Generalized methods and solvers for noise removal from piecewise constant signals. I. Background theory

Modeling basal body temperature data using horseshoe process regression

Biomedical data often exhibit jumps or abrupt changes. For example, women's basal body temperature may jump at ovulation, menstruation, implantation, and miscarriage. These sudden changes make these data challenging to model: many methods will oversmooth the sharp changes or overfit in response to measurement error. We develop horseshoe process regression (HPR) to address this problem. We define a horseshoe process as a stochastic process in which each increment is horseshoe-distributed. We use the horseshoe process as a nonparametric Bayesian prior for modeling a potentially nonlinear association between an outcome and its continuous predictor, which we implement via Stan and in the R package HPR. We provide guidance and extensions to advance HPR's use in applied practice: we introduce a Bayesian imputation scheme to allow for interpolation at unobserved values of the predictor within the HPR; include additional covariates via a partial linear model framework; and allow for monotonicity constraints. We find that HPR performs well when fitting functions that have sharp changes. We apply HPR to model women's basal body temperatures over the course of the menstrual cycle.

3D Printable Soft Sensory Fiber Networks for Robust and Complex Tactile Sensing

The human tactile system is composed of multi-functional mechanoreceptors distributed in an optimized manner. Having the ability to design and optimize multi-modal soft sensory systems can further enhance the capabilities of current soft robotic systems. This work presents a complete framework for the fabrication of soft sensory fiber networks for contact localization, using pellet-based 3D printing of piezoresistive elastomers to manufacture flexible sensory networks with precise and repeatable performances. Given a desirable soft sensor property, our methodology can design and fabricate optimized sensor morphologies without human intervention. Extensive simulation and experimental studies are performed on two printed networks, comparing a baseline network to one optimized via an existing information theory based approach. Machine learning is used for contact localization based on the sensor responses. The sensor responses match simulations with tunable performances and good localization accuracy, even in the presence of damage and nonlinear material properties. The potential of the networks to function as capacitive sensors is also demonstrated.

AutoStepfinder: A fast and automated step detection method for single-molecule analysis

Single-molecule techniques allow the visualization of the molecular dynamics of nucleic acids and proteins with high spatiotemporal resolution. Valuable kinetic information of biomolecules can be obtained when the discrete states within single-molecule time trajectories are determined. Here, we present a fast, automated, and bias-free step detection method, AutoStepfinder, that determines steps in large datasets without requiring prior knowledge on the noise contributions and location of steps. The analysis is based on a series of partition events that minimize the difference between the data and the fit. A dual-pass strategy determines the optimal fit and allows AutoStepfinder to detect steps of a wide variety of sizes. We demonstrate step detection for a broad variety of experimental traces. The user-friendly interface and the automated detection of AutoStepfinder provides a robust analysis procedure that enables anyone without programming knowledge to generate step fits and informative plots in less than an hour.

•

Fast, automated, and bias-free detection of steps within single-molecule trajectories

•

Robust step detection without any prior knowledge on the data

•

A dual-pass strategy for the detection of steps over a wide variety of scales

•

A user-friendly interface for a simplified step fitting procedure

Single-molecule techniques have made it possible to track individual protein complexes in real time with a nanometer spatial resolution and a millisecond timescale. Accurate determination of the dynamic states within single-molecule time traces provides valuable kinetic information that underlie the function of biological macromolecules. Here, we present a new automated step detection method called AutoStepfinder, a versatile, robust, and easy-to-use algorithm that allows researchers to determine the kinetic states within single-molecule time trajectories without any bias.

