Myocardial Contractile Mechanics in Ischemic Mitral Regurgitation: Multicenter Data Using Stress Perfusion Cardiovascular Magnetic Resonance.

BACKGROUND: Left ventricular (LV) ischemia has been variably associated with functional mitral regurgitation (FMR). Determinants of FMR in patients with ischemia are poorly understood. OBJECTIVES: This study sought to test whether contractile mechanics in ischemic myocardium underlying the mitral valve have an impact on likelihood of FMR. METHODS: Vasodilator stress perfusion cardiac magnetic resonance was performed in patients with coronary artery disease (CAD) at multiple centers. FMR severity was confirmed quantitatively via core lab analysis. To test relationship of contractile mechanics with ischemic FMR, regional wall motion and strain were assessed in patients with inducible ischemia and minimal (≤5% LV myocardium, nontransmural) infarction. RESULTS: A total of 2,647 patients with CAD were studied; 34% had FMR (7% moderate or greater). FMR severity increased with presence (P < 0.001) and extent (P = 0.01) of subpapillary ischemia: patients with moderate or greater FMR had more subpapillary ischemia (odds ratio [OR]: 1.13 per 10% LV; 95% CI: 1.05-1.21; P = 0.001) independent of ischemia in remote regions (P = NS); moderate or greater FMR prevalence increased stepwise with extent of ischemia and infarction in subpapillary myocardium (P < 0.001); stronger associations between FMR and infarction paralleled greater wall motion scores in infarct-affected territories. Among patients with inducible ischemia and minimal infarction (n = 532), wall motion and radial strain analysis showed impaired subpapillary contractile mechanics to associate with moderate or greater FMR (P < 0.05) independent of remote regions (P = NS). Conversely, subpapillary ischemia without contractile dysfunction did not augment FMR likelihood. Mitral and interpapillary dimensions increased with subpapillary radial strain impairment; each remodeling parameter associated with impaired subpapillary strain (P < 0.05) independent of remote strain (P = NS). Subpapillary radial strain (OR: 1.13 per 5% [95% CI: 1.02-1.25]; P = 0.02) and mitral tenting area (OR: 1.05 per 10 mm2 [95% CI: 1.00-1.10]; P = 0.04) were associated with moderate or greater FMR controlling for global remodeling represented by LV end-systolic volume (P = NS): when substituting sphericity for LV volume, moderate or greater FMR remained independently associated with subpapillary radial strain impairment (OR: 1.22 per 5% [95% CI: 1.02-1.47]; P = 0.03). CONCLUSIONS: Among patients with CAD and ischemia, FMR severity and adverse mitral apparatus remodeling increase in proportion to contractile dysfunction underlying the mitral valve.

Growing optimal scale-free networks via likelihood.

Preferential attachment, by which new nodes attach to existing nodes with probability proportional to the existing nodes' degree, has become the standard growth model for scale-free networks, where the asymptotic probability of a node having degree k is proportional to k^{-γ}. However, the motivation for this model is entirely ad hoc. We use exact likelihood arguments and show that the optimal way to build a scale-free network is to attach most new links to nodes of low degree. Curiously, this leads to a scale-free network with a single dominant hub: a starlike structure we call a superstar network. Asymptotically, the optimal strategy is to attach each new node to one of the nodes of degree k with probability proportional to 1/N+ζ(γ)(k+1)(γ) (in a N node network): a stronger bias toward high degree nodes than exhibited by standard preferential attachment. Our algorithm generates optimally scale-free networks (the superstar networks) as well as randomly sampling the space of all scale-free networks with a given degree exponent γ. We generate viable realization with finite N for 1≪γ<2 as well as γ>2. We observe an apparently discontinuous transition at γ≈2 between so-called superstar networks and more treelike realizations. Gradually increasing γ further leads to reemergence of a superstar hub. To quantify these structural features, we derive a new analytic expression for the expected degree exponent of a pure preferential attachment process and introduce alternative measures of network entropy. Our approach is generic and can also be applied to an arbitrary degree distribution.

Networked dynamical systems with linear coupling: synchronisation patterns, coherence and other behaviours.

Many physical and biochemical systems are well modelled as a network of identical non-linear dynamical elements with linear coupling between them. An important question is how network structure affects chaotic dynamics, for example, by patterns of synchronisation and coherence. It is shown that small networks can be characterised precisely into patterns of exact synchronisation and large networks characterised by partial synchronisation at the local and global scale. Exact synchronisation modes are explained using tools of symmetry groups and invariance, and partial synchronisation is explained by finite-time shadowing of exact synchronisation modes.

Forecasting: it is not about statistics, it is about dynamics.

In 1963, the mathematician and meteorologist Edward Lorenz published a paper (Lorenz 1963 J. Atmos. Sci. 20, 130-141) that changed the way scientists think about the prediction of geophysical systems, by introducing the ideas of chaos, attractors, sensitivity to initial conditions and the limitations to forecasting nonlinear systems. Three years earlier, the mathematician and engineer Rudolf Kalman had published a paper (Kalman 1960 Trans. ASME Ser. D, J. Basic Eng. 82, 35-45) that changed the way engineers thought about prediction of electronic and mechanical systems. Ironically, in recent years, geophysicists have become increasingly interested in Kalman filters, whereas engineers have become increasingly interested in chaos. It is argued that more often than not the tracking and forecasting of nonlinear systems has more to do with the nonlinear dynamics that Lorenz considered than it has to do with statistics that Kalman considered. A position with which both Lorenz and Kalman would appear to agree.

