Modeling brain connectivity dynamics in functional magnetic resonance imaging via particle filtering

Interest in the studying of functional connections in the brain has grown considerably in the last decades, as many studies have pointed out that alterations in the interaction among brain areas can play a role as markers of neurological diseases. Most studies in this field treat the brain network as a system of connections stationary in time, but dynamic features of brain connectivity can provide useful information, both on physiology and pathological conditions of the brain. In this paper, we propose the application of a computational methodology, named Particle Filter (PF), to study non-stationarities in brain connectivity in functional Magnetic Resonance Imaging (fMRI). The PF algorithm estimates time-varying hidden parameters of a first-order linear time-varying Vector Autoregressive model (VAR) through a Sequential Monte Carlo strategy. On simulated time series, the PF approach effectively detected and enabled to follow time-varying hidden parameters and it captured causal relationships among signals. The method was also applied to real fMRI data, acquired in presence of periodic tactile or visual stimulations, in different sessions. On these data, the PF estimates were consistent with current knowledge on brain functioning. Most importantly, the approach enabled to detect statistically significant modulations in the cause-effect relationship between brain areas, which correlated with the underlying visual stimulation pattern presented during the acquisition.

Hidden Parameters Impacting Resurgence of SARS-CoV-2 Pandemic*

The spread of the COVID-19 virus has had an enormous impact on the world’s health and socioeconomic system. While lockdowns, which severely limit the movement of the population, have been implemented in March 2020 and again recently, the psychological and economic cost are severe. Removal of these restrictions occurred with varying degrees of success.To study the resurgence of the virus in some communities we consider an epidemiological model, SIR-SD-L, that incorporates introduction of new population due to the removal of lockdown and identify parameters that impact the spread of the virus. This compartmental model of the epidemic incorporates a social distance metric based on progression of the infections; it models the dynamic propensity of infection spread based on the current infections relative to the susceptible population. The model is validated using data on growth of infections, hospitalizations and death, considering 24 counties in multiple US states and a categorization of the lockdown removal policies after the first lockdown. Model parameters, which include a compartment for the isolated population, are used to determine the rate at which the susceptible population increases to fit the rate of infections. Along with social distancing mandates, we identify active infections and the susceptible population as important factors in the resurgence of infections. We measure the efficacy of the lockdown removal policy via a ratio, PIR, which evaluates to less than 1 for counties where social distancing measures were mandated and which delayed complete re-opening of closed spaces like bars and restaurants. For other counties this ratio is greater than 1.We also studied infection growth in the 24 US counties with respect to a release policy derived from CDC guidelines and compared against strategies that delay the removal of lockdown.Our results illustrate that guidelines for deciding when lockdown rules are to be relaxed should consider the current state of the infectious population and the remaining susceptible population, hidden parameters that are deducible from models such as SIR-SD-L, and not limit policy considerations to the rate of new infections alone. This is especially true for counties where the growth rate of the virus is initially slow and misleading. Emphasis on social distancing is critical.

Modeling Brain Connectivity Dynamics in Functional Magnetic Resonance Imaging via Particle Filtering

Interest in the studying of functional connections in the brain has grown considerably in the last decades, as many studies have pointed out that these interactions can play a role as markers of neurological diseases. Most studies in this field treat the brain network as a system of connections stationary in time, but dynamic features of brain connectivity can provide useful information, both on physiology and pathological conditions of the brain. In this paper, we propose the application of a computational methodology, named Particle Filter (PF), to study non-stationarities in brain connectivity in functional Magnetic Resonance Imaging (fMRI). The PF algorithm estimates time-varying hidden parameters of a first-order linear time-varying Vector Autoregressive model (VAR) through a Sequential Monte Carlo strategy. On simulated time series, the PF approach effectively detected and enabled to follow time-varying hidden parameters and it captured causal relationships among signals. The method was also applied to real fMRI data, acquired in presence of periodic tactile or visual stimulations, in different sessions. On these data, the PF estimates were consistent with current knowledge on brain functioning. Most importantly, the approach enabled to detect statistically significant modulations in the cause-effect relationship between brain areas, which correlated with the underlying visual stimulation pattern presented during the acquisition.

Quantum Hologram of Dynamic Universe

Quantum physics and quantum cosmology were originated and remain today self-informational metric systems based on long-term multiple experiments with subsequent statistical averaging of results and spectral description of motion of material bodies and waves in subatomic and cosmic space. For the first time in scientific and engineering practice, it is logically and mathematically substantiated, experimentally, metrically and arithmetically confirmed that for the absolute assessment of the hidden parameters of the motion of matter, it is sufficient evaluate the vibrational, rotational and translational speed, as well as the amplitudes and phases of spatial displacement of a sphere with a diameter of "e" inside a sphere with a diameter of "pi", but if and only if the length of mantissa of decimally normalized fractions is at least 64 bits – to frequency 10^64 Hz, well above the Planck barrier

Analytical solution of equivalent SEIR and agent-based model of COVID-19; showing the bounds of contact tracing

Mathematical models not only forecast the possible future but also is used to find hidden parameters of the COVID-19 pandemic. Numerical estimates can inform us of both goals. Still, the interdependencies of parameters stay obscure. Many numerical solutions have been proposed so far; however, the analytical relationship between the outbreak growth, decay and equilibrium are much less studied. In this study, we have employed both an equivalent agent-based model and a Susceptible-Exposed-Infected-Recovered (SEIR)-like model to prove that the growth rate can be determined analytically in terms of other model parameters, including contact tracing rate. We identify the most sensitive parameters as undocumented transmission rate and documentation ratio. Unfortunately, these are the parameters we have the least knowledge. We derived an identity that predicts the effectiveness of contact tracing in a country from observable parameters. We underline an unavoidable dilemma: that even in the case of high contact tracing, we cannot bring the outbreak to stalemate without applying substantial quarantine; however, some countries are benefiting from contact tracing. Besides, we have shown that the seemingly same parameters of the SEIR models and agent-based models are not equivalent. We propose a correction to bridge both models.