Unbiased and efficient sampling of timeseries reveals redundancy of brain network and gradient structure.

Many studies in human neuroscience seek to understand the structure of brain networks and gradients. Few studies, however, have tested the redundancy between these outwardly distinct features. Here, we developed methods to directly enable such tests. We built on insights from linear algebra to develop methods for unbiased and efficient sampling of timeseries with network or gradient constraints. We used these methods to show considerable redundancy between popular definitions of network and gradient structure in functional MRI data. On the one hand, we found that network constraints largely accounted for the structure of three major gradients. On the other hand, we found that gradient constraints largely accounted for the structure of seven major networks. Our results imply that some networks and gradients may denote discrete and continuous representations of the same aspects of functional MRI data. We suggest that integrated explanations can reduce redundancy by avoiding the attribution of independent existence or function to these features.

Time-resolved correlation of distributed brain activity tracks E-I balance and accounts for diverse scale-free phenomena.

Much of systems neuroscience posits the functional importance of brain activity patterns that lack natural scales of sizes, durations, or frequencies. The field has developed prominent, and sometimes competing, explanations for the nature of this scale-free activity. Here, we reconcile these explanations across species and modalities. First, we link estimates of excitation-inhibition (E-I) balance with time-resolved correlation of distributed brain activity. Second, we develop an unbiased method for sampling time series constrained by this time-resolved correlation. Third, we use this method to show that estimates of E-I balance account for diverse scale-free phenomena without need to attribute additional function or importance to these phenomena. Collectively, our results simplify existing explanations of scale-free brain activity and provide stringent tests on future theories that seek to transcend these explanations.

One-way sound propagation via spatio-temporal modulation of magnetorheological fluid.

This manuscript details the possibility of achieving one-way sound propagation using a smart fluid such as magnetorheological fluid (MRF) by subjecting it to a spatio-temporally varying magnetic field. The local speed of sound in MRF is dependent on applied magnetic field as demonstrated in several experimental works and this property of MRF has been leveraged, in this work, to induce one-way bandgaps. Initially, a general wave equation pertaining to fluid with space-and-time-varying material properties was derived. Assuming plane wave propagation in one dimension, an approximate Floquet solution was imposed and the dispersion relationship was obtained. A comprehensive finite element analysis was conducted and good agreement was noted between the numerical and theoretical dispersion relations. It was concluded that space-time periodic modulation of fluid density and local sound speed is necessary to induce asymmetry in the band diagram around the ω axis. The feasibility of real-world implementation using MRF has been discussed. A parametric study detailing the effect of viscosity on the one-way bandgaps has been undertaken. It was found that one-way bandgaps formed at relatively lower frequencies are more robust to viscous corruption. A real-world implementation may be feasible if the viscosity of MRF is less than 3000 Pa-s.

Conjugate unscented transformation-based uncertainty analysis of energy harvesters.

This article presents a probabilistic approach to investigate the effect of parametric uncertainties on the mean power, tip deflection, and tip velocity of linear and nonlinear energy harvesting systems. Recently developed conjugate unscented transformation algorithm is used to compute the statistical moments of the output variables with multidimensional Gaussian uncertainty in parameters. The principle of maximum entropy is used to construct the probability density function of output variables from the knowledge of obtained statistical moments. The probability density functions for mean power were significantly complicated in shape with two and three distinct peaks for the nonlinear monostable and nonlinear bistable harvesters, respectively. Monte-Carlo simulations with N = 8 × 104 samples for monostable harvester and N = 6.5 × 104 samples for bistable harvester were used for validating the probability density functions. It is concluded that conjugate unscented transformation methodology affords a significant computational advantage without compromising accuracy. In addition, using conjugate unscented transformation method, we show that the dependence of mean power on parameters (excitation frequency, excitation amplitude, etc.), when multidimensional uncertainties are present, is decidedly different relative to a purely deterministic trend. The discrepancy in predicted power between the deterministic and uncertain trends for the monostable harvester, for instance, reach a maximum of 100%, 234%, and 110% for base frequency, base acceleration, and magnet gap, respectively. The deterministic trend consistently overestimates the harvested power relative to the uncertain trends. This work, therefore, may have applications in evaluating "worst case scenario" for harvested power. The major advantage of the presented methodology relative to extant techniques in energy harvesting literature is the accurate and computationally effective applicability to multidimensional uncertainty in parameters.