I. Perez Marino

Dissipative structures are open dynamical systems that sustain coherent macroscopic organization by continuously exchanging energy and matter with their environment and generating entropy. A recent thermodynamic analysis of the paradigmatic Malkus–Lorenz waterwheel interpreted the Lorenz system as an engine, deriving an exact formula for its thermodynamic efficiency and showing that efficiency tends to increase as the system is driven far from equilibrium while displaying sharp drops near the Hopf subcritical bifurcation to chaos. Here, we extend that single-engine framework to coupled dissipative structures. We introduce two canonical couplings—master–slave coupling (series) and symmetric diffusive coupling (parallel)—and prove two fundamental association laws allowing us to reduce the composite systems to an equivalent engine with a specified efficiency. We then apply these abstract results to coupled Lorenz waterwheels, deriving efficiency formulas consistent with the underlying power balance. We perform numerical simulations confirming that (a) series coupling induces an increase in thermodynamic efficiency, (b) parallel coupling averages the efficiency of engines and increases total energy flow, (c) synchronization is typically neutral or beneficial for efficiency except in narrow parameter regions, and (d) coupling modifies the curvature of entropy-generation trends. Our theorems suggest a mathematically rigorous and transparent route to define and compute thermodynamic efficiency for generalized flow networks, with potential application to complex systems energetics.

The problem of estimating the constant parameters of the Kuramoto-Sivashinsky (KS) equation from observed data has received attention from researchers in physics, applied mathematics, and statistics. This is motivated by the various physical applications of the equation and also because it often serves as a test model for the study of space-time pattern formation. Remarkably, most existing inference techniques rely on statistical tools, which are computationally very costly yet do not exploit the dynamical features of the system. In this paper, we introduce a simple, online parameter estimation method that relies on the synchronization properties of the KS equation. In particular, we describe a master-slave setup where the slave model is driven by observations from the master system. The slave dynamics are data-driven and designed to continuously adapt the model parameters until identical synchronization with the master system is achieved. We provide a simple analysis that supports the proposed approach and also present and discuss the results of an extensive set of computer simulations. Our numerical study shows that the proposed method is computationally fast and also robust to initialization errors, observational noise, and variations in the spatial resolution of the numerical scheme used to integrate the KS equation.

In this work we propose a machine learning (ML) method to aid in the diagnosis of schizophrenia using electroencephalograms (EEGs) as input data. The computational algorithm not only yields a proposal of diagnostic but, even more importantly, it provides additional information that admits clinical interpretation. It is based on an ML model called random forest that operates on connectivity metrics extracted from the EEG signals. Specifically, we use measures of generalized partial directed coherence (GPDC) and direct directed transfer function (dDTF) to construct the input features to the ML model. The latter allows the identification of the most performance-wise relevant features which, in turn, provide some insights about EEG signals and frequency bands that are associated with schizophrenia. Our preliminary results on real data show that signals associated with the occipital region seem to play a significant role in the diagnosis of the disease. Moreover, although every frequency band might yield useful information for the diagnosis, the beta and theta (frequency) bands provide features that are ultimately more relevant for the ML classifier that we have implemented.

Longitudinal CA125 algorithms are the current basis of ovarian cancer screening. We report on longitudinal algorithms incorporating multiple markers. In the multimodal arm of United Kingdom Collaborative Trial of Ovarian Cancer Screening (UKCTOCS), 50,640 postmenopausal women underwent annual screening using a serum CA125 longitudinal algorithm. Women (cases) with invasive tubo-ovarian cancer (WHO 2014) following outcome review with stored annual serum samples donated in the 5 years preceding diagnosis were matched 1:1 to controls (no invasive tubo-ovarian cancer) in terms of the number of annual samples and age at randomisation. Blinded samples were assayed for serum human epididymis protein 4 (HE4), CA72-4 and anti-TP53 autoantibodies. Multimarker method of mean trends (MMT) longitudinal algorithms were developed using the assay results and trial CA125 values on the training set and evaluated in the blinded validation set. The study set comprised of 1363 (2–5 per woman) serial samples from 179 cases and 181 controls. In the validation set, area under the curve (AUC) and sensitivity of longitudinal CA125-MMT algorithm were 0.911 (0.871–0.952) and 90.5% (82.5–98.6%). None of the longitudinal multi-marker algorithms (CA125-HE4, CA125-HE4-CA72-4, CA125-HE4-CA72-4-anti-TP53) performed better or improved on lead-time. Our population study suggests that longitudinal HE4, CA72-4, anti-TP53 autoantibodies adds little value to longitudinal serum CA125 as a first-line test in ovarian cancer screening of postmenopausal women.

