Related papers: Path Integral Approach to Uncertainties in SIR-typ…
Path integral solutions with kinetic coupling potentials $\propto p_1p_2$ are evaluated. As examples I give a Morse oscillator, i.e., a model in molecular physics, and the double pendulum in the harmonic approximation. The former is solved…
Inertial-aided systems require continuous motion excitation among other reasons to characterize the measurement biases that will enable accurate integration required for localization frameworks. This paper proposes the use of informative…
The electron motion along a chain is described by a continuum version of the Su-Schrieffer-Heeger Hamiltonian in which phonon fields and electronic coordinates are mapped onto the time scale. The path integral formalism allows us to derive…
The path integral for the propagator is expanded into a perturbation series, which can be exactly summed in the case of $\delta$-function perturbations giving a closed expression for the (energy-dependent) Green function. Making the…
Model-based iterative reconstruction (MBIR) techniques have demonstrated many advantages in X-ray CT image reconstruction. The MBIR approach is often modeled as a convex optimization problem including a data fitting function and a penalty…
We introduce a new approach to solving path-finding problems under uncertainty by representing them as probabilistic models and applying domain-independent inference algorithms to the models. This approach separates problem representation…
The intrinsic nature of a problem usually suggests a first suitable method to deal with it. Unfortunately, the apparent ease of application of these initial approaches may make their possible flaws seem to be inherent to the problem and…
Causal inference identifies cause-and-effect relationships between variables. While traditional approaches rely on data to reveal causal links, a recently developed method, assimilative causal inference (ACI), integrates observations with…
The SIR model is a classical model characterizing the spreading of infectious diseases. This model describes the time-dependent quantity changes among Susceptible, Infectious, and Recovered groups. By introducing space-depend effects such…
Radiative transfer (RT) problems in which the source function includes a scattering-like integral are typical two-points boundary problems. Their solution via differential equations implies to make hypotheses on the solution itself, namely…
Partial differential equation (PDE) models are widely used in engineering and natural sciences to describe spatio-temporal processes. The parameters of the considered processes are often unknown and have to be estimated from experimental…
Sliced inverse regression (SIR) is a popular sufficient dimension reduction method that identifies a few linear transformations of the covariates without losing regression information with the response. In high-dimensional settings, SIR can…
We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic…
In this work, we present a new approach to the construction of variational integrators. In the general case, the estimation of the action integral in a time interval $[q_k,q_{k+1}]$ is used to construct a symplectic map $(q_k,q_{k+1})\to…
The in-in path integral of a scalar field propagating in a fixed background is formulated in a suitable function space. The free kinetic operator, whose inverse gives the propagators of the in-in perturbation theory, becomes essentially…
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. We discuss analytical and numerical methods for the solution of master equations, keeping our focus on…
The simplest epidemiologic model composed by mutually exclusive compartments SIR (susceptible-infected-susceptible) is presented to describe a reality. From health concerns to situations related with marketing, informatics or even…
State estimation for hybrid systems that undergo intermittent contact with their environments, such as extraplanetary robots and satellites undergoing docking operations, is difficult due to the discrete uncertainty propagation during…
The main contribution of this paper is to develop a hierarchical Bayesian formulation of PINNs for linear inverse problems, which is called BPINN-IP. The proposed methodology extends PINN to account for prior knowledge on the nature of the…
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…