Minimal energy control of a nanoelectromechanical memory element

The Pontryagin minimal energy control approach has been applied to minimise the switching energy in a nanoelectromechanical memory system and to characterise global stability of the oscillatory states of the bistable memory element. A comparison of two previously experimentally determined pulse-type control signals with Pontryagin control function has been performed, and the superiority of the Pontryagin approach with regard to power consumption has been demonstrated. An analysis of global stability shows how values of minimal energy can be utilized in order to specify equally stable states

A model describing the multiphasic dynamics of mixed meal glucose responses in healthy subjects

Modelling of the glucose metabolism for the purpose of improving the diagnosis and therapy of diabetes mellitus has been the subject of research for decades. Despite this effort, conventional models describing postprandial glucose profiles of healthy subjects fail to include the phenomenon of biphasic glucose responses. Continuous glucose monitoring data recorded from five healthy subjects show that mono- and biphasic glucose responses from regular meals are equally common. We therefore developed a suitable parametric model, capable of producing mono- as well as biphasic meal responses. It is expressed by linear second order differential equation with a dual Gaussian input function. Additionally, a simple method for classifying meal responses into mono- or biphasic profiles was developed. Model inversion was performed using a fully Bayesian method. R2 values of model output compared to CGM data was 91.6 ± 8.3%, indicating the models ability of accurately describing a wide range of mixed meal glucose responses. Parameters were found to be associated with characteristics of individual meals. We suggest that the model could be used to objectively assess postprandial hyperglycemia, one of the main measures for glycemic control

A data driven nonlinear stochastic model for blood glucose dynamics

The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose–insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose–insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles

Physical fitness contributes to cardio-respiratory synchronization

Cardio-respiratory synchronization is a phenomenon of particular interest- especially at a 1:1 ratio- and may give greater insight into the underlying mechanisms of cardio-respiratory communication. Synchronization of this ratio is hypothesised to occur when breathing rate exceeds heart rate, which is the premise of this research. A novel experimental design focused on guiding elevated respiration to induce the entrainment of heart rate, and produce an equivalent rise in value. Application of instantaneous phase for identification and analysis of synchronization allowed for a reliable method of measuring the interaction between these stochastic processes. We have identified 1:1 phase synchronization in all volunteers measured. Longer synchronization episodes were observed reliably in athletic individuals, corroborating previous research for spontaneous breathing. This observation suggests that cardio-respiratory synchronization at all respiration rates is associated with a common underlying communication mechanism. Furthermore, it presents cardio-respiratory synchronization as a potential future measurement of fitness and autonomic health

Handling limited datasets with neural networks in medical applications : a small-data approach

Motivation: Single-centre studies in medical domain are often characterised by limited samples due to the complexity and high costs of patient data collection. Machine learning methods for regression modelling of small datasets (less than 10 observations per predictor variable) remain scarce. Our work bridges this gap by developing a novel framework for application of artificial neural networks (NNs) for regression tasks involving small medical datasets. Methods: In order to address the sporadic fluctuations and validation issues that appear in regression NNs trained on small datasets, the method of multiple runs and surrogate data analysis were proposed in this work. The approach was compared to the state-of-the-art ensemble NNs; the effect of dataset size on NN performance was also investigated. Results: The proposed framework was applied for the prediction of compressive strength (CS) of femoral trabecular bone in patients suffering from severe osteoarthritis. The NN model was able to estimate the CS of osteoarthritic trabecular bone from its structural and biological properties with a standard error of 0.85 MPa. When evaluated on independent test samples, the NN achieved accuracy of 98.3%, outperforming an ensemble NN model by 11%. We reproduce this result on CS data of another porous solid (concrete) and demonstrate that the proposed framework allows for an NN modelled with as few as 56 samples to generalise on 300 independent test samples with 86.5% accuracy, which is comparable to the performance of an NN developed with 18 times larger dataset (1030 samples). Conclusion: The significance of this work is two-fold: the practical application allows for non-destructive prediction of bone fracture risk, while the novel methodology extends beyond the task considered in this study and provides a general framework for application of regression NNs to medical problems characterised by limited dataset sizes

The role of noise in forming the dynamics of a quasiperiodic system

The dynamical properties of the quasiperiodic logistic map with and without a very weak noise are compared, and the influence of noise on its strange nonchaotic attractor (SNA) is investigated. It is found that, in the presence of weak noise, the largest Lyapunov exponent gives misleading information about the dynamical properties of the attractor. We have shown that, in the presence of noise, the properties of strangeness and chaos are invariably associated, so that SNAs are not then observed during the transition to chaos from the torus

