Parametric Representation Research Articles

NUMERICAL-ANALYTICAL METHOD OF DECOMPOSITION-AUTOCOMPENSATION FOR SOLVING THE SIGNAL RECOGNITION PROBLEM BASED ON INACCURATE OBSERVATIONS

A numerical-analytical method is developed to solve the problem of optimal recognition of a set of possible signals observed as an additive mixture containing not only a fluctuation observation error (with an unknown statistical distribution) but also a singular interference (with parametric uncertainty). The method allows for both the detection of signals present in the mixture and the estimation of their parameters within a specified quality criterion and associated constraints. The proposed method, based on the idea of generalized invariant-unbiased estimation of linear functional values, enables decomposition of the computational procedure and autocompensation of singular interference without resorting to the traditional expansion of the state space. Linear spectral decompositions in specified functional bases are used for the parametric finite-dimensional representation of signals and interference, while knowledge of the correlation matrix of the observation error is sufficient for error description. Random and systematic errors are analyzed, and an illustrative example is provided.

On factorization hierarchy of equations for banana Feynman integrals

We present a review of the relations between various equations for maximal cut banana Feynman diagrams, i.e. integrals with propagators substituted with δ-functions. We consider both equal and generic masses. There are three types of equation to consider: those in coordinate space, their Fourier transform and Picard-Fuchs equations originating from the parametric representation. First we review the properties of the corresponding differential operators themselves, mainly their factorization properties at the equal mass locus and their form at special values of the dimension. Then we study the relation between the Fourier transform of the coordinate space equations and the Picard-Fuchs equations and show that they are related by factorization as well. The equations in question are the counterparts of the Virasoro constraints in the much-better studied theory of eigenvalue matrix models and are the first step towards building a full-fledged theory of Feynman integrals, which will reveal their hidden integrable structure.

Parametrization and Cartesian representation techniques for robust resolution of chemical equilibria

Chemical equilibria computations, especially those with vanishing species in the aqueous phase, lead to nonlinear systems that are difficult to solve due to gradient blow up. Instead of the commonly used ad hoc treatments, we propose two reformulations of the single-phase chemical equilibrium problem which are in line with the spirit of preconditioning but whose actual aims are to guarantee a better stability of Newton's method. The first reformulation is a parametrization of the graph linking species mole fractions to their chemical potentials. The second is based on an augmented system where this relationship is relaxed for the iterates by means of a Cartesian representation. We theoretically prove the local quadratic convergence of Newton's method for both reformulations. From a numerical point of view, we demonstrate that the two techniques are accurate, allowing to compute equilibria with chemical species having very low concentrations. Moreover, the robustness of our methods combined with a globalization strategy is superior to that of the literature.

Characterizing Hardware Utilization on Edge Devices when Inferring Compressed Deep Learning Models

Implementing edge AI involves running AI algorithms near the sensors. Deep Learning (DL) Model has successfully tackled image classification tasks with remarkable performance. However, their requirements for huge computing resources hinder the implementation of edge devices. Compressing the model is an essential task to allow the implementation of the DL model on edge devices. Post-training quantization (PTQ) is a compression technique that reduces the bit representation of the model weight parameters. This study looks at the impact of memory allocation on the latency of compressed DL models on Raspberry Pi 4 Model B (RPi4B) and NVIDIA Jetson Nano (J. Nano). This research aims to understand hardware utilization in central processing units (CPU), graphics processing units (GPU),and memory. This study focused on the quantitative method, which controls memory allocation and measures warm-up time, latency, CPU, and GPU utilization. Speed comparison among inference of DL models on RPi4B and J. Nano. This paper observes the correlation between hardware utilization versus the various DL inference latencies. According to our experiment, we concluded that smaller memory allocation led to high latency on both RPi4B and J. Nano. CPU utilization on RPi4B. CPU utilization in RPi4B increases along with the memory allocation; however, the opposite is shown on J. Nano since the GPU carries out the main computation on the device. Regarding computation, thesmaller DL Size and smaller bit representation lead to faster inference (low latency), while bigger bit representation on the same DL model leads to higher latency.

