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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. Here we present Koopman Mode Analysis (KMA) as such a tool. KMA uncovers exponentially growing, decaying or oscillating collective patterns in dynamical data. We apply the methodology to two problems, both of which exhibit a bifurcation in dynamical behavior, but feature very different dynamics: Medical Treatment Facility (MTF) logistics and ship fueling (SF) logistics. The MTF problem features a transition between efficient operation at low casualty rates and inefficient operation beyond a critical casualty rate, while the SF problem features a transition between short mission life at low initial fuel levels and sustained mission beyond a critical initial fuel level. Both bifurcations are detected by analyzing the spectrum of the associated Koopman operator. Mathematical analysis is provided justifying the use of the Dynamic Mode Decomposition algorithm in punctuated linear decay dynamics that is featured in the SF problem.

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 inclusion of a moderate number of sites decreases the number of large-scale outbursts. Having no gathering sites or a large number of gathering sites has a dilutive effect on the number of large-scale outbursts. Thus, this non-monotonicity indicates that a small number of organized units produces a larger insurgency effect than a larger number of distributed units. It is also shown, using Koopman mode analysis, that the spatial morphology of agents due to the gathering sites gives rise to temporal organization of the model dynamics; there is a prominent quasi-periodic component in the number of active and intimidated citizens and in the spatial distribution of the LEOs.

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. We further derived a new index, D, to specify the direction of spectral redistribution and clarify physiological interpretation. We examined gender differences in real time RRI spectral power response to alcohol, placebo and visual cue challenges. Adaptive changes were observed as changes in power of the various spectral frequency bands (i.e., standard frequency domain HRV indices) and, during both placebo and alcohol intoxication challenges, as changes in the structure (shape) of the RRI spectrum, with a redistribution towards lower frequency oscillations. The overall conclusions from the present study are that the RRI spectrum is capable of a fluid and highly flexible response, even when oscillations (and thus activity at the sinoatrial node) are pharmacologically suppressed, and that low frequency oscillations serve a crucial but less studied role in physical and mental health.