Fractals for physicians

There is increasing interest in the study of fractals in medicine. In this review, we provide an overview of fractals, of techniques available to describe fractals in physiological data, and we propose some reasons why a physician might benefit from an understanding of fractals and fractal analysis, with an emphasis on paediatric respiratory medicine where possible. Among these reasons are the ubiquity of fractal organisation in nature and in the body, and how changes in this organisation over the lifespan provide insight into development and senescence. Fractal properties have also been shown to be altered in disease and even to predict the risk of worsening of disease. Finally, implications of a fractal organisation include robustness to errors during development, ability to adapt to surroundings, and the restoration of such organisation as targets for intervention and treatment.

Forbidden ordinal patterns of periictal intracranial EEG indicate deterministic dynamics in human epileptic seizures

Epileptic seizures typically reveal a high degree of stereotypy, that is, for an individual patient they are characterized by an ordered and predictable sequence of symptoms and signs with typically little variability. Stereotypy implies that ictal neuronal dynamics might have deterministic characteristics, presumably most pronounced in the ictogenic parts of the brain, which may provide diagnostically and therapeutically important information. Therefore the goal of our study was to search for indications of determinism in periictal intracranial electroencephalography (EEG) studies recorded from patients with pharmacoresistent epilepsy.

Intermittent spike-wave dynamics in a heterogeneous, spatially extended neural mass model

Generalised epileptic seizures are frequently accompanied by sudden, reversible transitions from low amplitude, irregular background activity to high amplitude, regular spike-wave discharges (SWD) in the EEG. The underlying mechanisms responsible for SWD generation and for the apparently spontaneous transitions to SWD and back again are still not fully understood. Specifically, the role of spatial cortico-cortical interactions in ictogenesis is not well studied. We present a macroscopic, neural mass model of a cortical column which includes two distinct time scales of inhibition. This model can produce both an oscillatory background and a pathological SWD rhythm. We demonstrate that coupling two of these cortical columns can lead to a bistability between out-of-phase, low amplitude background dynamics and in-phase, high amplitude SWD activity. Stimuli can cause state-dependent transitions from background into SWD. In an extended local area of cortex, spatial heterogeneities in a model parameter can lead to spontaneous reversible transitions from a desynchronised background to synchronous SWD due to intermittency. The deterministic model is therefore capable of producing absence seizure-like events without any time dependent adjustment of model parameters. The emergence of such mechanisms due to spatial coupling demonstrates the importance of spatial interactions in modelling ictal dynamics, and in the study of ictogenesis.

Spike-based decision learning of nash equilibria in two-player games

Humans and animals face decision tasks in an uncertain multi-agent environment where an agent's strategy may change in time due to the co-adaptation of others strategies. The neuronal substrate and the computational algorithms underlying such adaptive decision making, however, is largely unknown. We propose a population coding model of spiking neurons with a policy gradient procedure that successfully acquires optimal strategies for classical game-theoretical tasks. The suggested population reinforcement learning reproduces data from human behavioral experiments for the blackjack and the inspector game. It performs optimally according to a pure (deterministic) and mixed (stochastic) Nash equilibrium, respectively. In contrast, temporal-difference(TD)-learning, covariance-learning, and basic reinforcement learning fail to perform optimally for the stochastic strategy. Spike-based population reinforcement learning, shown to follow the stochastic reward gradient, is therefore a viable candidate to explain automated decision learning of a Nash equilibrium in two-player games.

Simulating the impact of four control strategies on the population dynamics of Neospora caninum infection in Swiss dairy cattle

A dynamic deterministic simulation model was developed to assess the impact of different putative control strategies on the seroprevalence of Neospora caninum in female Swiss dairy cattle. The model structure comprised compartments of "susceptible" and "infected" animals (SI-model) and the cattle population was divided into 12 age classes. A reference model (Model 1) was developed to simulate the current (status quo) situation (present seroprevalence in Switzerland 12%), taking into account available demographic and seroprevalence data of Switzerland. Model 1 was modified to represent four putative control strategies: testing and culling of seropositive animals (Model 2), discontinued breeding with offspring from seropositive cows (Model 3), chemotherapeutic treatment of calves from seropositive cows (Model 4), and vaccination of susceptible and infected animals (Model 5). Models 2-4 considered different sub-scenarios with regard to the frequency of diagnostic testing. Multivariable Monte Carlo sensitivity analysis was used to assess the impact of uncertainty in input parameters. A policy of annual testing and culling of all seropositive cattle in the population reduced the seroprevalence effectively and rapidly from 12% to <1% in the first year of simulation. The control strategies with discontinued breeding with offspring from all seropositive cows, chemotherapy of calves and vaccination of all cattle reduced the prevalence more slowly than culling but were still very effective (reduction of prevalence below 2% within 11, 23 and 3 years of simulation, respectively). However, sensitivity analyses revealed that the effectiveness of these strategies depended strongly on the quality of the input parameters used, such as the horizontal and vertical transmission factors, the sensitivity of the diagnostic test and the efficacy of medication and vaccination. Finally, all models confirmed that it was not possible to completely eradicate N. caninum as long as the horizontal transmission process was not interrupted.

