First-order Kernel Research Articles

A Framework for the Continuous Evaluation of 3D Motion Perception in Virtual Reality.

We present a novel framework for the detection and continuous evaluation of 3D motion perception by deploying a virtual reality environment with built-in eye tracking. We created a biologically-motivated virtual scene that involved a ball moving in a restricted Gaussian random walk against a background of 1/f noise. Sixteen visually healthy participants were asked to follow the moving ball while their eye movements were monitored binocularly using the eye tracker. We calculated the convergence positions of their gaze in 3D using their fronto-parallel coordinates and linear least-squares optimization. Subsequently, to quantify 3D pursuit performance, we employed a first-order linear kernel analysis known as the Eye Movement Correlogram technique to separately analyze the horizontal, vertical and depth components of the eye movements. Finally, we checked the robustness of our method by adding systematic and variable noise to the gaze directions and re-evaluating 3D pursuit performance. We found that the pursuit performance in the motion-through depth component was reduced significantly compared to that for fronto-parallel motion components. We found that our technique was robust in evaluating 3D motion perception, even when systematic and variable noise was added to the gaze directions. The proposed framework enables the assessment of 3D Motion perception by evaluating continuous pursuit performance through eye-tracking. Our framework paves the way for a rapid, standardized and intuitive assessment of 3D motion perception in patients with various eye disorders.

Is Newey–West optimal among first-order kernels?

Newey–West (1987) standard errors are the dominant standard errors used for heteroskedasticity and autocorrelation robust (HAR) inference in time series regression. The Newey–West estimator uses the Bartlett kernel, which is a first-order kernel, meaning that its characteristic exponent, q, is equal to 1, where q is defined as the largest value of r for which the quantity k[r](0)=limt→0|t|−r(k(0)−k(t)) is defined and finite. This raises the apparently uninvestigated question of whether the Bartlett kernel is optimal among first-order kernels. We demonstrate that, for q<2, there is no optimal qth-order kernel for HAR testing in the Gaussian location model or for minimizing the MSE in spectral density estimation. In fact, for any q<2, the space of qth-order positive-semidefinite kernels is not closed and, moreover, all continuous qth-order kernels can be decomposed into a weighted sum of qth and second-order kernels, which suggests that there is no meaningful notion of ‘pure’ qth-order kernels for q<2. Nevertheless, it is possible to rank any given collection of qth-order kernels using the functional Iq[k]=k[q](0)1/q∫k2(t)dt with smaller values corresponding to better asymptotic performance. We examine the value of Iq[k] for a wide variety of first-order estimators and find that none improve upon the Bartlett kernel. These comparisons provide additional justification for the continued use of the Newey–West estimator with testing-optimal smoothing parameters and fixed-b critical values despite the lack of optimality of Bartlett among first-order kernels.

Multifocal electroretinography increases following experimental glaucoma in nonhuman primates with retinal ganglion cell axotomy.

To determine whether short-latency changes in multifocal electroretinography (mfERG) observed in experimental glaucoma (EG) are secondary solely to retinal ganglion cell (RGC) loss or whether there is a separate contribution from elevated intraocular pressure (IOP). Prior to operative procedures, a series of baseline mfERGs were recorded from six rhesus macaques using a 241-element unstretched stimulus. Animals then underwent hemiretinal endodiathermy axotomy (HEA) by placing burns along the inferior 180° of the optic nerve margin in the right eye (OD). mfERG recordings were obtained in each animal at regular intervals following for 3-4months to allow stabilization of the HEA effects. Laser trabecular meshwork destruction (LTD) to elevate IOP was then performed; first-order kernel (K1) waveform root-mean-square (RMS) amplitudes for the short-latency segment of the mfERG wave (9-35ms) were computed for two 7-hexagon groupings-the first located within the superior (non-axotomized) macula and the second within the inferior (axotomized) macula. Immunohistochemistry for glial fibrillary acidic protein (GFAP) was done. By 3months post HEA, there was marked thinning of the inferior nerve fiber layer as measured by optical coherence tomography. Compared with baseline, no statistically significant changes in 9-35ms K1 RMS amplitudes were evident in either the axotomized or non-axotomized portions of the macula. Following LTD, mean IOP in HEA eyes rose to 46 ± 9 compared with 20 ± 2mmHg (SD) in the fellow control eyes. In the HEA + EG eyes, statistically significant increases in K1 RMS amplitude were present in both the axotomized inferior and non-axotomized superior portions of the OD retinas. No changes in K1 RMS amplitude were found in the fellow control eyes from baseline to HEA epoch, but there was a smaller increase from baseline to HEA + EG. Upregulation of GFAP in the Müller cells was evident in both non-axotomized and axotomized retina in eyes with elevated IOP. The RMS amplitudes of the short-latency mfERG K1 waveforms are not altered following axotomy but undergo marked increases following elevated IOP. This suggests that the increase in mfERG amplitude was not solely a result of RGC loss and may reflect photoreceptor and bipolar cell dysfunction and/or changes in Müller cells.

