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The Hamiltonian Monte Carlo (HMC) algorithm is a powerful Markov Chain Monte Carlo (MCMC) method that uses Hamiltonian dynamics to generate samples from a target distribution. To fully exploit its potential, we must understand how…
Recently, the full version of the Eigenstate Thermalization Hypothesis (ETH) has been systematized using Free Probability. In this paper, we present a detailed discussion of the Free Cumulants approach to many-body dynamics within the…
Functional mixed models are widely useful for regression analysis with dependent functional data, including longitudinal functional data with scalar predictors. However, existing algorithms for Bayesian inference with these models only…
Multimodal image fusion aims to integrate information from different imaging techniques to produce a comprehensive, detail-rich single image for downstream vision tasks. Existing methods based on local convolutional neural networks (CNNs)…
Conventional Magnetic Resonance Imaging (MRI) is hampered by long scan times and only qualitative image contrasts that prohibit a direct comparison between different systems. To address these limitations, model-based reconstructions…
The restricted Boltzmann machine (RBM) is a two-layer energy-based model that uses its hidden-visible connections to learn the underlying distribution of visible units, whose interactions are often complicated by high-order correlations.…
An analytical method to compute thermodynamic properties of a given Hamiltonian system is proposed. This method combines ideas of both dynamical systems and ensemble approaches to thermodynamics, providing de facto a possible alternative to…
The hierarchical equations of motion (HEOM) for a generalized quantum dissipative system is rigorously constructed in the frameworks of two different stochastic dynamical descriptions, i.e., the non-Markovian quantum state diffusion…
Spatial covariance matrix (SCM) is essential in many applications of multi-antenna systems such as massive multiple-input multiple-output (MIMO). For massive MIMO operating at millimeter-wave bands, hybrid analog-digital structure has been…
In this paper, we review the physical concepts of the nonequilibrium techniques for the calculation of free energies applied to magnetic systems using Monte Carlo simulations of different nonequilibrium processes. The methodology allows the…
Variational quantum algorithms are considered one of the most promising methods for obtaining near-term quantum advantages; however, most of these algorithms are only expressed in the conventional quantum circuit scheme. The roadblock to…
In classical canonical correlation analysis (CCA), the goal is to determine the linear transformations of two random vectors into two new random variables that are most strongly correlated. Canonical variables are pairs of these new random…
Stochastic models of varying complexity have been proposed to describe the dispersion of particles in turbulent flows, from simple Brownian motion to complex temporally and spatially correlated models. A method is needed to compare…
In this work we propose a Bayesian framework for data fusion of multivariate signals which arises in imaging systems. More specifically, we consider the case where we have observed two images of the same object through two different imaging…
One of the most tantalizing results from the WMAP experiment is the suggestion that the power at large scales is anomalously low when compared to the prediction of the ``standard'' Lambda-CDM model. The same anomaly, although with somewhat…
We study 1D Hamilton systems with homogeneous power law potential and their statistical behaviour, assuming the microcanonical distribution of the initial conditions and describing its change under monotonically increasing time-dependent…
Crucial to many measurements at the LHC is the use of correlated multi-dimensional information to distinguish rare processes from large backgrounds, which is complicated by the poor modeling of many of the crucial backgrounds in Monte Carlo…
In any valid Monte Carlo sampling that realizes microcanonical property we can collect statistics for a transition matrix in energy. This matrix is used to determine the density of states, from which most of the thermodynamical averages can…
Hamiltonian Monte Carlo (HMC) and related algorithms have become routinely used in Bayesian computation. In this article, we present a simple and provably accurate method to improve the efficiency of HMC and related algorithms with…
Missingness is a common issue for neuroimaging data, and neglecting it in downstream statistical analysis can introduce bias and lead to misguided inferential conclusions. It is therefore crucial to conduct appropriate statistical methods…