Optimal phase-selective entrainment of electrochemical oscillators with different phase response curves.

We investigate the entrainment of electrochemical oscillators with different phase response curves (PRCs) using a global signal: the goal is to achieve the desired phase configuration using a minimum-power waveform. Establishing the desired phase relationships in a highly nonlinear networked system exhibiting significant heterogeneities, such as different conditions or parameters for the oscillators, presents a considerable challenge because different units respond differently to the common global entraining signal. In this work, we apply an optimal phase-selective entrainment technique in both a kinetic model and experiments involving electrochemical oscillators in achieving phase synchronized states. We estimate the PRCs of the oscillators at different circuit potentials and external resistance, and entrain pairs and small sets of four oscillators in various phase configurations. We show that for small PRC variations, phase assignment can be achieved using an averaged PRC in the control design. However, when the PRCs are sufficiently different, individual PRCs are needed to entrain the system with the expected phase relationships. The results show that oscillator assemblies with heterogeneous PRCs can be effectively entrained to desired phase configurations in practical settings. These findings open new avenues to applications in biological and engineered oscillator systems where synchronization patterns are essential for system performance.

A moment-based Kalman filtering approach for estimation in ensemble systems.

A persistent challenge in tasks involving large-scale dynamical systems, such as state estimation and error reduction, revolves around processing the collected measurements. Frequently, these data suffer from the curse of dimensionality, leading to increased computational demands in data processing methodologies. Recent scholarly investigations have underscored the utility of delineating collective states and dynamics via moment-based representations. These representations serve as a form of sufficient statistics for encapsulating collective characteristics, while simultaneously permitting the retrieval of individual data points. In this paper, we reshape the Kalman filter methodology, aiming its application in the moment domain of an ensemble system and developing the basis for moment ensemble noise filtering. The moment system is defined with respect to the normalized Legendre polynomials, and it is shown that its orthogonal basis structure introduces unique benefits for the application of Kalman filter for both i.i.d. and universal Gaussian disturbances. The proposed method thrives from the reduction in problem dimension, which is unbounded within the state-space representation, and can achieve significantly smaller values when converted to the truncated moment-space. Furthermore, the robustness of moment data toward outliers and localized inaccuracies is an additional positive aspect of this approach. The methodology is applied for an ensemble of harmonic oscillators and units following aircraft dynamics, with results showcasing a reduction in both cumulative absolute error and covariance with reduced calculation cost due to the realization of operations within the moment framework conceived.

Identification of network interactions from time series data: An iterative approach.

The first step toward advancing our understanding of complex networks involves determining their connectivity structures from the time series data. These networks are often high-dimensional, and in practice, only a limited amount of data can be collected. In this work, we formulate the network inference task as a bilinear optimization problem and propose an iterative algorithm with sequential initialization to solve this bilinear program. We demonstrate the scalability of our approach to network size and its robustness against measurement noise, hyper-parameter variation, and deviations from the network model. Results across experimental and simulated datasets, comprising oscillatory, non-oscillatory, and chaotic dynamics, showcase the superior inference accuracy of our technique compared to existing methods.

Data-driven control of oscillator networks with population-level measurement.

Controlling complex networks of nonlinear limit-cycle oscillators is an important problem pertinent to various applications in engineering and natural sciences. While in recent years the control of oscillator populations with comprehensive biophysical models or simplified models, e.g., phase models, has seen notable advances, learning appropriate controls directly from data without prior model assumptions or pre-existing data remains a challenging and less developed area of research. In this paper, we address this problem by leveraging the network's current dynamics to iteratively learn an appropriate control online without constructing a global model of the system. We illustrate through a range of numerical simulations that the proposed technique can effectively regulate synchrony in various oscillator networks after a small number of trials using only one input and one noisy population-level output measurement. We provide a theoretical analysis of our approach, illustrate its robustness to system variations, and compare its performance with existing model-based and data-driven approaches.

Finding influential nodes in networks using pinning control: Centrality measures confirmed with electrochemical oscillators.

