Computational capacity of LRC, memristive, and hybrid reservoirs.

Reservoir computing is a machine learning paradigm that uses a high-dimensional dynamical system, or reservoir, to approximate and predict time series data. The scale, speed, and power usage of reservoir computers could be enhanced by constructing reservoirs out of electronic circuits, and several experimental studies have demonstrated promise in this direction. However, designing quality reservoirs requires a precise understanding of how such circuits process and store information. We analyze the feasibility and optimal design of electronic reservoirs that include both linear elements (resistors, inductors, and capacitors) and nonlinear memory elements called memristors. We provide analytic results regarding the feasibility of these reservoirs and give a systematic characterization of their computational properties by examining the types of input-output relationships that they can approximate. This allows us to design reservoirs with optimal properties. By introducing measures of the total linear and nonlinear computational capacities of the reservoir, we are able to design electronic circuits whose total computational capacity scales extensively with the system size. Our electronic reservoirs can match or exceed the performance of conventional "echo state network" reservoirs in a form that may be directly implemented in hardware.

Global minimization via classical tunneling assisted by collective force field formation.

Simple elements interacting in networks can give rise to intricate emergent behaviors. Examples such as synchronization and phase transitions often apply in many contexts, as many different systems may reduce to the same effective model. Here, we demonstrate such a behavior in a model inspired by memristors. When weakly driven, the system is described by movement in an effective potential, but when strongly driven, instabilities cause escapes from local minima, which can be interpreted as an unstable tunneling mechanism. We dub this collective and nonperturbative effect a "Lyapunov force," which steers the system toward the global minimum of the potential function, even if the full system has a constellation of equilibrium points growing exponentially with the system size. This mechanism is appealing for its physical relevance in nanoscale physics and for its possible applications in optimization, Monte Carlo schemes, and machine learning.

Conducting-insulating transition in adiabatic memristive networks.

The development of neuromorphic systems based on memristive elements-resistors with memory-requires a fundamental understanding of their collective dynamics when organized in networks. Here, we study an experimentally inspired model of two-dimensional disordered memristive networks subject to a slowly ramped voltage and show that they undergo a discontinuous transition in the conductivity for sufficiently high values of memory, as quantified by the memristive ON-OFF ratio. We investigate the consequences of this transition for the memristive current-voltage characteristics both through simulation and theory, and demonstrate the role of current-voltage duality in relating forward and reverse switching processes. Our work sheds considerable light on the statistical properties of memristive networks that are presently studied both for unconventional computing and as models of neural networks.

Predicting cognitive decline in subjects at risk for Alzheimer disease by using combined cerebrospinal fluid, MR imaging, and PET biomarkers.

PURPOSE: To assess the extent to which multiple Alzheimer disease (AD) biomarkers improve the ability to predict future decline in subjects with mild cognitive impairment (MCI) compared with predictions based on clinical parameters alone. MATERIALS AND METHODS: All protocols were approved by the institutional review board at each site, and written informed consent was obtained from all subjects. The study was HIPAA compliant. Alzheimer's Disease Neuroimaging Initiative (ADNI) baseline magnetic resonance (MR) imaging and fluorine 18 fluorodeoxyglucose (FDG) positron emission tomography (PET) studies for 97 subjects with MCI were used. MR imaging-derived gray matter probability maps and FDG PET images were analyzed by using independent component analysis, an unbiased data-driven method to extract independent sources of information from whole-brain data. The loading parameters for all MR imaging and FDG components, along with cerebrospinal fluid (CSF) proteins, were entered into logistic regression models (dependent variable: conversion to AD within 4 years). Eight models were considered, including all combinations of MR imaging, PET, and CSF markers with the covariates (age, education, apolipoprotein E genotype, Alzheimer's Disease Assessment Scale-Cognitive subscale score). RESULTS: Combining MR imaging, FDG PET, and CSF data with routine clinical tests significantly increased the accuracy of predicting conversion to AD compared with clinical testing alone. The misclassification rate decreased from 41.3% to 28.4% (P < .00001). FDG PET contributed more information to routine tests (P < .00001) than CSF (P = .32) or MR imaging (P = .08). CONCLUSION: Imaging and CSF biomarkers can improve prediction of conversion from MCI to AD compared with baseline clinical testing. FDG PET appears to add the greatest prognostic information.