Smoothing Procedure Research Articles

Analytic Smoothing and Nekhoroshev Estimates for Hölder Steep Hamiltonians

In this paper we prove the first result of Nekhoroshev stability for steep Hamiltonians in Hölder class. Our new approach combines the classical theory of normal forms in analytic category with an improved smoothing procedure to approximate an Hölder Hamiltonian with an analytic one. It is only for the sake of clarity that we consider the (difficult) case of Hölder perturbations of an analytic integrable Hamiltonian, but our method is flexible enough to work in many other functional classes, including the Gevrey one. The stability exponents can be taken to be (ell -1)/(2n{varvec{alpha }}_1...{varvec{alpha }}_{n-2})+1/2 for the time of stability and 1/(2n{varvec{alpha }}_1...{varvec{alpha }}_{n-1}) for the radius of stability, n being the dimension, ell >n+1 being the regularity and the {varvec{{alpha }}}_i’s being the indices of steepness. Crucial to obtain the exponents above is a new non-standard estimate on the Fourier norm of the smoothed function. As a byproduct we improve the stability exponents in the C^k class, with integer k.

Quantitative Analysis by 3D Graphics of Thoraco-Abdominal Surface Shape and Breathing Motion

Chest wall motion can provide information on respiratory muscles' action and on critical vital signs, like respiration and cardiac activity. The chest wall is a structure with three compartments that are independent to each other and can move paradoxically according to the pathophysiology of the disease. Opto-electronic plethysmography (OEP) allows for non-invasively 3D tracking of body movements. We aimed to extend the characteristics of OEP analysis to local analyses of thoraco-abdominal surface geometry and kinematics during respiration. Starting from the OEP output file, the 3D markers’ coordinates were combined with a triangulation matrix. A smoothing procedure (an automatic and iterative interpolation process to increase the number of vertices from 93 to 548) was applied to allow for precise local analysis of the thoraco-abdominal surface. A series of measurements can be performed to characterize the geometry of the trunk and its three compartments, in terms of volumes, height, diameters, perimeters, and area. Some shape factors, such as surface-to-volume ratio or height-to-perimeter ratio, can be also computed. It was also possible to build the vector field associated with the breathing motion of all the vertices, in terms of magnitude and motion direction. The vector field data were analyzed and displayed through two graphic tools: a 3D heatmap, in which the magnitude of motion was associated to different colors, and a 3D arrow plot, that allowed us to visualize both the magnitude and the direction of motion with color-coded arrows. The methods were applied to 10 healthy subjects (5 females) and also applied to two cases: a pregnant woman at each trimester of gestation and a patient before and after a demolition thoracic surgery. The results proved to be coherent with the physiology of healthy subjects and the physiopathology of the cases. We developed a new non-invasive method for respiratory analysis that allowed for the creation of realistic 3D models of the local and global trunk surface during respiration. The proposed representation constituted a very intuitive method to visualize and compare thoraco-abdominal surface movements within and between subjects, therefore enforcing the potential clinical translational value of the method.

Smoothing algorithms for projected center-vortex gauge fields

We study the application of SU(3) gauge field smoothing methods to $Z(3)$-projected center-vortex gauge fields. Due to the proportionality of the vortex links to the identity, naive applications of these methods are either ineffectual or limited in scope, containing subtle issues that are not obviously manifest. To overcome these issues, we introduce centrifuge preconditioning, a novel method applied prior to smoothing that rotates the links away from the center while preserving the fundamental structure of the vortex field. Additionally, the concept of vortex-preserved annealed smoothing is formulated to ensure the smoothing procedure maintains the underlying vortex structure. The application of these new methods in the context of annealed smoothing applied to vortex fields is shown to successfully achieve the desired smoothness condition required for the study of more advanced operators.

Robotic Assisted-Bronchoscopy With Cone-Beam CT ICG Dye Marking for Lung Nodule Localization: Experience Beyond USA.