Long-range correlations in rectal temperature fluctuations of healthy infants during maturation

BACKGROUND: Control of breathing, heart rate, and body temperature are interdependent in infants, where instabilities in thermoregulation can contribute to apneas or even life-threatening events. Identifying abnormalities in thermoregulation is particularly important in the first 6 months of life, where autonomic regulation undergoes critical development. Fluctuations in body temperature have been shown to be sensitive to maturational stage as well as system failure in critically ill patients. We thus aimed to investigate the existence of fractal-like long-range correlations, indicative of temperature control, in night time rectal temperature (T(rec)) patterns in maturing infants. METHODOLOGY/PRINCIPAL FINDINGS: We measured T(rec) fluctuations in infants every 4 weeks from 4 to 20 weeks of age and before and after immunization. Long-range correlations in the temperature series were quantified by the correlation exponent, alpha using detrended fluctuation analysis. The effects of maturation, room temperature, and immunization on the strength of correlation were investigated. We found that T(rec) fluctuations exhibit fractal long-range correlations with a mean (SD) alpha of 1.51 (0.11), indicating that T(rec) is regulated in a highly correlated and hence deterministic manner. A significant increase in alpha with age from 1.42 (0.07) at 4 weeks to 1.58 (0.04) at 20 weeks reflects a change in long-range correlation behavior with maturation towards a smoother and more deterministic temperature regulation, potentially due to the decrease in surface area to body weight ratio in the maturing infant. alpha was not associated with mean room temperature or influenced by immunization CONCLUSIONS: This study shows that the quantification of long-range correlations using alpha derived from detrended fluctuation analysis is an observer-independent tool which can distinguish developmental stages of night time T(rec) pattern in young infants, reflective of maturation of the autonomic system. Detrended fluctuation analysis may prove useful for characterizing thermoregulation in premature and other infants at risk for life-threatening events.

Mineralogy-based quantitative precipitation and temperature reconstructions from annually laminated lake sediments (Swiss Alps) since AD 1580

[1] We present quantitative autumn, summer and annual precipitation and summer temperature reconstructions from proglacial annually laminated Lake Silvaplana, eastern Swiss Alps back to AD 1580. We used X-ray diffraction peak intensity ratios of minerals in the sediment layers (quartz qz, plagioclase pl, amphibole am, mica mi) that are diagnostic for different source areas and hydro-meteorological transport processes in the catchment. XRD data were calibrated with meteorological data (AD 1800/1864–1950) and revealed significant correlations: mi/pl with SON precipitation (r = 0.56, p < 0.05) and MJJAS precipitation (r = 0.66, p < 0.01); qz/mi with MJJAS temperature (r = −0.72, p < 0.01)and qz/am with annual precipitation (r = −0.54, p < 0.05). Geological catchment settings and hydro-meteorological processes provide deterministic explanations for the correlations. Our summer temperature reconstruction reproduces the typical features of past climate variability known from independent data sets. The precipitation reconstructions show a LIA climate moister than today. Exceptionally wet periods in our reconstruction coincide with regional glacier advances.

Morphological Diversity and the Roles of Contingency, Chance and Determinism in African Cichlid Radiations

Background: Deterministic evolution, phylogenetic contingency and evolutionary chance each can influence patterns of morphological diversification during adaptive radiation. In comparative studies of replicate radiations, convergence in a common morphospace implicates determinism, whereas non-convergence suggests the importance of contingency or chance. Methodology/Principal Findings: The endemic cichlid fish assemblages of the three African great lakes have evolved similar sets of ecomorphs but show evidence of non-convergence when compared in a common morphospace, suggesting the importance of contingency and/or chance. We then analyzed the morphological diversity of each assemblage independently and compared their axes of diversification in the unconstrained global morphospace. We find that despite differences in phylogenetic composition, invasion history, and ecological setting, the three assemblages are diversifying along parallel axes through morphospace and have nearly identical variance-covariance structures among morphological elements. Conclusions/Significance: By demonstrating that replicate adaptive radiations are diverging along parallel axes, we have shown that non-convergence in the common morphospace is associated with convergence in the global morphospace. Applying these complimentary analyses to future comparative studies will improve our understanding of the relationship between morphological convergence and non-convergence, and the roles of contingency, chance and determinism in driving morphological diversification.

Continuum percolation for Gibbs point processes

We consider percolation properties of the Boolean model generated by a Gibbs point process and balls with deterministic radius. We show that for a large class of Gibbs point processes there exists a critical activity, such that percolation occurs a.s. above criticality. For locally stable Gibbs point processes we show a converse result, i.e. they do not percolate a.s. at low activity.

Case and partnership reproduction numbers for a curable sexually transmitted infection

Sexually transmitted infections (STIs) are, by definition, transmitted between sexual partners. For curable STIs an infected index case can potentially re-infect the same partner multiple times. Thus, R0, the average number of secondary infections one typical infected individual will produce during his or her infectious period is not necessarily the same as the average number of secondary cases (infected persons). Here we introduce the new concept of the case reproduction number (Rc). In addition, we define the partnership reproduction number (Rp) as the average number of secondary partnerships consisting of two infected individuals one typical infected individual will produce over his or her infectious lifetime. Rp takes into account clearance and re-infection within partnerships, which results in a prolongation of the duration of the infectious period. The two new reproduction numbers were derived for a deterministic pair model with serial monogamous partnerships using infection parameters for Chlamydia trachomatis, an example of a curable STI. We showed that re-infection within partnerships means that curable STIs can be sustained endemically even when the average number of secondary cases a person produces during his or her infectious period is below one.