Related papers: Temporal correlations and chaos from spacetime ker…
Identifying coherent spatiotemporal patterns generated by complex dynamical systems is a central problem in many science and engineering disciplines. Here, we combine ideas from the theory of operator-valued kernels with delay-embedding…
The spectral form factor (SFF) plays a crucial role in revealing the statistical properties of energy level distributions in complex systems. It is one of the tools to diagnose quantum chaos and unravel the universal dynamics therein. The…
Gaussian processes provide a flexible, non-parametric framework for the approximation of functions in high-dimensional spaces. The covariance kernel is the main engine of Gaussian processes, incorporating correlations that underpin the…
A kernel-based framework for spatio-temporal data analysis is introduced that applies in situations when the underlying system dynamics are governed by a dynamic equation. The key ingredient is a representer theorem that involves…
We develop a comprehensive framework for spatio-temporal prediction of time-varying vector fields using operator-valued reproducing kernel Hilbert spaces (OV RKHS). By integrating Sobolev regularity with Koopman operator theory, we…
We calculate the expectation values of the stress-energy bitensor defined at two different spacetime points $x, x'$ of a massless, minimally coupled scalar field with respect to a quantum state at finite temperature $T$ in a flat…
We show the relation between the Heisenberg averaging of regularized 2-point out-of-time ordered correlation function and the 2-point spectral form factor in bosonic quantum mechanics. The generalization to all even-point is also discussed.…
Spiking neural networks (SNNs), inspired by the spiking behavior of biological neurons, offer a distinctive approach for capturing the complexities of temporal data. However, their potential for spatial modeling in multivariate time-series…
In this paper, we develop the general formalism and properties of the spacetime density matrix, which captures correlations among different Cauchy surfaces and can be regarded as a natural generalization of the standard density matrix…
We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of…
Entanglement entropy of quantum fields in gravitational settings is a topic of growing importance. This entropy of entanglement is conventionally computed relative to Cauchy hypersurfaces where it is possible via a partial tracing to…
We develop a unified framework for computing R\'enyi and entanglement entropies of arbitrary spacetime intervals in time-dependent states of $(1+1)$-dimensional conformal field theories. By combining the spacetime density matrix formalism…
Under the frequency domain framework for weakly dependent functional time series, a key element is the spectral density kernel which encapsulates the second-order dynamics of the process. We propose a class of spectral density kernel…
Time series forecasting (TSF) remains a challenging problem due to the intricate entanglement of intraperiod-fluctuations and interperiod-trends. While recent advances have attempted to reshape 1D sequences into 2D period-phase…
We introduce a hybrid approach for computing dynamical observables in strongly correlated systems using higher-order moments. This method integrates memory kernel coupling theory (MKCT) with the density matrix renormalization group (DMRG),…
We investigate timelike entanglement measures derived from the spacetime density kernel in the Rosenzweig-Porter model and show that they sharply diagnose both eigenvector ergodicity and spectral chaos. For several Hilbert-space…
High order correlations in the cosmic matter density have become increasingly valuable in cosmological analyses. However, computing such correlation functions is computationally expensive. We aim to circumvent these challenges by designing…
In this paper I propose a branch point twist field approach to computing a temporal entropy, that is, an entanglement measure across different time regions, as opposed to the usual spacial measures. I discuss how the shift to…
Sequential deep learning models such as RNN, causal CNN and attention mechanism do not readily consume continuous-time information. Discretizing the temporal data, as we show, causes inconsistency even for simple continuous-time processes.…
We present an improved model and theory for time-causal and time-recursive spatio-temporal receptive fields, based on a combination of Gaussian receptive fields over the spatial domain and first-order integrators or equivalently truncated…