A polynomial multiple variance method for impulse response measurement

This manuscript describes a methodology for measuring the first-order Volterra kernel of a discrete-time nonlinear system, that is, the impulse response for small signal amplitudes of the nonlinear system. In the proposed approach, multiple linear identifications are performed using the same excitation signal multiplied by different gains, and the first-order Volterra kernel is obtained from a polynomial interpolation of the measured values. Any linear identification method proposed in the literature can be used with this approach. The proposed approach is a multiple variance (MV) method that, in contrast to all other MV methods, aims to estimate one of the kernels of the Volterra model, the first-order kernel, with high precision. The manuscript discusses the proposed methodology, determines the mean square deviation (MSD) due to noise of the measured coefficients, and the value of the optimal gains that minimize the MSD. Remarkably, it is shown in the manuscript that the optimal gains assume only a reduced set of values that depends on the order of nonlinearity. The optimal number of measurements is also determined. The conditions under which the proposed methodology is more convenient than the classical linear methods are discussed. The experimental results demonstrate the proposed methodology and its strengths.

Asymptotic properties of the normalised discrete associated-kernel estimator for probability mass function

ABSTRACT Discrete kernel smoothing is now gaining importance in nonparametric statistics. In this paper, we investigate some asymptotic properties of the normalised discrete associated-kernel estimator of a probability mass function and make comparisons. We show, under some regularity and non-restrictive assumptions on the associated-kernel, that the normalising random variable converges in mean square to 1. We then derive the consistency and the asymptotic normality of the proposed estimator. Various families of discrete kernels already exhibited satisfy the conditions, including the refined CoM-Poisson which is underdispersed and of second-order. Finally, the first-order binomial kernel is discussed and, surprisingly, its normalised estimator has a suitable asymptotic behaviour through simulations.

Neuroretinal dysfunction in patients affected by neurofibromatosis type 1.

To examine neuroretinal function by using the multifocal electroretinography (mfERG) test in patients with neurofibromatosis type 1 (NF1) without optic pathway gliomas (OPGs). This study was conducted on 35 patients (35 eyes) with NF1 and 30 healthy subjects (30 eyes) for the control group. Each subject underwent a complete ophthalmological examination including spectral domain-optical coherence tomography (SD-OCT) and mfERG. The 1.5-Tesla magnetic resonance imaging (MRI) scan of the brain was performed in NF1 patients to assess the presence of OPGs. All participants were recruited having a best corrected visual acuity (BCVA) of no less than 20/20 in each eye. The amplitude and implicit time of the P1 wave (first-order Kernel component) were evaluated on mfERG. Data analysis was carried out in the two central degrees and in the four quadrants from two to 25 degrees of visual field. Statistically significant results were obtained for the P1 wave amplitudes in the 4 quadrants in NF1 patients compared to healthy controls, while the reduction was not significant in the 2 central degrees between the groups. A statistically significant difference was observed among the P1 wave amplitudes as recorded in the 4 quadrants within the NF1 group, with lower amplitudes detected in the nasal quadrants. No differences in the implicit times were recorded in the 2 central degrees and in the 4 quadrants as compared between NF1 patients and controls. Impaired neuroretinal function in NF1 patients is expressed in a decreased amplitude of the P1-wave between 2 and 25 central retinal degrees on mfERG. Altered intracellular signal transduction due to abnormal neurofibromin-mediated cyclic adenosine monophosphate (cAMP) generation, can be involved. The possible use of mfERG as subclinical retinal damage indicator has a potential utility in clinical practice for the follow-up of NF1 patients.

Trainable segmentation for transmission electron microscope images of inorganic nanoparticles.

