arXiv subjects

Ron D. Frostig

Publications and source records attributed to Ron D. Frostig.

7 recordsLinked to original sources

arXiv2024

High-Precision UWB-Based Real-Time Locating System for Rodent Behavioral Studies

Rodents have long been established as the premier model for behavioral studies, traditionally raised and maintained in conventional cage environments. However, these settings often limit rodents' ability to exhibit their full range of intrinsic behaviors and natural interactions. Precise tracking of animal movement is a critical component in behavioral research, but traditional methods, such as video tracking, present challenges, particularly with nocturnal species like rodents. This study introduces the application of ultra-wideband (UWB) sensor technology to develop a novel tracking system. The UWB DWM1001C sensor was integrated into a custom-made device worn by a single rat. A simplified habitat, measuring four-by-two feet, was used to evaluate system performance. The results show positioning accuracy errors of less than five millimeters for line-of-sight (LoS) and less than 50 millimeters for non-line-of-sight (NLoS) scenarios. This research provides a more accurate and reliable approach for animal localization, showcasing the potential of UWB sensor technology in enhancing precision in behavioral studies.

eess.IV↗

arXiv2022

Filtrated Common Functional Principal Components for Multivariate Functional data

Local field potentials (LFPs) are signals that measure electrical activity in localized cortical regions from implanted tetrodes in the human or animal brain. The LFP signals are curves observed at multiple tetrodes which are implanted across a patch on the surface of the cortex. Hence, they can be treated as multi-group functional data, where the trajectories collected across temporal epochs from one tetrode are viewed as a group of functions. In many cases, multi-tetrode LFP trajectories contain both global variation patterns (which are shared in common to all groups, due to signal synchrony) and isolated variation patterns (common only to a small subset of groups), and such structure is very informative to the analysis of such data. Therefore, one goal in this paper is to develop an efficient procedure that is able to capture and quantify both global and isolated features. We propose a novel tree-structured functional principal components (filt-fPC) analysis through finite-dimensional functional representation - specifically via filtration. A major advantage of the proposed filt-fPC method is the ability to extract the components that are common to multiple groups (or tetrodes) in a flexible "multi-resolution" manner and simultaneously preserve the idiosyncratic individual components of different tetrodes. The proposed filt-fPC approach is highly data-driven and no "ground-truth" model pre-specification is needed, making it a suitable approach for analyzing multi-group functional data that is complex. In addition, the filt-fPC method is able to produce a parsimonious, interpretable, and efficient low dimensional representation of multi-group functional data with orthonormal basis functions. Here, the proposed filt-fPCA method is employed to study the impact of a shock (induced stroke) on the synchrony structure of the rat brain.

stat.ME↗

arXiv2022

Variation Pattern Classification of Functional Data

A new classification method for functional data is proposed in this paper. This work is motivated by the need to identify features that discriminate between neurological conditions on which local field potentials (LFPs) were recorded. Regardless of the condition, these local field potentials have zero mean and thus the first moments of these random processes do not have discriminating power. We propose the variation pattern classification (VPC) method {which employs the (auto-)covariance operators as the discriminating features} and uses the Hilbert-Schmidt norm to measure the discrepancy between the (auto-)covariance operators of different groups. The proposed VPC method is demonstrated to be sensitive to the discrepancy, {potentially leading to a higher rate of classification}. One important innovation lies in the dimension reduction where the VPC method data-adaptively determines the basis functions (discriminative feature functions) that account for the major discrepancy. In addition, the selected discriminative feature functions provide insights on the discrepancy between different groups because they reveal the features of variation pattern that differentiate groups. Consistency properties are established and, furthermore, simulation studies and the analysis of rat brain LFP trajectories empirically demonstrate the advantages and effectiveness of the proposed method.