The spatiotemporal organization of networks of dynamical units can break down resulting in diseases (e.g., in the brain) or large-scale malfunctions (e.g., power grid blackouts). Re-establishment of function then requires identification of the optimal intervention site from which the network behavior is most efficiently re-stabilized. Here, we consider one such scenario with a network of units with oscillatory dynamics, which can be suppressed by sufficiently strong coupling and stabilizing a single unit, i.e., pinning control. We analyze the stability of the network with hyperbolas in the control gain vs coupling strength state space and identify the most influential node (MIN) as the node that requires the weakest coupling to stabilize the network in the limit of very strong control gain. A computationally efficient method, based on the Moore-Penrose pseudoinverse of the network Laplacian matrix, was found to be efficient in identifying the MIN. In addition, we have found that in some networks, the MIN relocates when the control gain is changed, and thus, different nodes are the most influential ones for weakly and strongly coupled networks. A control theoretic measure is proposed to identify networks with unique or relocating MINs. We have identified real-world networks with relocating MINs, such as social and power grid networks. The results were confirmed in experiments with networks of chemical reactions, where oscillations in the networks were effectively suppressed through the pinning of a single reaction site determined by the computational method.

Synchronization, clustering, and weak chimeras in a densely coupled transcription-based oscillator model for split circadian rhythms.

The synchronization dynamics for the circadian gene expression in the suprachiasmatic nucleus is investigated using a transcriptional circadian clock gene oscillator model. With global coupling in constant dark (DD) conditions, the model exhibits a one-cluster phase synchronized state, in dim light (dim LL), bistability between one- and two-cluster states and in bright LL, a two-cluster state. The two-cluster phase synchronized state, where some oscillator pairs synchronize in-phase, and some anti-phase, can explain the splitting of the circadian clock, i.e., generation of two bouts of daily activities with certain species, e.g., with hamsters. The one- and two-cluster states can be reached by transferring the animal from DD or bright LL to dim LL, i.e., the circadian synchrony has a memory effect. The stability of the one- and two-cluster states was interpreted analytically by extracting phase models from the ordinary differential equation models. In a modular network with two strongly coupled oscillator populations with weak intragroup coupling, with appropriate initial conditions, one group is synchronized to the one-cluster state and the other group to the two-cluster state, resulting in a weak-chimera state. Computational modeling suggests that the daily rhythms in sleep-wake depend on light intensity acting on bilateral networks of suprachiasmatic nucleus (SCN) oscillators. Addition of a network heterogeneity (coupling between the left and right SCN) allowed the system to exhibit chimera states. The simulations can guide experiments in the circadian rhythm research to explore the effect of light intensity on the complexities of circadian desynchronization.

A moment kernel machine for clinical data mining to inform medical decision making.

Machine learning-aided medical decision making presents three major challenges: achieving model parsimony, ensuring credible predictions, and providing real-time recommendations with high computational efficiency. In this paper, we formulate medical decision making as a classification problem and develop a moment kernel machine (MKM) to tackle these challenges. The main idea of our approach is to treat the clinical data of each patient as a probability distribution and leverage moment representations of these distributions to build the MKM, which transforms the high-dimensional clinical data to low-dimensional representations while retaining essential information. We then apply this machine to various pre-surgical clinical datasets to predict surgical outcomes and inform medical decision making, which requires significantly less computational power and time for classification while yielding favorable performance compared to existing methods. Moreover, we utilize synthetic datasets to demonstrate that the developed moment-based data mining framework is robust to noise and missing data, and achieves model parsimony giving an efficient way to generate satisfactory predictions to aid personalized medical decision making.

Engineering spatiotemporal patterns: information encoding, processing, and controllability in oscillator ensembles.

The ability to finely manipulate spatiotemporal patterns displayed in neuronal populations is critical for understanding and influencing brain functions, sleep cycles, and neurological pathologies. However, such control tasks are challenged not only by the immense scale but also by the lack of real-time state measurements of neurons in the population, which deteriorates the control performance. In this paper, we formulate the control of dynamic structures in an ensemble of neuron oscillators as a tracking problem and propose a principled control technique for designing optimal stimuli that produce desired spatiotemporal patterns in a network of interacting neurons without requiring feedback information. We further reveal an interesting presentation of information encoding and processing in a neuron ensemble in terms of its controllability property. The performance of the presented technique in creating complex spatiotemporal spiking patterns is demonstrated on neural populations described by mathematically ideal and biophysical models, including the Kuramoto and Hodgkin-Huxley models, as well as real-time experiments on Wein bridge oscillators.