We present a trainable segmentation method implemented within the python package ParticleSpy. The method takes user labelled pixels, which are used to train a classifier and segment images of inorganic nanoparticles from transmission electron microscope images. This implementation is based on the trainable Waikato Environment for Knowledge Analysis (WEKA) segmentation, but is written in python, allowing a large degree of flexibility and meaning it can be easily expanded using other python packages. We find that trainable segmentation offers better accuracy than global or local thresholding methods and requires as few as 100 user-labelled pixels to produce an accurate segmentation. Trainable segmentation presents a balance of accuracy and training time between global/local thresholding and neural networks, when used on transmission electron microscope images of nanoparticles. We also quantitatively investigate the effectiveness of the components of trainable segmentation, its filter kernels and classifiers, in order to demonstrate the use cases for the different filter kernels in ParticleSpy and the most accurate classifiers for different data types. A set of filter kernels is identified that are effective in distinguishing particles from background but that retain dissimilar features. In terms of classifiers, we find that different classifiers perform optimally for different image contrast; specifically, a random forest classifier performs best for high-contrast ADF images, but that QDA and Gaussian Naïve Bayes classifiers perform better for low-contrast TEM images.

Learning linear modules in a dynamic network using regularized kernel-based methods

In order to identify one system (module) in an interconnected dynamic network, one typically has to solve a Multi-Input-Single-Output (MISO) identification problem that requires identification of all modules in the MISO setup. For application of a parametric identification method this would require estimating a large number of parameters, as well as an appropriate model order selection step for a possibly large scale MISO problem, thereby increasing the computational complexity of the identification algorithm to levels that are beyond feasibility. An alternative identification approach is presented employing regularized kernel-based methods. Keeping a parametric model for the module of interest, we model the impulse response of the remaining modules in the MISO structure as zero mean Gaussian processes (GP) with a covariance matrix (kernel) given by the first-order stable spline kernel, accounting for the noise model affecting the output of the target module and also for possible instability of systems in the MISO setup. Using an Empirical Bayes (EB) approach the target module parameters are estimated through an Expectation–Maximization (EM) algorithm with a substantially reduced computational complexity, while avoiding extensive model structure selection. Numerical simulations illustrate the potentials of the introduced method in comparison with the state-of-the-art techniques for local module identification.

Hermite Expansion Model and LMMSE Analysis for Low-Resolution Quantized MIMO Detection

In this paper, the Hermite polynomials are employed to study linear approximation models of narrowband multiantenna signal reception (i.e., MIMO) with low-resolution quantizations. This study results in a novel linear approximation using the second-order Hermite expansion (SOHE). The SOHE model is not based on those assumptions often used in existing linear approximations. Instead, the quantization distortion is characterized by the second-order Hermite kernel, and the signal term is characterized by the first-order Hermite kernel. It is shown that the SOHE model can explain almost all phenomena and characteristics observed so far in the low-resolution MIMO signal reception. When the SOHE model is employed to analyze the linear minimum-mean-square-error (LMMSE) channel equalizer, it is revealed that the current LMMSE algorithm can be enhanced by incorporating a symbol-level normalization mechanism. The performance of the enhanced LMMSE algorithm is demonstrated through computer simulations for narrowband MIMO systems in Rayleigh fading channels.

A Room Impulse Response Measurement Method Robust Towards Nonlinearities Based on Orthogonal Periodic Sequences

An open problem in room impulse response (RIR) measurement is the effect of nonlinearities, especially those with memory, present in the measurement system, specifically in the power amplifier and in the loudspeaker. The nonlinearities can corrupt the measurement introducing artifacts. The paper discusses a RIR measurement method that is robust towards these nonlinearities. The proposed methodology allows measuring the RIR using the cross-correlation method, i.e., computing the cross-correlation between the output signal and an appropriate sequence. In contrast to other cross-correlation based methods, the proposed approach directly estimates the first-order kernel of the Volterra filter modeling the measurement systems, i.e., the system impulse response for small signals. The proposed approach exploits the concepts of orthogonal periodic sequences, recently proposed in the literature. The input signal can be any periodic persistently exciting sequence and can also be a quantized sequence. Measurements performed both on an emulated scenario and in real environments illustrate the validity of the approach and compare it with other competing RIR measurement methods.