Electromagnetic navigation bronchoscopy (ENB)-guided indocyanine green (ICG) fluorescence dye marking of subsolid, small and deep lung lesions facilitates subsequent minimally invasive lung resection surgeries. The novel robotic-assisted bronchoscopy (RAB) platform can improve the accuracy and yield of ENB biopsy, and the use of RAB has been extended to ICG dye marking. However, performing this procedure in the hybrid operating room guided by cone-beam CT (CBCT) with immediate proceed to lung surgery has not been well reported. We studied the safety, feasibility and clinical outcomes of 5 consecutive cases performed between December 2021 and March 2022. Navigation success was 100% while localization success using ICG was 80%. The benefits and pitfalls of robotic bronchoscopy procedures, and challenges of combining with hybrid operating room CBCT were discussed in detail. In conclusion, robotic-assisted bronchoscopy is a promising and useful tool for ICG fluorescence dye-marking, providing accurate navigation, superior maneuverability and improved ergonomics compared to conventional bronchoscopy-guided ENB procedures. Learning curve is reasonable, but meticulous system set up to incorporate the robotic system into existing CBCT platform may be required to ensure a smooth procedure.

Improved nonparametric penalized maximum likelihood estimation for arbitrarily censored survival data.

Nonparametric maximum likelihood estimation encompasses a group of classic methods to estimate distribution-associated functions from potentially censored and truncated data, with extensive applications in survival analysis. These methods, including the Kaplan-Meier estimator and Turnbull's method, often result in overfitting, especially when the sample size is small. We propose an improvement to these methods by applying kernel smoothing to their raw estimates, based on a BIC-type loss function that balances the trade-off between optimizing model fit and controlling model complexity. In the context of a longitudinal study with repeated observations, we detail our proposed smoothing procedure and optimization algorithm. With extensive simulation studies over multiple realistic scenarios, we demonstrate that our smoothing-based procedure provides better overall accuracy in both survival function estimation and individual-level time-to-event prediction (imputation) by reducing overfitting. Our smoothing procedure decreases the bias (discrepancy between the estimated and true simulated survival function) using interval-censored data by up to 48% compared to the raw un-smoothed estimate, with similar improvements of up to 34% and 23% in within-sample and out-of-sample prediction, respectively. Our smoothing algorithm also demonstrates significant overall improvement across all three metrics when compared to a popular semiparametric B-splines estimation method. Finally, we apply our method to real data on censored breast cancer diagnosis, which similarly shows improvement when compared to empirical survival estimates from uncensored data. We provide an R package, SISE, for implementing our penalized likelihood method.

Robotic Cochlear Implantation for Direct Cochlear Access

Robot-assisted systems offer great potential for gentler and more precise cochlear implantation. In this article, we provide a comprehensive overview of the clinical workflow for robotic cochlear implantation using a robotic system specifically developed for a minimally invasive, direct cochlear access. The clinical workflow involves experts from various disciplines and requires training to ensure a smooth and safe procedure. The protocol briefly summarizes the history of robotic cochlear implantation. The clinical sequence is explained in detail, beginning with the assessment of patient eligibility and covering surgical preparation, preoperative planning with the special planning software, drilling of the middle ear access, intraoperative imaging to confirm the trajectory, milling of the inner ear access, insertion of the electrode array, and implant management. The steps that require special attention are discussed. As an example, the postoperative outcome of robotic cochlear implantation in a patient with advanced otosclerosis is presented. Finally, the procedure is discussed in the context of the authors' experience.

Robotic Cochlear Implantation for Direct Cochlear Access.

Robot-assisted systems offer great potential for gentler and more precise cochlear implantation. In this article, we provide a comprehensive overview of the clinical workflow for robotic cochlear implantation using a robotic system specifically developed for a minimally invasive, direct cochlear access. The clinical workflow involves experts from various disciplines and requires training to ensure a smooth and safe procedure. The protocol briefly summarizes the history of robotic cochlear implantation. The clinical sequence is explained in detail, beginning with the assessment of patient eligibility and covering surgical preparation, preoperative planning with the special planning software, drilling of the middle ear access, intraoperative imaging to confirm the trajectory, milling of the inner ear access, insertion of the electrode array, and implant management. The steps that require special attention are discussed. As an example, the postoperative outcome of robotic cochlear implantation in a patient with advanced otosclerosis is presented. Finally, the procedure is discussed in the context of the authors' experience.

