system dynamics directly from data. Here, we employ Ornstein-Uhlenbeck process to derive analytic approximations for the lag-$\tau$ autocorrelation function prior to period-doubling bifurcation thereby estimating the dominant eigenvalue of dynamical systems, named dominant eigenvalue extracted from autocorrelation (DE-AC), and revealing its dynamic behaviour when approaching a period-doubling bifurcation. Theoretically, dominant eigenvalue tends to $-1$ when the system approaches a period-doubling bifurcation. In particular, we evaluated DE-AC on simulation data from cardiac alternans model and on experimental data from chick heart aggregates undergoing a period-doubling bifurcation. DE-AC reliably detected the beginning of the cardiac arrhythmia (period-doubling bifurcation) in most cases. Moreover, it demonstrated superior sensitivity and specificity as an early warning signal compared to the three widely used indicators -- variance, lag-1 autocorrelation, and dynamical eigenvalue. Our theoretical and empirical results suggest that DE-AC represents a quantitative measure for predicting the onset of potentially dangerous alternating rhythms in the heart.

nlin.CD↗

arXiv2026

Parapositronium decay into three photons and implications for the neutral pion

We complete the determination of the parapositronium decay into three photons by evaluating amplitudes mediated by the $Z$ boson. We show that, contrary to the expectation that the extra mass scale $m_e$ may bring an enhancement to the overall scaling, the amplitude turns out to start at $1/m_Z^6$ order, similarly to the $W$ boson mediated amplitude. The decay rate with both $W$ and $Z$ boson contributions is found to be $1.1\cdot 10^{-80}$ eV, about 47 orders of magnitude smaller than previously estimated. We also discuss its implication for the $\pi^0\to3\gamma$ amplitude.

hep-ph↗

arXiv2026

Symmetric joint measurement as a complement to the elegant joint measurement

Traditional Bell state measurement (BSM) and product basis measurements (PBM) have been integral to nearly the entire development of quantum computing. Unlike the BSM and the PBM, a recently proposed two-qubit joint measurement called the elegant joint measurement (EJM) exhibits novel tetrahedral symmetry in its single-qubit reduced states. In [Phys.Rev.Lett.126:220401], a parameterized two-qubit iso-entangled basis was proposed, with concurrence between 1/2 and 1, perfectly spanning the original EJM and conventional BSM. We present a two-qubit symmetric joint measurement having concurrence from 0 to 1/2, which is complementary to [Phys.Rev.Lett.126:220401] and contains the PBM and the original EJM. We investigate the symmetry of the current structure and its application in triangular networks. The results indicate that the reduction vectors of the current basis states exhibit rotational symmetry, rather than the aforementioned mirror symmetry; moreover, the output probability distributions of three parties in the network explicitly demonstrate the expected permutation symmetry. Furthermore, we generalize the two-qubit symmetric joint measurement to the multiqubit systems with an even number of qubits.

quant-ph↗

arXiv2026

Early warning prediction: Onsager-Machlup vs Schr\"{o}dinger

Predicting critical transitions in complex systems, such as epileptic seizures in the brain, represents a major challenge in scientific research. The high-dimensional characteristics and hidden critical signals further complicate early-warning tasks. This study proposes a novel early-warning framework that integrates manifold learning with stochastic dynamical system modeling. Through systematic comparison, six methods including diffusion maps (DM) are selected to construct low-dimensional representations. Based on these, a data-driven stochastic differential equation model is established to robustly estimate the probability evolution scoring function of the system. Building on this, a new Score Function (SF) indicator is defined by incorporating Schr\"{o}dinger bridge theory to quantify the likelihood of significant state transitions in the system. Experiments demonstrate that this indicator exhibits higher sensitivity and robustness in epilepsy prediction, enables earlier identification of critical points, and clearly captures dynamic features across various stages before and after seizure onset. This work provides a systematic theoretical framework and practical methodology for extracting early-warning signals from high-dimensional data.

q-bio.QM↗

arXiv2025

Learning L\'evy density via adaptive RKHS regression with bi-level optimization

We propose a nonparametric method to learn the L\'evy density from probability density data governed by a nonlocal Fokker-Planck equation. We recast the problem as identifying the kernel in a nonlocal integral operator from discrete data, which leads to an ill-posed inverse problem. To regularize it, we construct an adaptive reproducing kernel Hilbert space (RKHS) whose kernel is built directly from the data. Under standard source and spectral decay conditions, we show that the reconstruction error decays in the mesh size at a near optimal rate. Importantly, we develop a generalized singular value decomposition (GSVD)-based bilevel optimization algorithm to choose the regularization parameter, leading to efficient and robust computation of the regularized estimator. Numerical experiments for several L\'evy densities, drift fields and data types (PDE-based densities and sample ensemble-based KDE reconstructions) demonstrate that our bilevel RKHS method outperforms classical L-curve and generalized cross-validation strategies and that the adaptive RKHS norm is more accurate and robust than $L^2_\rho$- and $\ell^2$-based regularization.

math.NA↗

arXiv2025

Hidden Momentum and the Absence of the Gravitational Spin Hall Effect in a Uniform Field

We re-examine the recent claim that a Dirac particle freely falling in a uniform gravitational field exhibits a spin-dependent transverse deflection (gravitational spin Hall effect). Using a circulating mass model, we show that hidden momentum arises in uniform fields when an object carries angular momentum. On the quantum side, we analyze the Dirac Hamiltonian in a uniform potential, construct its Foldy--Wouthuysen form, and evaluate the Heisenberg evolution of spin-polarized Gaussian packets. The state used previously, with $\langle p\rangle =0$, is not at rest: because canonical and kinetic momenta differ, the packet carries a spin-dependent hidden momentum from $t=0$. Imposing $\langle x(0)\rangle =\langle v(0)\rangle=0$ requires a compensating spin-dependent $\langle p(0)\rangle$; with this preparation $\langle x(t)\rangle =0$ to leading order in the gravitational acceleration $g$. Generalizing, an exact Foldy--Wouthuysen transformation (linear in $g$ but to all orders in $1/c$) shows that spin-dependent transverse motion begins no earlier than at $O(g^2)$ for a broad class of wave packets. We conclude that a uniform field does not produce a gravitational spin Hall effect at linear order; the previously reported drift stems from inconsistent initial states and misinterpreting canonical momentum.

gr-qc↗

arXiv2025

Characterizing entanglement shareability and distribution in $N$-partite systems

Exploring the shareability and distribution of entanglement possesses fundamental significance in quantum information tasks. In this paper, we demonstrate that the square of bipartite entanglement measures $G_q$-concurrence, which is the generalization of concurrence, follows a set of hierarchical monogamy relations for any $N$-qubit quantum state. On the basis of these monogamy inequalities, we render two kinds of hierarchical indicators that exhibit evident advantages in the capacity of witnessing entanglement. Moreover, we show an analytical relation between $G_q$-concurrence and concurrence in $2\otimes d$ systems. Furthermore, we rigorously prove that the monogamy property of squared $G_q$-concurrence is superior to that of squared concurrence in $2\otimes d_2\otimes d_3\otimes\cdots\otimes d_N$ systems. In addition, several concrete examples are provided to illustrate that for multilevel systems, the squared $G_q$-concurrence satisfies the monogamy relation, even if the squared concurrence does not. These results better reveal the intriguing characteristic of multilevel entanglement and provide critical insights into the entanglement distribution within multipartite quantum systems.

quant-ph↗