Biological aging is a complex process involving multiple biological processes. These can be understood theoretically though considering them as individual networks – e.g. epigenetic networks, cell-cell networks (such as astro-glial networks) and population genetics. Mathematical modelling allows the combination of such networks so that they may be studied in unison, to better understand how the so called “seven pillars of aging” combine and to generate hypothesis for treating aging as a condition at relatively early biological ages. In this review, we consider how recent progression in mathematical modelling can be utilised to investigate aging, particular in, but not exclusive to, the context of degenerative neuronal disease. We also consider how the latest techniques for generating biomarker models for disease prediction, such as longitudinal analysis and parenclitic analysis can be applied to as both biomarker platforms for aging, as well as to better understand the inescapable condition. This review is written by a highly diverse and multi-disciplinary team of scientists from across the globe and calls for greater collaboration between diverse fields of research.

In this paper we investigate Monte Carlo methods for the approximation of the posterior probability distributions in stochastic kinetic models (SKMs). SKMs are multivariate Markov jump processes that model the interactions among species in biological systems according to a set of usually unknown parameters. The tracking of the species populations together with the estimation of the interaction parameters is a Bayesian inference problem for which Markov chain Monte Carlo (MCMC) methods have been a typical computational tool. Specifically, the particle MCMC (pMCMC) method has been shown to be effective, while computationally demanding method applicable to this problem. Recently, it has been shown that an alternative approach to Bayesian computation, namely, the class of adaptive importance samplers, may be more efficient than classical MCMC‐like schemes, at least for certain applications. For example, the nonlinear population Monte Carlo (NPMC) algorithm has yielded promising results with a low dimensional SKM (the classical predator‐prey model). In this paper we explore the application of both pMCMC and NPMC to analyze complex autoregulatory feedback networks modelled by SKMs. We demonstrate numerically how the populations of the relevant species in the network can be tracked and their interaction rates estimated, even in scenarios with partial observations. NPMC schemes attain an appealing trade‐off between accuracy and computational cost that can make them advantageous in many practical applications.

Many problems in physics demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially collected data. Here we introduce a general methodology for the joint estimation of the static parameters and the forecasting of the state variables of nonlinear stochastic dynamical models. The proposed scheme is essentially probabilistic. It aims at recursively computing the sequence of joint posterior probability distributions of the unknown model parameters and its (time-varying) state variables conditional on the available observations. This framework combines two layers of inference: In the first layer, a grid-based scheme is used to approximate the posterior probability distribution of the fixed parameters; in the second layer, filtering (or data assimilation) techniques are employed to track and predict different conditional probability distributions of the state variables. Various types of procedures (deterministic grids, Monte Carlo, Gaussian filters, etc.) can be plugged into both layers, leading to a wealth of algorithms. For this reason, we refer to the proposed methodology as nested hybrid filtering. In this paper we specifically explore the combination of Monte Carlo and quasi–Monte Carlo (deterministic) approximations in the first layer with Gaussian filtering methods in the second layer, but other approaches fit naturally within the framework. We prove a general convergence result for a class of procedures that use sequential Monte Carlo in the first layer. Then we turn to an illustrative numerical example. In particular, we apply and compare different implementations of the methodology to the tracking of the state, and the estimation of the fixed parameters, of a stochastic two-scale Lorenz 96 system. This model is commonly used to assess data assimilation procedures in meteorology. We show estimation and forecasting results, obtained with a desktop computer, for up to 5000 dynamic state variables.

Purpose: In the United Kingdom Collaborative Trial of Ovarian Cancer Screening (UKCTOCS), women in the multimodal (MMS) arm had a serum CA125 test (first-line), with those at increased risk, having repeat CA125/ultrasound (second-line test). CA125 was interpreted using the “Risk of Ovarian Cancer Algorithm” (ROCA). We report on performance of other serial algorithms and a single CA125 threshold as a first-line screen in the UKCTOCS dataset. Experimental Design: 50,083 post-menopausal women who attended 346,806 MMS screens were randomly split into training and validation sets, following stratification into cases (ovarian/tubal/peritoneal cancers) and controls. The two longitudinal algorithms, a new serial algorithm, method of mean trends (MMT) and the parametric empirical Bayes (PEB) were trained in the training set and tested in the blinded validation set and the performance characteristics, including that of a single CA125 threshold, were compared. Results: The area under receiver operator curve (AUC) was significantly higher (P = 0.01) for MMT (0.921) compared with CA125 single threshold (0.884). At a specificity of 89.5%, sensitivities for MMT [86.5%; 95% confidence interval (CI), 78.4–91.9] and PEB (88.5%; 95% CI, 80.6–93.4) were similar to that reported for ROCA (sensitivity 87.1%; specificity 87.6%; AUC 0.915) and significantly higher than the single CA125 threshold (73.1%; 95% CI, 63.6–80.8). Conclusions: These findings from the largest available serial CA125 dataset in the general population provide definitive evidence that longitudinal algorithms are significantly superior to simple cutoff values for ovarian cancer screening. Use of these newer algorithms requires incorporation into a multimodal strategy. The results highlight the importance of incorporating serial change in biomarker levels in cancer screening/early detection strategies. Clin Cancer Res; 24(19); 4726–33. ©2018 AACR.