A unified framework on defining depth for point process using function smoothing

The notion of statistical depth has been extensively studied in multivariate and functional data over the past few decades. In contrast, the depth on temporal point process is still under-explored. The problem is challenging because a point process has two types of randomness: 1) the number of events in a process, and 2) the distribution of these events. Recent studies proposed depths in a weighted product of two terms, describing the above two types of randomness, respectively. Under a new framework through a smoothing procedure, these two randomnesses can be unified. Basically, the point process observations are transformed into functions using conventional kernel smoothing methods, and then the well-known functional h-depth and its modified, center-based version are adopted to describe the center-outward rank in the original data. To do so, a proper metric is defined on the point processes with smoothed functions. Then an efficient algorithm is provided to estimate the defined “center”. The mathematical properties of the newly defined depths are explored and the asymptotic theories are studied. Simulation results show that the proposed depths can properly rank point process observations. Finally, the new methods are demonstrated in a classification task using a real neuronal spike train dataset.

An Improved Updatable Backpropagation Neural Network for Temperature Prognosis in Tunnel Fires

Because it is impossible to predict the temperature in advance, specific fire scenes (fire type, fire location, tunnel geometry, etc.) are unknown in traditional tunnel fire research. To address this difficulty, this work developed a novel algorithm to achieve temperature prognosis in tunnel fires that includes an updatable backpropagation (BP) neural network and a smoothing procedure. The data-driven algorithm is not limited to a specific fire scene, which makes it easy to fit real complex tunnel fire disasters. In addition, a full-scale fire test was conducted and utilized to verify the algorithm. Two innovations, including the updatable BP neural network and the smoothing procedure, made the predicted results match well with the experimental results. We can achieve a real-time precise temperature prediction 20 s in advance at a high accuracy of about 85.6%. If there is no sudden external factor intervention, the accuracy is about 99.4%. The algorithm provides an effective numerical tool for early fire warning and firefighting decision making that can address the temperature prognosis of tunnel fires.

Time to Try Something New: Establishing Rat Models of Lung Transplantation Under ECMO Support

<h3>Purpose</h3> Extracorporeal membrane oxygenation (ECMO) has emerged as an important preoperative, perioperative, and postoperative life-support requisite in lung transplantation. Therefore, we aimed to develop rat models of lung transplantation under veno-arterial (VA) and veno-venous (VV) ECMO support. <h3>Methods</h3> Adult male Sprague-Dawley rats weighing 400-450g (recipients, n=10; donors, n=10) were used. The ECMO circuits were initiated by venous drainage from the femoral vein with extracorporeal oxygen exchange and returned to the blood circulation through the right carotid artery (VA-ECMO) or external jugular vein (VV-ECMO). Before ECMO implantation, 5ml heparinized blood from the donor rat was drawn into tubes. Simultaneously, donor lungs were obtained after pulmonary arterial perfusion with low potassium dextran lung preservation solution. ECMO-supported orthotopic left lung transplantation was performed by using cuff technique. Arterial blood gases were measured at designated intervals throughout the experiments. <h3>Results</h3> We found that VA- and VV-ECMO provided sufficient oxygenation to support a smooth left single lung transplantation procedure. The intraoperative hemodynamic and blood gas parameters were maintained stable. <h3>Conclusion</h3> In this study, we first established rat models of lung transplantation under VA and VV ECMO support. This model provides an efficient, economical, and feasible platform for studying lung transplantation with ECMO. This model can be preclinically applied to unravel significant insights in support of further translational models in large animal and human lung transplantation.

Continuous Kubo-Greenwood formula: Theory and numerical implementation.