Moment-Based Reinforcement Learning for Ensemble Control.

Problems involving controlling the collective behavior of a population of structurally similar dynamical systems, the so-called ensemble control, arise in diverse emerging applications and pose a grand challenge in systems science and control engineering. Owing to the severely under-actuated nature and the difficulty of placing large-scale sensor networks, ensemble systems are limited to being actuated and monitored at the population level. Moreover, mathematical models describing the dynamics of ensemble systems are often elusive. Therefore, it is essential to design broadcast controls that excite the entire population in such a way that the heterogeneity in system dynamics is robustly compensated. In this article, we propose a reinforcement learning (RL)-based data-driven control framework incorporating population-level aggregated measurement data to learn a global control signal for steering a dynamic population in the desired manner. In particular, we introduce the notion of ensemble moments induced by aggregated measurements and derive the associated moment system to the original ensemble system. Then, using the moment system, we learn an approximation of optimal value functions and the associated policies in terms of ensemble moments through RL. We illustrate the feasibility and scalability of the proposed moment-based approach via numerical experiments using a population of linear, bilinear, and nonlinear dynamic ensemble systems. We report that the proposed method achieves the desired control objectives of various ensemble control tasks and obtains significantly better averaged-reward when compared with three existing methods.

Data-Driven Control of Neuronal Networks with Population-Level Measurement.

Controlling complex networks of nonlinear neurons is an important problem pertinent to various applications in engineering and natural sciences. While in recent years the control of neural populations with comprehensive biophysical models or simplified models, e.g., phase models, has seen notable advances, learning appropriate controls directly from data without any model assumptions remains a challenging and less developed area of research. In this paper, we address this problem by leveraging the network's local dynamics to iteratively learn an appropriate control without constructing a global model of the system. The proposed technique can effectively regulate synchrony in a neuronal network using only one input and one noisy population-level output measurement. We provide a theoretical analysis of our approach and illustrate its robustness to system variations and its generalizability to accommodate various physical constraints, such as charge-balanced inputs.

Interpretable Design of Reservoir Computing Networks Using Realization Theory.

The reservoir computing networks (RCNs) have been successfully employed as a tool in learning and complex decision-making tasks. Despite their efficiency and low training cost, practical applications of RCNs rely heavily on empirical design. In this article, we develop an algorithm to design RCNs using the realization theory of linear dynamical systems. In particular, we introduce the notion of α -stable realization and provide an efficient approach to prune the size of a linear RCN without deteriorating the training accuracy. Furthermore, we derive a necessary and sufficient condition on the irreducibility of the number of hidden nodes in linear RCNs based on the concepts of controllability and observability from systems theory. Leveraging the linear RCN design, we provide a tractable procedure to realize RCNs with nonlinear activation functions. We present numerical experiments on forecasting time-delay systems and chaotic systems to validate the proposed RCN design methods and demonstrate their efficacy.

Optimal phase-selective entrainment of heterogeneous oscillator ensembles.

We develop a framework to design optimal entrainment signals that entrain an ensemble of heterogeneous nonlinear oscillators, described by phase models, at desired phases. We explicitly take into account heterogeneity in both oscillation frequency and the type of oscillators characterized by different Phase Response Curves. The central idea is to leverage the Fourier series representation of periodic functions to decode a phase-selective entrainment task into a quadratic program. We demonstrate our approach using a variety of phase models, where we entrain the oscillators into distinct phase patterns. Also, we show how the generalizability gained from our formulation enables us to meet a wide range of design objectives and constraints, such as minimum-power, fast entrainment, and charge-balanced controls.

Data-Efficient Inference of Nonlinear Oscillator Networks.

Decoding the connectivity structure of a network of nonlinear oscillators from measurement data is a difficult yet essential task for understanding and controlling network functionality. Several data-driven network inference algorithms have been presented, but the commonly considered premise of ample measurement data is often difficult to satisfy in practice. In this paper, we propose a data-efficient network inference technique by combining correlation statistics with the model-fitting procedure. The proposed approach can identify the network structure reliably in the case of limited measurement data. We compare the proposed method with existing techniques on a network of Stuart-Landau oscillators, oscillators describing circadian gene expression, and noisy experimental data obtained from Rössler Electronic Oscillator network.