PLANT: A Method for Detecting Changes of Slope in Noisy Trajectories

Time traces obtained from a variety of biophysical experiments contain valuable information on underlying processes occurring at the molecular level. Accurate quantification of these data can help explain the details of the complex dynamics of biological systems. Here, we describe PLANT (Piecewise Linear Approximation of Noisy Trajectories), a segmentation algorithm that allows the reconstruction of time-trace data with constant noise as consecutive straight lines, from which changes of slopes and their respective durations can be extracted. We present a general description of the algorithm and perform extensive simulations to characterize its strengths and limitations, providing a rationale for the performance of the algorithm in the different conditions tested. We further apply the algorithm to experimental data obtained from tracking the centroid position of lymphocytes migrating under the effect of a laminar flow and from single myosin molecules interacting with actin in a dual-trap force-clamp configuration.

Topological data analysis for true step detection in periodic piecewise constant signals

This paper introduces a simple yet powerful approach based on topological data analysis for detecting true steps in a periodic, piecewise constant (PWC) signal. The signal is a two-state square wave with randomly varying in-between-pulse spacing, subject to spurious steps at the rising or falling edges which we call digital ringing. We use persistent homology to derive mathematical guarantees for the resulting change detection which enables accurate identification and counting of the true pulses. The approach is tested using both synthetic and experimental data obtained using an engine lathe instrumented with a laser tachometer. The described algorithm enables accurate and automatic calculations of the spindle speed without any choice of parameters. The results are compared with the frequency and sequency methods of the Fourier and Walsh–Hadamard transforms, respectively. Both our approach and the Fourier analysis yield comparable results for pulses with regular spacing and digital ringing while the latter causes large errors using the Walsh–Hadamard method. Further, the described approach significantly outperforms the frequency/sequency analyses when the spacing between the peaks is varied. We discuss generalizing the approach to higher dimensional PWC signals, although using this extension remains an interesting question for future research.

Automated Quality Control for Sensor Based Symptom Measurement Performed Outside the Lab

The use of wearable sensing technology for objective, non-invasive and remote clinimetric testing of symptoms has considerable potential. However, the accuracy achievable with such technology is highly reliant on separating the useful from irrelevant sensor data. Monitoring patient symptoms using digital sensors outside of controlled, clinical lab settings creates a variety of practical challenges, such as recording unexpected user behaviors. These behaviors often violate the assumptions of clinimetric testing protocols, where these protocols are designed to probe for specific symptoms. Such violations are frequent outside the lab and affect the accuracy of the subsequent data analysis and scientific conclusions. To address these problems, we report on a unified algorithmic framework for automated sensor data quality control, which can identify those parts of the sensor data that are sufficiently reliable for further analysis. Combining both parametric and nonparametric signal processing and machine learning techniques, we demonstrate that across 100 subjects and 300 clinimetric tests from three different types of behavioral clinimetric protocols, the system shows an average segmentation accuracy of around 90%. By extracting reliable sensor data, it is possible to strip the data of confounding factors in the environment that may threaten reproducibility and replicability.

Unraveling the Thousand Word Picture: An Introduction to Super-Resolution Data Analysis

Super-resolution microscopy provides direct insight into fundamental biological processes occurring at length scales smaller than light's diffraction limit. The analysis of data at such scales has brought statistical and machine learning methods into the mainstream. Here we provide a survey of data analysis methods starting from an overview of basic statistical techniques underlying the analysis of super-resolution and, more broadly, imaging data. We subsequently break down the analysis of super-resolution data into four problems: the localization problem, the counting problem, the linking problem, and what we've termed the interpretation problem.

Energy-based scheme for reconstruction of piecewise constant signals observed in the movement of molecular machines

Analyzing the physical and chemical properties of single DNA-based molecular machines such as polymerases and helicases requires to track stepping motion on the length scale of base pairs. Although high-resolution instruments have been developed that are capable of reaching that limit, individual steps are oftentimes hidden by experimental noise which complicates data processing. Here we present an effective two-step algorithm which detects steps in a high-bandwidth signal by minimizing an energy-based model (energy-based step finder, EBS). First, an efficient convex denoising scheme is applied which allows compression to tuples of amplitudes and plateau lengths. Second, a combinatorial clustering algorithm formulated on a graph is used to assign steps to the tuple data while accounting for prior information. Performance of the algorithm was tested on Poissonian stepping data simulated based on published kinetics data of RNA polymerase II (pol II). Comparison to existing step-finding methods shows that EBS is superior in speed while providing competitive step-detection results, especially in challenging situations. Moreover, the capability to detect backtracked intervals in experimental data of pol II as well as to detect stepping behavior of the Phi29 DNA packaging motor is demonstrated.

