Parameter estimation from an Ornstein-Uhlenbeck process with measurement noise

This article aims to investigate the impact of noise on parameter fitting for an Ornstein-Uhlenbeck process, focusing on the effects of multiplicative and thermal noise on the accuracy of signal separation. To address these issues, we propose algorithms and methods that can effectively distinguish between thermal and multiplicative noise and improve the precision of parameter estimation for optimal data analysis. Specifically, we explore the impact of both multiplicative and thermal noise on the obfuscation of the actual signal and propose methods to resolve them. Firstly, we present an algorithm that can effectively separate thermal noise with comparable performance to Hamilton Monte Carlo (HMC) but with significantly improved speed. Subsequently, we analyze multiplicative noise and demonstrate that HMC is insufficient for isolating thermal and multiplicative noise. However, we show that, with additional knowledge of the ratio between thermal and multiplicative noise, we can accurately distinguish between the two types of noise when provided with a sufficiently large sampling rate or an amplitude of multiplicative noise smaller than thermal noise. This finding results in a situation that initially seems counterintuitive. When multiplicative noise dominates the noise spectrum, we can successfully estimate the parameters for such systems after adding additional white noise to shift the noise balance.Comment: 16 pages, 4 figure

Second-Hand Stress: Neurobiological Evidence for a Human Alarm Pheromone

Alarm pheromones are airborne chemical signals, released by an individual into the environment, which transmit warning of danger to conspecifics via olfaction. Using fMRI, we provide the first neurobiological evidence for a human alarm pheromone. Individuals showed activation of the amygdala in response to sweat produced by others during emotional stress, with exercise sweat as a control; behavioral data suggest facilitated evaluation of ambiguous threat

FixFit: using parameter-compression to solve the inverse problem in overdetermined models

All fields of science depend on mathematical models. One of the fundamental problems with using complex nonlinear models is that data-driven parameter estimation often fails because interactions between model parameters lead to multiple parameter sets fitting the data equally well. Here, we develop a new method to address this problem, FixFit, which compresses a given mathematical model's parameters into a latent representation unique to model outputs. We acquire this representation by training a neural network with a bottleneck layer on data pairs of model parameters and model outputs. The bottleneck layer nodes correspond to the unique latent parameters, and their dimensionality indicates the information content of the model. The trained neural network can be split at the bottleneck layer into an encoder to characterize the redundancies and a decoder to uniquely infer latent parameters from measurements. We demonstrate FixFit in two use cases drawn from classical physics and neuroscience

Signal Fluctuation Sensitivity: An Improved Metric for Optimizing Detection of Resting-State fMRI Networks

Task-free connectivity analyses have emerged as a powerful tool in functional neuroimaging. Because the cross-correlations that underlie connectivity measures are sensitive to distortion of time-series, here we used a novel dynamic phantom to provide a ground truth for dynamic fidelity between blood oxygen level dependent (BOLD)-like inputs and fMRI outputs. We found that the de facto quality-metric for task-free fMRI, temporal signal to noise ratio (tSNR), correlated inversely with dynamic fidelity; thus, studies optimized for tSNR actually produced time-series that showed the greatest distortion of signal dynamics. Instead, the phantom showed that dynamic fidelity is reasonably approximated by a measure that, unlike tSNR, dissociates signal dynamics from scanner artifact. We then tested this measure, signal fluctuation sensitivity (SFS), against human resting-state data. As predicted by the phantom, SFS—and not tSNR—is associated with enhanced sensitivity to both local and long-range connectivity within the brain's default mode network

Chemosensory Cues to Conspecific Emotional Stress Activate Amygdala in Humans

Alarm substances are airborne chemical signals, released by an individual into the environment, which communicate emotional stress between conspecifics. Here we tested whether humans, like other mammals, are able to detect emotional stress in others by chemosensory cues. Sweat samples collected from individuals undergoing an acute emotional stressor, with exercise as a control, were pooled and presented to a separate group of participants (blind to condition) during four experiments. In an fMRI experiment and its replication, we showed that scanned participants showed amygdala activation in response to samples obtained from donors undergoing an emotional, but not physical, stressor. An odor-discrimination experiment suggested the effect was primarily due to emotional, and not odor, differences between the two stimuli. A fourth experiment investigated behavioral effects, demonstrating that stress samples sharpened emotion-perception of ambiguous facial stimuli. Together, our findings suggest human chemosensory signaling of emotional stress, with neurobiological and behavioral effects

Electrostatically Self-assembled Amphiplexes

This research will focus on characterizing the phase behavior of polyelectrolyte-surfactant microemulsions (PSM) that were recently discovered in our lab and indentifing possible uses of their long-range ordered nanostructures towards bioseparation, oil-recovery and drug delivery systems. In addition, we are proposing strategies for synthesizing solid and long-range ordered materials with unit cells on the nanometer scale using polymerization and/or cross-linking to solidify the soft template