In this paper, we present the so-called continuous Kubo-Greenwood formula intended for the numerical calculation of the dynamic Onsager coefficients and, in particular, the real part of dynamic electrical conductivity. In contrast to the usual Kubo-Greenwood formula, which contains the summation over a discrete set of transitions between electron energy levels, the continuous one is formulated as an integral over the whole energy range. This integral includes the continuous functions: the smoothed squares of matrix elements, D(ɛ,ɛ+ℏω), the densities of state, g(ɛ)g(ɛ+ℏω), and the difference of the Fermi weights, [f(ɛ)-f(ɛ+ℏω)]/(ℏω). The function D(ɛ,ɛ+ℏω) is obtained via the specially developed smoothing procedure. From the theoretical point of view, the continuous formula is an alternative to the usual one. Both can be used to calculate matter properties and produce close results. However, the continuous formula includes the smooth functions that can be plotted and examined. Thus, we can analyze the contributions of various parts of the electron spectrum to the obtained properties. The possibility of such analysis is the main advantage of the continuous formula. The continuous Kubo-Greenwood formula is implemented in the parallel code cubogram. Using the code we demonstrate the influence of technical parameters on the simulation results for liquid aluminum. We also analyze various methods of matrix elements computation and their effect on dynamic electrical conductivity.

Soft Coagulation Monopolar Suction for Rapid Resection of Supratentorial Brain Tumors: Feasibility of a New Technique and Outcomes

The aims of this study were to evaluate the feasibility of a new rapid tumor resection technique using soft coagulation monopolar suction (SCMS) and to strengthen neurosurgeons' understanding, use, and attention to this new electrosurgical technique. The rapid surgical resection technique used herein comprised monopolar suction in soft coagulation mode applied by the ERBE VIO 300s workstation and conventional microsurgical suction. We applied this technique to supratentorial tumors in 12 patients (5 with glioblastomas, 4 with astrocytomas, 2 with metastases, and one with lymphoma) as the SCMS group. The conventional bipolar electrocautery and suction method was used for another 12 patients (non-SCMS group). The surgical results and perioperative complications were retrospectively evaluated. Radiographic and histologic analyses were performed to describe the degree of thermal damage. The mean estimated operative time and total blood loss were 3.63±0.61hours (P= 0.0048) and 308.33±172.99mL(P= 0.0482) in the SCMS group, respectively, and these values were significantly lower than those in the non-SCMS group (4.33±0.49hours and 466.67±196.95mL, respectively). No significant differences in perioperative complications, Karnofsky Performance Status scores, perioperative area edema volumes, perioperative ischemic areas, or mean residual tumors were observed between the groups. Histological examination revealed that SCMS produced uniform coagulation and completely obstructed most small vessel structures on the tumor surface. This new technique involving SCMS allows for a smooth surgical procedure and appears to be safe and feasible for the rapid resection of supratentorial brain tumors. Thus, neurosurgeons should consider using this technique in the future.

A new filtering inference procedure for a GED state-space volatility model

A vast amount of methods have been developed to make inferences for volatility data, taking into account the stylized facts of rate/return data. However, the common problem is that the latent parameters of many volatility models are high-dimensional and analytically intractable. Therefore, their inference procedure requires numerical approximations using intensive computational techniques, as the Markov chain Monte Carlo, Laplace, and particle filter methods. A common strategy to overcome this problem is model linearization. This approach consists of writing the stochastic volatility model as a linear Gaussian state-space model, leading to an approximated marginal likelihood using the Kalman filter, reducing the problem’s dimensionality. This paper proposes a new filtering inference procedure with an integrated likelihood for a Generalized Error Distribution (GED) state-space volatility model without model linearization. Also, we evaluate the quality of our method approximation and introduce an approximated smoothing procedure. We use the Bayesian methods for making the inference of static parameters and perform a simulation exercise to study the estimators’ properties. Our results show that the proposed model can be reasonably estimated, and the approximation of our method is reasonable. Furthermore, we provide a case study of the pound/dollar and real/dollar exchange rate to illustrate our approach’s performance. For the real/dollar time series, the model captures a high volatility pattern due to the COVID-19 pandemic.