An information-based approach to change-point analysis with applications to biophysics and cell biology

This article describes the application of a change-point algorithm to the analysis of stochastic signals in biological systems whose underlying state dynamics consist of transitions between discrete states. Applications of this analysis include molecular-motor stepping, fluorophore bleaching, electrophysiology, particle and cell tracking, detection of copy number variation by sequencing, tethered-particle motion, etc. We present a unified approach to the analysis of processes whose noise can be modeled by Gaussian, Wiener, or Ornstein-Uhlenbeck processes. To fit the model, we exploit explicit, closed-form algebraic expressions for maximum-likelihood estimators of model parameters and estimated information loss of the generalized noise model, which can be computed extremely efficiently. We implement change-point detection using the frequentist information criterion (which, to our knowledge, is a new information criterion). The frequentist information criterion specifies a single, information-based statistical test that is free from ad hoc parameters and requires no prior probability distribution. We demonstrate this information-based approach in the analysis of simulated and experimental tethered-particle-motion data.

The Development of an Information Criterion for Change-Point Analysis

Change-point analysis is a flexible and computationally tractable tool for the analysis of times series data from systems that transition between discrete states and whose observables are corrupted by noise. The change point algorithm is used to identify the time indices (change points) at which the system transitions between these discrete states. We present a unified information-based approach to testing for the existence of change points. This new approach reconciles two previously disparate approaches to change-point analysis (frequentist and information based) for testing transitions between states. The resulting method is statistically principled, parameter and prior free, and widely applicable to a wide range of change-point problems.

Iterative Potts and Blake-Zisserman minimization for the recovery of functions with discontinuities from indirect measurements

Signals with discontinuities appear in many problems in the applied sciences ranging from mechanics, electrical engineering to biology and medicine. The concrete data acquired are typically discrete, indirect and noisy measurements of some quantities describing the signal under consideration. The task is to restore the signal and, in particular, the discontinuities. In this respect, classical methods perform rather poor, whereas non-convex non-smooth variational methods seem to be the correct choice. Examples are methods based on Mumford-Shah and piecewise constant Mumford-Shah functionals and discretized versions which are known as Blake-Zisserman and Potts functionals. Owing to their non-convexity, minimization of such functionals is challenging. In this paper, we propose a new iterative minimization strategy for Blake-Zisserman as well as Potts functionals and a related jump-sparsity problem dealing with indirect, noisy measurements. We provide a convergence analysis and underpin our findings with numerical experiments.

Cell adhesion. The minimal cadherin-catenin complex binds to actin filaments under force

Linkage between the adherens junction (AJ) and the actin cytoskeleton is required for tissue development and homeostasis. In vivo findings indicated that the AJ proteins E-cadherin, β-catenin, and the filamentous (F)-actin binding protein αE-catenin form a minimal cadherin-catenin complex that binds directly to F-actin. Biochemical studies challenged this model because the purified cadherin-catenin complex does not bind F-actin in solution. Here, we reconciled this difference. Using an optical trap-based assay, we showed that the minimal cadherin-catenin complex formed stable bonds with an actin filament under force. Bond dissociation kinetics can be explained by a catch-bond model in which force shifts the bond from a weakly to a strongly bound state. These results may explain how the cadherin-catenin complex transduces mechanical forces at cell-cell junctions.