Uncertainty propagation in dynamics of composite plates: A semi-analytical non-sampling-based approach

In this study, the influences of spatially varying stochastic properties on free vibration analysis of composite plates were investigated via development of a new approach named the deterministic-stochastic Galerkin-based semi-analytical method. The material properties including tensile modulus, shear modulus, and density of the plate were assumed to be spatially varying and uncertain. Gaussian fields with first-order Markov kernels were utilized to define the aforementioned material properties. The stochastic fields were decomposed via application of the Karhunen-Loeve theorem. A first-order shear deformation theory was assumed, following which the displacement field was defined using admissible trigonometric modes to derive the potential and kinetic energies. The stochastic equations of motion of the plate were obtained using the variational principle. The deterministic-stochastic Galerkin-based method was utilized to find the probability space of natural frequencies, and the corresponding mode shapes of the plate were determined using a polynomial chaos approach. The proposed method significantly reduced the size of the mathematical models of the structure, which is very useful for enhancing the computational efficiency of stochastic simulations. The methodology was verified using a stochastic finite element method and the available results in literature. The sensitivity of natural frequencies and corresponding mode shapes due to the uncertainty of material properties was investigated, and the results indicated that the higher-order modes are more sensitive to uncertainty propagation in spatially varying properties.

Multifocal electroretinography in patients with macular telangiectasia type 2.

To evaluate the multifocal electroretinographic (mfERG) response in patients with macular telangiectasia (MacTel) type 2. Prospective, observational case series. Thirty-four eyes of 18 patients diagnosed with nonproliferative MacTel type 2 underwent recording of best-corrected visual acuity (BCVA), fundus fluorescein angiography, spectral domain optical coherence tomography (SD-OCT) and mfERG using 61 hexagonal elements, in accordance with ISCEV guidelines. The P1 average response densities and implicit times of the first-order kernel responses were grouped into five concentric rings centred on the fovea. Data from the left eyes of cases (18 eyes) were compared with 34 eyes of age- and sex-matched controls. Correlation analyses were performed between BCVA, mfERG parameters and SD-OCT measurements. Mean BCVA of the cases was 0.3 ± 0.26 ranging from 0 to 1. On SD-OCT, mean central foveal thickness was 205.78 ± 40.92μm and average mean macular thickness was 248.22 ± 23.08μm. Mean P1 amplitudes were significantly decreased in eyes with MacTel type 2 as compared to controls in ring 1 (p = 0.039). Mean P1 implicit time in all the rings was comparable between the two groups. BCVA was significantly and negatively correlated with P1 amplitude in ring 1 (r = - 0.518, p = 0.028) in eyes with MacTel type 2. mfERG reflects localised inner retinal dysfunction in MacTel type 2. Correlation with BCVA reinforces that mfERG should be used to objectively assess the macular function in these patients.

Continuous-Time DC Kernel—A Stable Generalized First-Order Spline Kernel

The stable spline (SS) kernel and the diagonal correlated (DC) kernel are two kernels that have been applied and studied extensively for kernel-based regularized LTI system identification. In this note, we show that similar to the derivation of the SS kernel, the continuous-time DC kernel can be derived by applying the same “stable” coordinate change to a “generalized” first-order spline kernel, and thus, can be interpreted as a stable generalized first-order spline kernel. This interpretation provides new facets to understand the properties of the DC kernel. In particular, we derive a new orthonormal basis expansion of the DC kernel and the explicit expression of the norm of the reproducing kernel Hilbert space associated with the DC kernel. Moreover, for the nonuniformly sampled DC kernel, we derive its maximum entropy property and show that its kernel matrix has tridiagonal inverse.

Multifocal Electroretinography in Diabetic Retinopathy With and Without Macular Edema.