Low-Altitude Sensing of Urban Atmospheric Turbulence with UAV

The capabilities of a quadcopter in the hover mode for low-altitude sensing of atmospheric turbulence with high spatial resolution in urban areas characterized by complex orography are investigated. The studies were carried out in different seasons (winter, spring, summer, and fall), and the quadcopter hovered in the immediate vicinity of ultrasonic weather stations. The DJI Phantom 4 Pro quadcopter and AMK-03 ultrasonic weather stations installed in different places of the studied territory were used in the experiment. The smoothing procedure was used to study the behavior of the longitudinal and lateral spectra of turbulence in the inertial and energy production ranges. The longitudinal and lateral turbulence scales were estimated by the least-square fit method with the von Karman model as a regression curve. It is shown that the turbulence spectra obtained with DJI Phantom 4 Pro and AMK-03 generally coincide, with minor differences observed in the high-frequency region of the spectrum. In the inertial range, the behavior of the turbulence spectra shows that they obey the Kolmogorov–Obukhov “5/3” law. In the energy production range, the longitudinal and lateral turbulence scales and their ratio measured by DJI Phantom 4 Pro and AMK-03 agree to a good accuracy. Discrepancies in the data obtained with the quadcopter and the ultrasonic weather stations at the territory with complex orography are explained by the partial correlation of the wind velocity series at different measurement points and the influence of the inhomogeneous surface.

Challenges in Device Closure of Secundum Atrial Septal Defect in Older Patients in Their Fifth Decade and Beyond.

ObjectiveTranscatheter atrial septal defect (ASD) device closure in the older population presents a greater challenge due to the long-standing effect of atrial left-to-right shunt. This study analyzes the challenges encountered in transcatheter ASD device closure in older patients in their fifth decade and beyond.MethodsAdults aged 40 years and above with significant secundum ASD who underwent transcatheter ASD device closure between June 2015 and April 2021 were analyzed. Challenges were classified as major and minor challenges based on their impact on the alteration of the treatment protocol. Patients were categorized into three subgroups according to age. Group 1 consisted of patients aged 40-49 years (n = 13), Group 2 consisted of patients aged 50-59 years (n = 16), and Group 3 consisted of patients aged 60 years and above (n = 8).ResultsA total of 37 patients were analyzed. The challenges encountered were arrhythmia, pulmonary hypertension, left ventricular diastolic dysfunction, bleeding, stroke, coronary artery disease (CAD), hypertension, and airway disease. Thirteen percent of challenges were seen in pre-procedure time, whereas 79% of challenges during the procedure and 8% of challenges during post-procedure were seen. Thirty-five patients (94.6%) underwent transcatheter ASD device closure. Two patients (5.4%) did not undergo transcatheter ASD device closure due to severe diastolic dysfunction and associated CAD, respectively. Eleven major challenges were encountered in 10 patients in which one patient had a dual challenge of bleeding and arrhythmia. Thirteen patients (35.1%) had smooth procedures without any challenges encountered. Twenty-seven minor challenges were encountered in 20 patients with some patients having an overlap of multiple major and minor challenges. The patients were doing well at the mean follow-up of 28 months.ConclusionsTranscatheter ASD device closure in older patients who are 40 years and above is safe and effective. Such high-risk patients are prone to various challenges that can be effectively managed if optimally monitored on the basis of a proper understanding of the altered physiology and anticipation of the deviated course at various stages of the procedure.

L-Spline Interpolation for Differential Operators of Order 4 with Constant Coefficients

&#x0D; &#x0D; &#x0D; In this paper it is shown that many features from polynomial spline methods used in nonparametric regression and smoothing procedures carry over to the class of L-splines where L is a linear differential operator of order 4 with constant coefficients. Special attention is given to the question whether an analogue of the Reinsch algorithm is valid and criteria are given such that the associated matrix R is strictly diagonal dominant&#x0D; &#x0D; &#x0D;

Signal smoothing for score-driven models: a linear approach

In the present article, a linear approach of signal smoothing for nonlinear score-driven models is suggested, by using results from the literature on minimum mean squared error signals. Score-driven location, trend, and seasonality models with constant and score-driven scale parameters are used, for which the parameters are estimated by using the maximum likelihood method. The smoothing procedure is computationally fast, and it uses closed-form formulas for smoothed signals. Applications for monthly data of the seasonally adjusted and the not seasonally adjusted the United States inflation rate variables for the period of 1948–2020 are presented.