LICRE: unsupervised feature correlation reduction for lipidomics

MOTIVATION

Recent advances in high-throughput lipid profiling by liquid chromatography electrospray ionization tandem mass spectrometry (LC-ESI-MS/MS) have made it possible to quantify hundreds of individual molecular lipid species (e.g. fatty acyls, glycerolipids, glycerophospholipids, sphingolipids) in a single experimental run for hundreds of samples. This enables the lipidome of large cohorts of subjects to be profiled to identify lipid biomarkers significantly associated with disease risk, progression and treatment response. Clinically, these lipid biomarkers can be used to construct classification models for the purpose of disease screening or diagnosis. However, the inclusion of a large number of highly correlated biomarkers within a model may reduce classification performance, unnecessarily inflate associated costs of a diagnosis or a screen and reduce the feasibility of clinical translation. An unsupervised feature reduction approach can reduce feature redundancy in lipidomic biomarkers by limiting the number of highly correlated lipids while retaining informative features to achieve good classification performance for various clinical outcomes. Good predictive models based on a reduced number of biomarkers are also more cost effective and feasible from a clinical translation perspective.

RESULTS

The application of LICRE to various lipidomic datasets in diabetes and cardiovascular disease demonstrated superior discrimination in terms of the area under the receiver operator characteristic curve while using fewer lipid markers when predicting various clinical outcomes.

AVAILABILITY AND IMPLEMENTATION

The MATLAB implementation of LICRE is available from http://ww2.cs.mu.oz.au/∼gwong/LICRE

Progressive image denoising through hybrid graph Laplacian regularization: a unified framework

Recovering images from corrupted observations is necessary for many real-world applications. In this paper, we propose a unified framework to perform progressive image recovery based on hybrid graph Laplacian regularized regression. We first construct a multiscale representation of the target image by Laplacian pyramid, then progressively recover the degraded image in the scale space from coarse to fine so that the sharp edges and texture can be eventually recovered. On one hand, within each scale, a graph Laplacian regularization model represented by implicit kernel is learned, which simultaneously minimizes the least square error on the measured samples and preserves the geometrical structure of the image data space. In this procedure, the intrinsic manifold structure is explicitly considered using both measured and unmeasured samples, and the nonlocal self-similarity property is utilized as a fruitful resource for abstracting a priori knowledge of the images. On the other hand, between two successive scales, the proposed model is extended to a projected high-dimensional feature space through explicit kernel mapping to describe the interscale correlation, in which the local structure regularity is learned and propagated from coarser to finer scales. In this way, the proposed algorithm gradually recovers more and more image details and edges, which could not been recovered in previous scale. We test our algorithm on one typical image recovery task: impulse noise removal. Experimental results on benchmark test images demonstrate that the proposed method achieves better performance than state-of-the-art algorithms.

BOBA FRET: bootstrap-based analysis of single-molecule FRET data

Time-binned single-molecule Förster resonance energy transfer (smFRET) experiments with surface-tethered nucleic acids or proteins permit to follow folding and catalysis of single molecules in real-time. Due to the intrinsically low signal-to-noise ratio (SNR) in smFRET time traces, research over the past years has focused on the development of new methods to extract discrete states (conformations) from noisy data. However, limited observation time typically leads to pronounced cross-sample variability, i.e., single molecules display differences in the relative population of states and the corresponding conversion rates. Quantification of cross-sample variability is necessary to perform statistical testing in order to assess whether changes observed in response to an experimental parameter (metal ion concentration, the presence of a ligand, etc.) are significant. However, such hypothesis testing has been disregarded to date, precluding robust biological interpretation. Here, we address this problem by a bootstrap-based approach to estimate the experimental variability. Simulated time traces are presented to assess the robustness of the algorithm in conjunction with approaches commonly used in thermodynamic and kinetic analysis of time-binned smFRET data. Furthermore, a pair of functionally important sequences derived from the self-cleaving group II intron Sc.ai5γ (d3'EBS1*/IBS1*) is used as a model system. Through statistical hypothesis testing, divalent metal ions are shown to have a statistically significant effect on both thermodynamic and kinetic aspects of their interaction. The Matlab source code used for analysis (bootstrap-based analysis of smFRET data, BOBA FRET), as well as a graphical user interface, is available via http://www.aci.uzh.ch/rna/.