To characterize the electroretinographic response of the macula by multifocal electroretinography (mfERG) in nonproliferative diabetic retinopathy (NPDR) with and without diabetic macular edema (DME) and correlate it with best-corrected visual acuity (BCVA) and foveal thickness on spectral-domain optical coherence tomography (SD-OCT). Prospective, observational case series. Forty eyes of 22 patients with treatment-naïve NPDR underwent recording of BCVA, fundus fluorescein angiography (FFA), and SD-OCT. Groups A and B were classified as 20 eyes each having NPDR with DME (central foveal thickness [CFT] ≥ 275 μm) and without DME (CFT < 275 μm), respectively. First-order kernel mfERG responses recorded according to ISCEV guidelines were grouped into five concentric rings centered on the fovea for analysis. Mean P1 and N1 amplitudes (nv/deg2) were significantly decreased compared to normal values in each of the five rings in both groups (P < .01); however, the values between the two groups were comparable. BCVA was significantly and positively correlated with P1 (r = 0.454, P = .003) and N1 amplitude (r = 0.468, P = .002) and significantly and negatively correlated with P1 (r= -0.534, P < .01) and N1 implicit times (r= -0.570, P < .01) in all patients. P1 (r= -0.531, P < .01) and N1 amplitude (r= -0.367, P = .02) in the central ring of mfERG had a significant negative correlation with macular thickness in the corresponding foveal ring of SD-OCT in all patients. mfERG reflects retinal dysfunction irrespective of the occurrence of DME in patients with NPDR. Correlation with BCVA reinforces that mfERG should be used to objectively assess the macular function in these patients. [Ophthalmic Surg Lasers Imaging Retina. 2018;49:780-786.].

Model-based dose reconstruction for CT dose estimation.

Our goal is to develop a model-based approach for CT dose estimation. We previously presented a CT dose estimation method that offered good accuracy in soft tissue regions but lower accuracy in bone regions. In this work, we propose an improved physic-based approach to achieve high accuracy for any materials and realistic clinical anatomies. Like Monte Carlo techniques, we start from a model or image of the patient and we model all relevant x-ray interaction processes. Unlike Monte Carlo techniques, we do not track each individual photon, but we compute the average behavior of the x-ray interactions, combining pencil-beam calculations for the first-order interactions and kernels for the higher order interactions. The new algorithm more accurately models the variation of materials in the human body, especially for higher attenuation materials such as bone, as well as the various x-ray attenuation processes. We performed validation experiments with analytic phantoms and a polychromatic x-ray spectrum, comparing to Monte Carlo simulation (GEANT4) as the ground truth. The results show that the proposed method has improved accuracy in both soft tissue region and bone region: less than 6% voxel-wise errors and less than 3.2% ROI-based errors in an anthropomorphic phantom. The computational cost is on the order of a low-resolution filtered backprojection reconstruction. We introduced improved physics-based models in a fast CT dose reconstruction approach. The improved approach demonstrated quantitatively good correspondence to a Monte Carlo gold standard in both soft tissue and bone regions in a chest phantom with a realistic polychromatic spectrum and could potentially be used for real-time applications such as patient- and organ-specific scan planning and organ dose reporting.

Novel age estimation model based on development of permanent teeth compared with classical approach and other modern data mining methods

In order to analyze and improve the dental age estimation in children and adolescents for forensic purposes, 22 age estimation methods were compared to a sample of 976 orthopantomographs (662 males, 314 females) of healthy Czech children and adolescents aged between 2.7 and 20.5 years. All methods are compared in terms of the accuracy and complexity and are based on various data mining methods or on simple mathematical operations. The winning method is presented in detail.The comparison showed that only three methods provide the best accuracy while remaining user-friendly. These methods were used to build a tabular multiple linear regression model, an M5P tree model and support vector machine model with first-order polynomial kernel. All of them have mean absolute error (MAE) under 0.7 years for both males and females. The other well-performing data mining methods (RBF neural network, K-nearest neighbors, Kstar, etc.) have similar or slightly better accuracy, but they are not user-friendly as they require computing equipment and the implementation as computer program. The lowest estimation accuracy provides the traditional model based on age averages (MAE under 0.96 years). Different relevancy of various teeth for the age estimation was found. This finding also explains the lowest accuracy of the traditional averages-based model.In this paper, a technique for missing data replacement for the cases with missing teeth is presented in detail as well as the constrained tabular multiple regression model. Also, we provide free age prediction software based on this wining model.

Multifocal electroretinography changes at the 1-year follow-up in a cohort of diabetic macular edema patients treated with ranibizumab