Deep multi-modal learning for joint linear representation of nonlinear dynamical systems.

Dynamical systems pervasively seen in most real-life applications are complex and behave by following certain evolution rules or dynamical patterns, which are linear, non-linear, or stochastic. The underlying dynamics (or evolution rule) of such complex systems, if found, can be used for understanding the system behavior, and furthermore for system prediction and control. It is common to analyze the system's dynamics through observations in different modality approaches. For instance, to recognize patient deterioration in acute care, it usually relies on monitoring and analyzing vital signs and other observations, such as blood pressure, heart rate, respiration, and electroencephalography. These observations convey the information describing the same target system, but the dynamics is not able to be directly characterized due to high complexity of individual modality and maybe time-delay interactions among modalities. In this work, we suppose that the state behavior of a dynamical system follows an intrinsic dynamics shared among these modalities. We specifically propose a new deep auto-encoder framework using the Koopman operator theory to derive the joint linear dynamics for a target system in a space spanned by the intrinsic coordinates. The proposed method aims to reconstruct the original system states by learning the information provided among multiple modalities. Furthermore, with the derived intrinsic dynamics, our method is capable of restoring the missing observations within and across modalities, and used for predicting the future states of the system that follows the same evolution rule.

Model Learning and Knowledge Sharing for Cooperative Multiagent Systems in Stochastic Environment.

An imposing task for a reinforcement learning agent in an uncertain environment is to expeditiously learn a policy or a sequence of actions, with which it can achieve the desired goal. In this article, we present an incremental model learning scheme to reconstruct the model of a stochastic environment. In the proposed learning scheme, we introduce a clustering algorithm to assimilate the model information and estimate the probability for each state transition. In addition, utilizing the reconstructed model, we present an experience replay strategy to create virtual interactive experiences by incorporating a balance between exploration and exploitation, which greatly accelerates learning and enables planning. Furthermore, we extend the proposed learning scheme for a multiagent framework to decrease the effort required for exploration and to reduce the learning time in a large environment. In this multiagent framework, we introduce a knowledge-sharing algorithm to share the reconstructed model information among the different agents, as needed, and develop a computationally efficient knowledge fusing mechanism to fuse the knowledge acquired using the agents' own experience with the knowledge received from its teammates. Finally, the simulation results with comparative analysis are provided to demonstrate the efficacy of the proposed methods in the complex learning tasks.

Parallel residual projection: a new paradigm for solving linear inverse problems.

A grand challenge to solve a large-scale linear inverse problem (LIP) is to retain computational efficiency and accuracy regardless of the growth of the problem size. Despite the plenitude of methods available for solving LIPs, various challenges have emerged in recent times due to the sheer volume of data, inadequate computational resources to handle an oversized problem, security and privacy concerns, and the interest in the associated incremental or decremental problems. Removing these barriers requires a holistic upgrade of the existing methods to be computationally efficient, tractable, and equipped with scalable features. We, therefore, develop the parallel residual projection (PRP), a parallel computational framework involving the decomposition of a large-scale LIP into sub-problems of low complexity and the fusion of the sub-problem solutions to form the solution to the original LIP. We analyze the convergence properties of the PRP and accentuate its benefits through its application to complex problems of network inference and gravimetric survey. We show that any existing algorithm for solving an LIP can be integrated into the PRP framework and used to solve the sub-problems while handling the prevailing challenges.

Diffusion Histology Imaging Combining Diffusion Basis Spectrum Imaging (DBSI) and Machine Learning Improves Detection and Classification of Glioblastoma Pathology.