Signal processing for molecular and cellular biological physics: an emerging field

Recent advances in our ability to watch the molecular and cellular processes of life in action--such as atomic force microscopy, optical tweezers and Forster fluorescence resonance energy transfer--raise challenges for digital signal processing (DSP) of the resulting experimental data. This article explores the unique properties of such biophysical time series that set them apart from other signals, such as the prevalence of abrupt jumps and steps, multi-modal distributions and autocorrelated noise. It exposes the problems with classical linear DSP algorithms applied to this kind of data, and describes new nonlinear and non-Gaussian algorithms that are able to extract information that is of direct relevance to biological physicists. It is argued that these new methods applied in this context typify the nascent field of biophysical DSP. Practical experimental examples are supplied.

Sodium concentration coding gives way to evaluative coding in cortex and amygdala

Typically, stimulus batteries used to characterize sensory neural coding span physical parameter spaces (e.g., concentration: from low to high). For awake animals, however, psychological variables (e.g., pleasantness/palatability) with complicated relationships to the physical often dominate neural responses. Here we pit physical and psychological axes against one another, presenting awake rats with a stimulus set including 4 NaCl concentrations (0.01, 0.1, 0.3, and 1.0 m) plus palatable (0.3 m sucrose) and aversive (0.001 m quinine) benchmarks, while recording the activity of neurons in two sites vital for NaCl taste processing, gustatory cortex (GC) and central amygdala (CeA). Since NaCl palatability (i.e., preference) follows a non-monotonic, "inverted-U-shaped" curve while concentration increases monotonically, this stimulus battery allowed us to test whether GC and CeA responses better reflect external or internal variables. As predicted, GC single-neuron and population responses reflected both parameters in separate response epochs: sodium concentration-related information appeared with the earliest taste-specific responses, giving way to palatability-related information, in an overlapping subset of neurons, several hundred milliseconds later. CeA single-neuron and population responses, meanwhile, contained only a brief period of concentration specificity, occurring just before palatability-related information emerged (simultaneously with, or slightly later than, in GC). Thus, cortex and amygdala both prominently reflect NaCl palatability late in their responses; CeA neurons largely respond to either palatable or aversive stimuli, while GC responses tend to reflect the entire palatability spectrum in a graded fashion.

Sodium concentration coding gives way to evaluative coding in cortex and amygdala

Typically, stimulus batteries used to characterize sensory neural coding span physical parameter spaces (e.g., concentration: from low to high). For awake animals, however, psychological variables (e.g., pleasantness/palatability) with complicated relationships to the physical often dominate neural responses. Here we pit physical and psychological axes against one another, presenting awake rats with a stimulus set including 4 NaCl concentrations (0.01, 0.1, 0.3, and 1.0 m) plus palatable (0.3 m sucrose) and aversive (0.001 m quinine) benchmarks, while recording the activity of neurons in two sites vital for NaCl taste processing, gustatory cortex (GC) and central amygdala (CeA). Since NaCl palatability (i.e., preference) follows a non-monotonic, "inverted-U-shaped" curve while concentration increases monotonically, this stimulus battery allowed us to test whether GC and CeA responses better reflect external or internal variables. As predicted, GC single-neuron and population responses reflected both parameters in separate response epochs: sodium concentration-related information appeared with the earliest taste-specific responses, giving way to palatability-related information, in an overlapping subset of neurons, several hundred milliseconds later. CeA single-neuron and population responses, meanwhile, contained only a brief period of concentration specificity, occurring just before palatability-related information emerged (simultaneously with, or slightly later than, in GC). Thus, cortex and amygdala both prominently reflect NaCl palatability late in their responses; CeA neurons largely respond to either palatable or aversive stimuli, while GC responses tend to reflect the entire palatability spectrum in a graded fashion.