Failures of sequential Bayesian filters and the successes of shadowing filters in tracking of nonlinear deterministic and stochastic systems.

Sequential Bayesian filters, such as particle filters, are often presented as an ideal means of tracking the state of nonlinear systems. Here shadowing filters are demonstrated to perform better than sequential filters at tracking under specific circumstances. The success of shadowing filters is attributed to avoiding both well-known deficiencies of particle filters, and some newly identified problems.

The seasonal relationship between assault and homicide in England and Wales.

Investigating the seasonal asymmetry of violent behaviour has a long history. Despite this, there still remains considerable debate about the nature and aetiology of this phenomenon. Reports on homicide, for example, are mixed: some have found homicide seasonality but most have not. In contrast, all published studies on assault report that this behaviour is seasonal. Moreover, only two studies, both using US data, have examined the seasonal variation of assault and homicide in the same population over the same period of time. One group found assault was seasonal but homicide was not, whilst the other found, overall, that both homicide and assault were seasonal. This first of these findings seems paradoxical, in that there is no seasonal variation in injury related deaths (i.e. homicides), despite the antecedent behaviour (i.e. assaults) having a seasonal pattern of occurrence. We examined the seasonal variation in homicide and assault in UK and found a similar result. Furthermore, our findings are not easily understandable using conventional social models of seasonal behaviour and we suggest biologically mediated seasonal variation in the capacity of equally injured individuals to survive trauma may also play a role, which should be investigated further.

Failure of maximum likelihood methods for chaotic dynamical systems.

The maximum likelihood method is a basic statistical technique for estimating parameters and variables, and is the starting point for many more sophisticated methods, like Bayesian methods. This paper shows that maximum likelihood fails to identify the true trajectory of a chaotic dynamical system, because there are trajectories that appear to be far more (infinitely more) likely than truth. This failure occurs for unbounded noise and for bounded noise when it is sufficiently large and will almost certainly have consequences for parameter estimation in such systems. The reason for the failure is rather simple; in chaotic dynamical systems there can be trajectories that are consistently closer to the observations than the true trajectory being observed, and hence their likelihood dominates truth. The residuals of these truth-dominating trajectories are not consistent with the noise distribution; they would typically have too small standard deviation and many outliers, and hence the situation may be remedied by using methods that examine the distribution of residuals and are not entirely maximum likelihood based.

Degeneracy of time series models: the best model is not always the correct model.

There are a number of good techniques for finding, in some sense, the best model of a deterministic system given a time series of observations. We examine a problem called model degeneracy, which has the consequence that even when a perfect model of a system exists, one does not find it using the best techniques currently available. The problem is illustrated using global polynomial models and the theory of Grobner bases.

Constructing dynamical systems with specified symbolic dynamics.

In this paper we demonstrate how to construct signals (time series) of continuous-time dynamical systems that exhibit a given symbolic dynamics. This is achieved without construction of the ordinary differential equations that generate the flow. This construction is of theoretical interest and is useful as a source of dynamical data that can be used to test various data analysis algorithms.

Estimating a generating partition from observed time series: symbolic shadowing.

We propose a deterministic algorithm for approximating a generating partition from a time series using tessellations. Using data generated by Hénon and Ikeda maps, we demonstrate that the proposed method produces partitions that uniquely encode all the periodic points up to some order, and provide good estimates of the metric and topological entropies. The algorithm gives useful results even with a short noisy time series.

Chaotic-time-series reconstruction by the Bayesian paradigm: right results by wrong methods.

Recently, papers have appeared that champion the Bayesian approach to the analysis of experimental data. From reading these papers, the physicist could be forgiven for believing that Bayesian methods reveal deep truths about physical systems and are the correct paradigm for the analysis of all experimental data. This paper makes a contrary argument and is deliberately provocative. It is argued that the Bayesian approach to reconstruction of chaotic time series is fundamentally flawed, and the apparent successes result not from any degree of correctness of the paradigm, but by an accidental and unintended property of an algorithm. We also argue that (non-Bayesian) shadowing techniques provide all the information the erroneous Bayesian methods obtain, but much more efficiently, and also provide a wealth of additional useful information.

Modeling continuous processes from data.

Experimental and simulated time series are necessarily discretized in time. However, many real and artificial systems are more naturally modeled as continuous-time systems. This paper reviews the major techniques employed to estimate a continuous vector field from a finite discrete time series. We compare the performance of various methods on experimental and artificial time series and explore the connection between continuous (differential) and discrete (difference equation) systems. As part of this process we propose improvements to existing techniques. Our results demonstrate that the continuous-time dynamics of many noisy data sets can be simulated more accurately by modeling the one-step prediction map than by modeling the vector field. We also show that radial basis models provide superior results to global polynomial models.

Starting a canine program.

If it is done properly, a program of canine patrols in a healthcare setting can produce a number of benefits, not the least of which is a decline in criminal activity. In this article, the author shares his experiences in developing and implementing a successful program.