stat.ME↗

arXiv2022

Break Point Detection for Functional Covariance

Many experiments record sequential trajectories where each trajectory consists of oscillations and fluctuations around zero. Such trajectories can be viewed as zero-mean functional data. When there are structural breaks (on the sequence of trajectories) in higher order moments, it is not always easy to spot these by mere visual inspection. Motivated by this challenging problem in brain signal analysis, we propose a detection and testing procedure to find the change point in functional covariance. The detection procedure is based on the cumulative sum statistics (CUSUM). The classical testing procedure for functional data depends on a null distribution which depends on infinitely many unknown parameters, though in practice only a finite number of these can be included for the hypothesis test of the existence of change point. This paper provides some theoretical insights on the influence of the number of parameters. Meanwhile, the asymptotic properties of the estimated change point are developed. The effectiveness of the proposed method is numerically validated in simulation studies and an application to investigate changes in rat brain signals following an experimentally-induced stroke.

stat.ME↗

arXiv2019

Modeling Spectral Properties in Stationary Processes of Varying Dimensions with Applications to Brain Local Field Potential Signals

A common class of methods for analyzing of multivariate time series, stationary and nonstationary, decomposes the observed series into latent sources. Methods such as principal compoment analysis (PCA), independent component analysis (ICA) and Stationary Subspace Analysis (SSA) assume the observed multivariate process is generated by latent sources that are stationary or nonstationary. We develop a method that tracks changes in the complexity of a 32-channel local field potential (LFP) signal from a rat following an experimentally induced stroke. We study complexity through the latent sources and their dimensions that can change across epochs due to an induced shock to the cortical system. Our method compares the spread of spectral information in several multivariate stationary processes with different dimensions. A frequency specific spectral ratio (FS-ratio) statistic is proposed and its asymptotic properties are derived. The FS-ratio is blind to the dimension of the stationary process and captures the proportion of spectral information in various (user-specified) frequency bands. We apply our method to study differences in complexity and structure of the LFP before and after system shock. The analysis indicates that spectral information in the beta frequency band (12-30 Hertz) demonstrated the greatest change in structure and complexity due to the stroke.

stat.ME↗

arXiv2018

Modeling Dependence via Copula of Functionals of Fourier Coefficients

The goal of this paper is to develop a measure for characterizing complex dependence between stationary time series that cannot be captured by traditional measures such as correlation and coherence. Our approach is to use copula models of functionals of the Fourier coefficients which is a generalization of coherence. Here, we use standard parametric copula models with a single parameter both from elliptical and Archimedean families. Our approach is to analyze changes in local field potentials in the rat cortex prior to and immediately following the onset of stroke. We present the necessary theoretical background, the multivariate models and an illustration of our methodology on these local field potential data. Simulations with non-linear dependent data show information that were missed by not taking into account dependence on specific frequencies. Moreover, these simulations demonstrate how our proposed method captures more complex non-linear dependence between time series. Finally, we illustrate our copula-based approach in the analysis of local field potentials of rats.

stat.ME↗

arXiv2018

Modeling non-linear spectral domain dependence using copulas with applications to rat local field potentials

This paper intends to develop tools for characterizing non-linear spectral dependence between spontaneous brain signals. We use parametric copula models (both bivariate and vine models) applied on the magnitude of Fourier coefficients rather than using coherence. The motivation behind this work is an experiment on rats that studied the impact of stroke on the connectivity structure (dependence) between local field potentials recorded at various channels. We address the following major questions. First, we ask whether one can detect any changepoint in the regime of a brain channel for a given frequency band based on a difference between the cumulative distribution functions modeled for each epoch (small window of time). Our proposed approach is an iterative algorithm which compares each successive bivariate copulas on all the epochs range, using a bivariate Kolmogorov-Smirnov statistic. Second, we ask whether stroke can alter the dependence structure of brain signals; and examine whether changes in dependence are present only in some channels or generalized across channels. These questions are addressed by comparing Vine-copulas models fitted for each epoch. We provide the necessary framework and show the effectiveness of our methods through the results for the local field potential data analysis of a rat.

stat.AP↗