PurposeTo determine the changes in the multifocal electroretinogram (mfERG) at 1 year in a clinical series of diabetic macular edema (DME) patients treated with ranibizumab (RNBZ) using a pro re nata protocol.MethodsWe analyzed a clinical series of 35 eyes of 35 patients with DME at baseline and after treating them with RNBZ over 1 year, in order to determine the change in the macular function, which was assessed by means of the response density and the implicit time of the first-order kernel (FOK) P1 wave of the mfERG at the foveola (R1), fovea (R2) and parafovea (R3). These electrophysiological parameters were studied taking into account different independent variables, such as DME type, degree of diabetic retinopathy (DR), level of preservation of both the ellipsoid zone (IS/OS) and the external limiting membrane (ELM) and changes in central retinal thickness (CRT) and total macular volume (TMV). We also studied the relationship between the response density and the best-corrected visual acuity (BCVA).ResultsEyes with cystic and spongiform DME showed better response density with respect to the serous type (p < 0.001) at baseline. Similarly, eyes with high IS/OS and ELM preservation rates showed higher initial response density compared to the others (p < 0.001). Eyes with moderate DR had better response density compared to those with severe and proliferative DR (p = 0.001). At the beginning of the study, those eyes with proliferative and severe DR showed longer implicit times with respect to those with moderate DR (p = 0.04). The response density significantly increased in eyes that anatomically restored the IS/OS and the ELM after being treated with RNBZ (both p < 0.001). Similarly, eyes with spongiform DME further improved the response density with respect to those with cystic and serous DME (p < 0.001). On the contrary, eyes with hard exudates showed less improvement in their response density at the end of the study (p < 0.001). We observed a significant relationship between BCVA and the response density achieved at the end of the study (p = 0.012). Eyes with severe and proliferative DR significantly shortened implicit time compared to those with moderate DR (p = 0.04).ConclusionsThe multifocal electroretinogram allowed us to differentiate groups of eyes with DME according to their electrophysiological profile, both initially and after being treated with RNBZ. Ranibizumab increased the response density in all DME types included in the study, with a maximum response in those eyes with spongiform type. Once treated with RNBZ, the macular electrophysiological activity improved in eyes that had a well-preserved ellipsoid zone and ELM. The presence of hard exudates was a limitation to the response density achieved at the foveola.

Extension of First-Order Stable Spline Kernel to Encode Relative Degree

This paper focuses on the kernel-based system identification methods, which estimate the impulse response of the target system in the Bayesian estimation framework. This paper discusses about continuous-time systems, and proposes a new kernel based on a prior that the relative degree of the target system is higher than or equal to two. Such a prior is identical to a prior on the continuity of the impulse response at time zero. The proposed kernel is an extension of the first-order Stable Spline kernel, which is one of the most famous kernels. Numerical examples are shown to demonstrate the effectiveness of the proposed kernel.

Modelling of Violent Water Wave Propagation and Impact by Incompressible SPH with First-Order Consistent Kernel Interpolation Scheme

The Smoothed Particle Hydrodynamics (SPH) method has proven to have great potential in dealing with the wave–structure interactions since it can deal with the large amplitude and breaking waves and easily captures the free surface. The paper will adopt an incompressible SPH (ISPH) approach to simulate the wave propagation and impact, in which the fluid pressure is solved using a pressure Poisson equation and thus more stable and accurate pressure fields can be obtained. The focus of the study is on comparing three different pressure gradient calculation models in SPH and proposing the most efficient first-order consistent kernel interpolation (C1_KI) numerical scheme for modelling violent wave impact. The improvement of the model is validated by the benchmark dam break flows and laboratory wave propagation and impact experiments.

Detection of Impaired Sympathetic Cerebrovascular Control Using Functional Biomarkers Based on Principal Dynamic Mode Analysis.

This study sought to determine whether models of cerebrovascular function based on Laguerre-Volterra kernels that account for nonlinear cerebral blood flow (CBF) dynamics can detect the effects of functional cerebral sympathetic blockade. We retrospectively analyzed continuous beat-to-beat blood pressure, middle cerebral blood velocity, and partial-pressure of end-tidal CO2 (PETCO2) recordings from eighteen healthy individuals who were treated with either an oral dose of the α1-adrenergic receptor blocker Prazosin or a placebo treatment. The global principal dynamic modes (PDMs) were analyzed using Laguerre-Volterra kernels to examine the nonlinear system dynamics. Our principal findings were: (1) very low frequency (<0.03 Hz) linear components of first-order kernels for BP and PETCO2 are mutually coupled to CBF dynamics with the ability to separate individuals between control and blockade conditions, and (2) the gains of the nonlinear functions associated with low-pass and ≈0.03 Hz global PDMs for the BP are sensitive to sympathetic blockade. Collectively these results suggest that very low frequency global PDMs for BP may have potential utility as functional biomarkers of sympathetic neurovascular dysfunction which can occur in conditions like autonomic failure, stroke and traumatic brain injury.