Rhythmic dynamics and synchronization via dimensionality reduction : application to human gait

Reliable characterization of locomotor dynamics of human walking is vital to understanding the neuromuscular control of human locomotion and disease diagnosis. However, the inherent oscillation and ubiquity of noise in such non-strictly periodic signals pose great challenges to current methodologies. To this end, we exploit the state-of-the-art technology in pattern recognition and, specifically, dimensionality reduction techniques, and propose to reconstruct and characterize the dynamics accurately on the cycle scale of the signal. This is achieved by deriving a low-dimensional representation of the cycles through global optimization, which effectively preserves the topology of the cycles that are embedded in a high-dimensional Euclidian space. Our approach demonstrates a clear advantage in capturing the intrinsic dynamics and probing the subtle synchronization patterns from uni/bivariate oscillatory signals over traditional methods. Application to human gait data for healthy subjects and diabetics reveals a significant difference in the dynamics of ankle movements and ankle-knee coordination, but not in knee movements. These results indicate that the impaired sensory feedback from the feet due to diabetes does not influence the knee movement in general, and that normal human walking is not critically dependent on the feedback from the peripheral nervous system

Methods for Joint Normalization and Comparison of Hi-C data

The development of chromatin conformation capture technology has opened new avenues of study into the 3D structure and function of the genome. Chromatin structure is known to influence gene regulation, and differences in structure are now emerging as a mechanism of regulation between, e.g., cell differentiation and disease vs. normal states. Hi-C sequencing technology now provides a way to study the 3D interactions of the chromatin over the whole genome. However, like all sequencing technologies, Hi-C suffers from several forms of bias stemming from both the technology and the DNA sequence itself. Several normalization methods have been developed for normalizing individual Hi-C datasets, but little work has been done on developing joint normalization methods for comparing two or more Hi-C datasets. To make full use of Hi-C data, joint normalization and statistical comparison techniques are needed to carry out experiments to identify regions where chromatin structure differs between conditions. We develop methods for the joint normalization and comparison of two Hi-C datasets, which we then extended to more complex experimental designs. Our normalization method is novel in that it makes use of the distance-dependent nature of chromatin interactions. Our modification of the Minus vs. Average (MA) plot to the Minus vs. Distance (MD) plot allows for a nonparametric data-driven normalization technique using loess smoothing. Additionally, we present a simple statistical method using Z-scores for detecting differentially interacting regions between two datasets. Our initial method was published as the Bioconductor R package HiCcompare [http://bioconductor.org/packages/HiCcompare/](http://bioconductor.org/packages/HiCcompare/). We then further extended our normalization and comparison method for use in complex Hi-C experiments with more than two datasets and optional covariates. We extended the normalization method to jointly normalize any number of Hi-C datasets by using a cyclic loess procedure on the MD plot. The cyclic loess normalization technique can remove between dataset biases efficiently and effectively even when several datasets are analyzed at one time. Our comparison method implements a generalized linear model-based approach for comparing complex Hi-C experiments, which may have more than two groups and additional covariates. The extended methods are also available as a Bioconductor R package [http://bioconductor.org/packages/multiHiCcompare/](http://bioconductor.org/packages/multiHiCcompare/). Finally, we demonstrate the use of HiCcompare and multiHiCcompare in several test cases on real data in addition to comparing them to other similar methods (https://doi.org/10.1002/cpbi.76)

Preventing extinction and outbreaks in chaotic populations

Interactions in ecological communities are inherently nonlinear and can lead to complex population dynamics including irregular fluctuations induced by chaos. Chaotic population dynamics can exhibit violent oscillations with extremely small or large population abundances that might cause extinction and recurrent outbreaks, respectively. We present a simple method that can guide management efforts to prevent crashes, peaks, or any other undesirable state. At the same time, the irregularity of the dynamics can be preserved when chaos is desirable for the population. The control scheme is easy to implement because it relies on time series information only. The method is illustrated by two examples: control of crashes in the Ricker map and control of outbreaks in a stage-structured model of the flour beetle Tribolium. It turns out to be effective even with few available data and in the presence of noise, as is typical for ecological settings.Comment: 10 pages, 6 figure

Breast Cancer: Modelling and Detection

This paper reviews a number of the mathematical models used in cancer modelling and then chooses a specific cancer, breast carcinoma, to illustrate how the modelling can be used in aiding detection. We then discuss mathematical models that underpin mammographic image analysis, which complements models of tumour growth and facilitates diagnosis and treatment of cancer. Mammographic images are notoriously difficult to interpret, and we give an overview of the primary image enhancement technologies that have been introduced, before focusing on a more detailed description of some of our own recent work on the use of physics-based modelling in mammography. This theoretical approach to image analysis yields a wealth of information that could be incorporated into the mathematical models, and we conclude by describing how current mathematical models might be enhanced by use of this information, and how these models in turn will help to meet some of the major challenges in cancer detection