Koopman learning with episodic memory.

Koopman operator theory has found significant success in learning models of complex, real-world dynamical systems, enabling prediction and control. The greater interpretability and lower computational costs of these models, compared to traditional machine learning methodologies, make Koopman learning an especially appealing approach. Despite this, little work has been performed on endowing Koopman learning with the ability to leverage its own failures.

A Koopman operator-based prediction algorithm and its application to COVID-19 pandemic and influenza cases.

Future state prediction for nonlinear dynamical systems is a challenging task. Classical prediction theory is based on a, typically long, sequence of prior observations and is rooted in assumptions on statistical stationarity of the underlying stochastic process. These algorithms have trouble predicting chaotic dynamics, "Black Swans" (events which have never previously been seen in the observed data), or systems where the underlying driving process fundamentally changes.

Predicting the Critical Number of Layers for Hierarchical Support Vector Regression.

Hierarchical support vector regression (HSVR) models a function from data as a linear combination of SVR models at a range of scales, starting at a coarse scale and moving to finer scales as the hierarchy continues. In the original formulation of HSVR, there were no rules for choosing the depth of the model. In this paper, we observe in a number of models a phase transition in the training error-the error remains relatively constant as layers are added, until a critical scale is passed, at which point the training error drops close to zero and remains nearly constant for added layers.

Exponentially decaying modes and long-term prediction of sea ice concentration using Koopman mode decomposition.

Sea ice cover in the Arctic and Antarctic is an important indicator of changes in the climate, with important environmental, economic and security consequences. The complexity of the spatio-temporal dynamics of sea ice makes it difficult to assess the temporal nature of the changes-e.g.

Koopman Mode Analysis of agent-based models of logistics processes.

Modern logistics processes and systems can feature extremely complicated dynamics. Agent Based Modeling is emerging as a powerful modeling tool for design, analysis and control of such logistics systems. However, the complexity of the model itself can be overwhelming and mathematical meta-modeling tools are needed that aggregate information and enable fast and accurate decision making and control system design.

An agent-based model of urban insurgence: Effect of gathering sites and Koopman mode analysis.

The paper investigates the effect of preferential gathering sites on urban insurgency in an agent-based model (ABM). The ABM model was proposed in earlier work and has been validated using FBI data. There is a nonlinear tradeoff between the local density of citizens due to the number of preferential gathering sites and the ability of law enforcement officers (LEOs) to adequately patrol that leads to a non-monotonic behavior in the number of large scale outburst of insurgency with respect to the number of gathering sites.

The Translational Value of Psychophysiology Methods and Mechanisms: Multilevel, Dynamic, Personalized.

Objective: It has been nearly 15 years since Kazdin and Nock published methodological and research recommendations for understanding mechanisms of change in child and adolescent therapy. Their arguments and enthusiasm for research on mechanisms of behavior change (MOBCs) resonated across disciplines and disorders, as it shined a light on the crucial importance of understanding how and for whom treatments instigate behavior change and how therapeutic mechanisms might be extended to "situations and settings of everyday life." Initial efforts focused on how psychotherapy works and linear models, yet the use of theory to guide the study of mechanisms, and laboratory experiments to manipulate them, is broadly applicable.

A computational physiology approach to personalized treatment models: the beneficial effects of slow breathing on the human cardiovascular system.

Heart rate variability biofeedback intervention involves slow breathing at a rate of ∼6 breaths/min (resonance breathing) to maximize respiratory and baroreflex effects on heart period oscillations. This intervention has wide-ranging clinical benefits and is gaining empirical support as an adjunct therapy for biobehavioral disorders, including asthma and depression. Yet, little is known about the system-level cardiovascular changes that occur during resonance breathing or the extent to which individuals differ in cardiovascular benefit.

Model reduction for agent-based social simulation: coarse-graining a civil violence model.

Agent-based modeling (ABM) constitutes a powerful computational tool for the exploration of phenomena involving emergent dynamic behavior in the social sciences. This paper demonstrates a computer-assisted approach that bridges the significant gap between the single-agent microscopic level and the macroscopic (coarse-grained population) level, where fundamental questions must be rationally answered and policies guiding the emergent dynamics devised. Our approach will be illustrated through an agent-based model of civil violence.

The redistribution of power: neurocardiac signaling, alcohol and gender.

Human adaptability involves interconnected biological and psychological control processes that determine how successful we are in meeting internal and environmental challenges. Heart rate variability (HRV), the variability in consecutive R-wave to R-wave intervals (RRI) of the electrocardiogram, captures synergy between the brain and cardiovascular control systems that modulate adaptive responding. Here we introduce a qualitatively new dimension of adaptive change in HRV quantified as a redistribution of spectral power by applying the Wasserstein distance with exponent 1 metric (W(1)) to RRI spectral data.