PURPOSE: Glioblastoma (GBM) is one of the deadliest cancers with no cure. While conventional MRI has been widely adopted to examine GBM clinically, accurate neuroimaging assessment of tumor histopathology for improved diagnosis, surgical planning, and treatment evaluation remains an unmet need in the clinical management of GBMs. EXPERIMENTAL DESIGN: We employ a novel diffusion histology imaging (DHI) approach, combining diffusion basis spectrum imaging (DBSI) and machine learning, to detect, differentiate, and quantify areas of high cellularity, tumor necrosis, and tumor infiltration in GBM. RESULTS: Gadolinium-enhanced T1-weighted or hyperintense fluid-attenuated inversion recovery failed to reflect the morphologic complexity underlying tumor in patients with GBM. Contrary to the conventional wisdom that apparent diffusion coefficient (ADC) negatively correlates with increased tumor cellularity, we demonstrate disagreement between ADC and histologically confirmed tumor cellularity in GBM specimens, whereas DBSI-derived restricted isotropic diffusion fraction positively correlated with tumor cellularity in the same specimens. By incorporating DBSI metrics as classifiers for a supervised machine learning algorithm, we accurately predicted high tumor cellularity, tumor necrosis, and tumor infiltration with 87.5%, 89.0%, and 93.4% accuracy, respectively. CONCLUSIONS: Our results suggest that DHI could serve as a favorable alternative to current neuroimaging techniques in guiding biopsy or surgery as well as monitoring therapeutic response in the treatment of GBM.

Real-time Inference and Detection of Disruptive EEG Networks for Epileptic Seizures.

Recent studies in brain science and neurological medicine paid a particular attention to develop machine learning-based techniques for the detection and prediction of epileptic seizures with electroencephalogram (EEG). As a noninvasive monitoring method to record brain electrical activities, EEG has been widely used for capturing the underlying dynamics of disruptive neuronal responses across the brain in real-time to provide clinical guidance in support of epileptic seizure treatments in practice. In this study, we introduce a novel dynamic learning method that first infers a time-varying network constituted by multivariate EEG signals, which represents the overall dynamics of the brain network, and subsequently quantifies its topological property using graph theory. We demonstrate the efficacy of our learning method to detect relatively strong synchronization (characterized by the algebraic connectivity metric) caused by abnormal neuronal firing during a seizure onset. The computational results for a realistic scalp EEG database show a detection rate of 93.6% and a false positive rate of 0.16 per hour (FP/h); furthermore, our method observes potential pre-seizure phenomena in some cases.

Learning to Control Neurons using Aggregated Measurements.

Controlling a population of neurons with one or a few control signals is challenging due to the severely underactuated nature of the control system and the inherent nonlinear dynamics of the neurons that are typically unknown. Control strategies that incorporate deep neural networks and machine learning techniques directly use data to learn a sequence of control actions for targeted manipulation of a population of neurons. However, these learning strategies inherently assume that perfect feedback data from each neuron at every sampling instant are available, and do not scale gracefully as the number of neurons in the population increases. As a result, the learning models need to be retrained whenever such a change occurs. In this work, we propose a learning strategy to design a control sequence by using population-level aggregated measurements and incorporate reinforcement learning techniques to find a (bounded, piecewise constant) control policy that fulfills the given control task. We demonstrate the feasibility of the proposed approach using numerical experiments on a finite population of nonlinear dynamical systems and canonical phase models that are widely used in neuroscience.

Biophysically interpretable inference of single neuron dynamics.

Identification of key ionic channel contributors to the overall dynamics of a neuron is an important problem in experimental neuroscience. Such a problem is challenging since even in the best cases, identification relies on noisy recordings of membrane potential only, and strict inversion to the constituent channel dynamics is mathematically ill-posed. In this work, we develop a biophysically interpretable, learning-based strategy for data-driven inference of neuronal dynamics. In particular, we propose two optimization frameworks to learn and approximate neural dynamics from an observed voltage trajectory. In both the proposed strategies, the membrane potential dynamics are approximated as a weighted sum of ionic currents. In the first strategy, the ionic currents are represented using voltage dependent channel conductances and membrane potential in a parametric form, while in the second strategy, the currents are represented as a linear combination of generic basis functions. A library of channel activation/inactivation and time-constant curves describing prototypical channel kinetics are used to provide estimates of the channel variables to approximate the ionic currents. Finally, a linear optimization problem is solved to infer the weights/scaling variables in the membrane-potential dynamics. In the first strategy, the weights can be used to recover the channel conductances, and the reversal potentials while in the second strategy, using the estimated weights, active channels can be inferred and the trajectory of the gating variables are recovered, allowing for biophysically salient inference. Our results suggest that the complex nonlinear behavior of the neural dynamics over a range of temporal scales can be efficiently inferred in a data-driven manner from noisy membrane potential recordings.