Numerical simulations versus theoretical predictions for a non-Gaussian noise induced escape problem in application to full counting statistics

A theoretical approach for characterizing the influence of asymmetry of noise distribution on the escape rate of a multistable system is presented. This was carried out via the estimation of an action, which is defined as an exponential factor in the escape rate, and discussed in the context of full counting statistics paradigm. The approach takes into account all cumulants of the noise distribution and demonstrates an excellent agreement with the results of numerical simulations. An approximation of the third-order cumulant was shown to have limitations on the range of dynamic stochastic system parameters. The applicability of the theoretical approaches developed so far is discussed for an adequate characterization of the escape rate measured in experiments

A new data-driven model for post-transplant antibody dynamics in high risk kidney transplantation

The dynamics of donor specific human leukocyte antigen (HLA) antibodies during early stage after transplantation are of great clinical interest as they are considered to be associated with short and long term outcomes (graft function and rejection). However, the limited number of such detailed donor-specific antibody (DSA) time series currently available and their diverse patterns have made the task of modelling difficult. Focusing on one typical dynamic pattern with rapid falls and stable settling levels, a novel data-driven model in the form of a third order differential equation has been developed to describe such post-transplant dynamics in DSAs for the first time. A variational Bayesian inference method has been applied to select a model and learn its parameters for 39 time series from two groups of graft recipients, i.e. patients with and without acute antibody-mediated rejection (AMR) episodes. Linear and nonlinear dynamic models of different order were attempted to fit the time series, and the third order linear model provided the best description of the common features in both groups. Both deterministic and stochastic parameters are found to be significantly different in the AMR and no-AMR groups. Eigenvalues have been calculated for each fitting, and phase portraits have been plotted to show the trajectories of the system states for both groups. The results from our previous study with fewer cases have been further confirmed: the time series in the AMR group have significantly higher frequency of oscillations and faster dissipation rates, which may potentially lead to better laboratory measurement strategy and a better chance of understanding the underlying immunological mechanisms

Subclass analysis of donor HLA-specific IgG in antibody-incompatible renal transplantation reveals a significant association of IgG4 with rejection and graft failure

Donor HLA-specific antibodies (DSAs) can cause rejection and graft loss after renal transplantation, but their levels measured by the current assays are not fully predictive of outcomes. We investigated whether IgG subclasses of DSA were associated with early rejection and graft failure. DSA levels were determined pretreatment, at the day of peak pan-IgG level and at 30 days post-transplantation in eighty HLA antibody-incompatible kidney transplant recipients using a modified microbead assay. Pretreatment IgG4 levels were predictive of acute antibody-mediated rejection (P = 0.003) in the first 30 days post-transplant. Pre-treatment presence of IgG4 DSA (P = 0.008) and day 30 IgG3 DSA (P = 0.03) was associated with poor graft survival. Multivariate regression analysis showed that in addition to pan-IgG levels, total IgG4 levels were an independent risk factor for early rejection when measured pretreatment, and the presence of pretreatment IgG4 DSA was also an independent risk factor for graft failure. Pretreatment IgG4 DSA levels correlated independently with higher risk of early rejection episodes and medium-term death-censored graft survival. Thus, pretreatment IgG4 DSA may be used as a biomarker to predict and risk stratify cases with higher levels of pan-IgG DSA in HLA antibody-incompatible transplantation. Further investigations are needed to confirm our results

Decision tree and random forest models for outcome prediction in antibody incompatible kidney transplantation

Clinical datasets are commonly limited in size, thus restraining applications of Machine Learning (ML)techniques for predictive modelling in clinical research and organ transplantation. We explored thepotential of Decision Tree (DT) and Random Forest (RF) classification models, in the context of smalldataset of 80 samples, for outcome prediction in high-risk kidney transplantation. The DT and RF modelsidentified the key risk factors associated with acute rejection: the levels of the donor specific IgG anti-bodies, the levels of IgG4 subclass and the number of human leucocyte antigen mismatches betweenthe donor and recipient. Furthermore, the DT model determined dangerous levels of donor-specific IgGsubclass antibodies, thus demonstrating the potential of discovering new properties in the data whentraditional statistical tools are unable to capture them. The DT and RF classifiers developed in this workpredicted early transplant rejection with accuracy of 85%, thus offering an accurate decision supporttool for doctors tasked with predicting outcomes of kidney transplantation in advance of the clinicalintervention