On the edge‐based smoothed finite element approximation of viscoelastic fluid flows

AbstractThis article discusses the numerical simulation of viscoelastic fluid flows using the edge‐based smoothed finite element method (ESFEM). The incompressible Navier–Stokes equations coupled with the Oldroyd‐B constitutive relation are decoupled via the characteristic‐based split scheme that enables the use of equal‐order interpolation for the triple primitive variables. For this reason, the spatial discretization is implemented with linear three‐node triangular elements which work very well with the ESFEM. Edge‐based smoothing cells (SCs) are constructed on grounds of existing elements, directly underpinning the essential gradient smoothing procedure. New integration points are proposed within local SCs since the ESFEM enjoys the tremendous flexibility of the smoothed Galerkin weak‐form integral. The discrete viscoelastic system is entirely formulated in the edge‐based notion such that all gradient‐related terms are readily smoothed cell‐by‐cell. Finally, several numerical examples are presented to demonstrate the desirable capability of the ESFEM.

Implicit shock tracking for unsteady flows by the method of lines

A recently developed high-order implicit shock tracking (HOIST) framework for resolving discontinuous solutions of inviscid, steady conservation laws [43,45] is extended to the unsteady case. Central to the framework is an optimization problem which simultaneously computes a discontinuity-aligned mesh and the corresponding high-order approximation to the flow, which provides nonlinear stabilization and a high-order approximation to the solution. This work extends the implicit shock tracking framework to the case of unsteady conservation laws using a method of lines discretization via a diagonally implicit Runge-Kutta method by “solving a steady problem at each timestep”. We formulate and solve an optimization problem that produces a feature-aligned mesh and solution at each Runge-Kutta stage of each timestep, and advance this solution in time by standard Runge-Kutta update formulas. A Rankine-Hugoniot based prediction of the shock location together with a high-order, untangling mesh smoothing procedure provides a high-quality initial guess for the optimization problem at each time, which results in rapid convergence of the sequential quadratic programing (SQP) optimization solver. This method is shown to deliver highly accurate solutions on coarse, high-order discretizations without nonlinear stabilization and recover the design accuracy of the Runge-Kutta scheme. We demonstrate this framework on a series of inviscid, unsteady conservation laws in both one- and two- dimensions. We also verify that our method is able to recover the design order of accuracy of our time integrator in the presence of a strong discontinuity.

АЛГОРИТМ КОНСЕРВАТИВНОГО СГЛАЖИВАНИЯ РАЗРЫВНЫХ ВОЛН НАПРЯЖЕНИЙ В МКЭ

Three-dimensional geometrically and physically nonlinear problems of nonstationary deformation of structures are considered. The defining system of equations is formulated in Lagrange variables. The equation of motion is derived from the balance of virtual work capacities. The elastic-plastic deformation of structural materials is described by the relations of the flow theory with isotropic hardening. The solution of the problem is based on the moment scheme of the finite element method. The discretization of the problem by spatial variables is carried out by eight nodal finite elements with multilinear functions of the approximation form of the displacement velocity. Time integration is performed according to an explicit finite-difference scheme of the “cross” type, which does not have the monotonicity property. Due to the dispersion in the vicinity of the gap, it generates non-physical oscillations, which significantly limits the scope of its applicability. In this paper, to suppress high-frequency oscillations, it is proposed to use an algorithm for conservative smoothing of a numerical solution with a space-time monotony analyzer. Based on it, software modules have been developed for the “Dynamics-3” computing complex. Verification of the developed technique and its software implementation was carried out by solving a one-dimensional problem in a three-dimensional formulation of the compression wave passing through a fixed elastic layer. For comparison, the results of numerical solution of the problem according to the “cross” scheme without smoothing, with linear viscosity, with conservative smoothing using spatial and spatiotemporal monotonicity analyzers are obtained. The problem of penetration of an elastic cylinder into a round steel plate is solved in a three-dimensional formulation. It is shown that the developed technique not only suppresses high-frequency oscillations, but also prevents the occurrence of zero-energy modes. So, in the second problem, without using the procedure of conservative smoothing of the numerical solution, the final elements of the plate in the collision zone are significantly distorted, which leads to an early interruption of the calculation.