Intelligent Fault Diagnosis Method Based on Neural Network Compression for Rolling Bearings

Rolling bearings are often exposed to high speeds and pressures, leading to the symmetry in their rotating structure being disrupted, which can lead to serious failures. Intelligent rolling bearing fault diagnosis is a critical part of ensuring operation of machinery, and it has been facilitated by the growing popularity of convolutional neural networks (CNNs). The outstanding performance of fault diagnosis CNNs results from complex and redundant network structures and parameters, resulting in huge storage and computational requirements, which makes it challenging to implement these models in resource-limited industrial devices. This study aims to address this problem by proposing a comprehensive compression method for CNNs that is applied to intelligent fault diagnosis. It involves several different compression methods, including tensor train decomposition, parameter quantization, and knowledge distillation for deep network compression. This results in a significant decrease in redundancy and speeding up the training of CNN models. Firstly, tensor train decomposition is applied to reduce redundant connections in both convolutional and fully connected layers. The next step is to perform parameter quantization to minimize the bits needed for parameter representation and storage. Finally, knowledge distillation is used to restore accuracy to the compressed model. The effectiveness of the proposed approach is confirmed by an experiment and ablation study with different models on several datasets. The results show that it can significantly reduce redundant information and floating-point operations with little degradation in accuracy. Notably, on the CWRU dataset, with about 60% parameter reduction, there is no degradation in our model’s accuracy. The proposed approach is a new attempt at the intelligent fault diagnosis of rolling bearings in industrial equipment.

Graph‐Based Representation Approach for Deep Learning of Organic Light‐Emitting Diode Devices

The performance prediction of organic light‐emitting diode (OLED) devices using artificial intelligence is significantly limited due to the lack of representational feature data. This study proposes a novel graph‐based representation methodology to effectively address these challenges. Various graph convolution methods are explored, resulting in an ideal representation of the device parameters in the static equilibrium state, which is crucial for accurate modeling. This representation not only exhibits parameter‐like characteristics but also encapsulates essential physical meanings that enhance interpretability. Additionally, the trained predictive model demonstrates relatively high accuracy, making it a reliable tool for practical applications. Finally, this research serves as a valuable initial study for predicting and designing OLED devices, paving the way for future advancements in the field.

An analytical study of Euler angle and Rodrigues parameter representations of $\mathbb{SO}(3)$ towards describing subsets of ${\mathbb{SO}}(3)$ geometrically and establishing the relations between these

Abstract Descriptions of various subsets of $\mathbb{SO}(3)$ are encountered frequently in robotics, for example, in the context of specifying the orientation workspaces of manipulators. Often, the Cartesian concept of a cuboid is extended into the domain of Euler angles, notwithstanding the fact that the physical implications of this practice are not documented. Motivated by this lacuna in the existing literature, this article focuses on studying sets of rotations described by such cuboids by mapping them to the space of Rodrigues parameters, where a physically meaningful measure of distance from the origin is available and the spherical geometry is intrinsically pertinent. It is established that the planar faces of the said cuboid transform into hyperboloids of one sheet and hence, the cuboid itself maps into a solid of complicated non-convex shape. To quantify the extents of these solids, the largest spheres contained within them are computed analytically. It is expected that this study would help in the process of design and path planning of spatial robots, especially those of parallel architecture, due to a better and quantitative understanding of their orientation workspaces.

A New Link to Helices in Euclidean $3$-Space

In this paper, we introduce a novel approach for obtaining the parametric expression and description of a general helix, slant helix, and Darboux helix. The new method involves projecting $\alpha $ onto a plane passing through $\alpha \left( 0\right) $ and orthogonal to the unit axis vector $U$ in order to determine the position vector of the general helix $\alpha $. The position vector of the helix with the plane curve $\gamma $ and its axis $U$ is then established. Additionally, a relation between the curvatures of $\alpha $ and $\gamma $ is presented. The proposed technique is then applied to derive the parametric representation of a slant helix and Darboux helix, followed by the provision of various examples obtained through the application of this methodology.

Calibration of a hybrid model for HVAC systems for fault data generation

The application of automated fault detection and diagnosis algorithms has proven to be an effective way to increase the energy efficiency of buildings. While data-driven strategies have demonstrated their potential in developing such algorithms, they require a set of historical data that represents both healthy and faulty equipment operation, which is not a common scenario in real facilities. This article presents a methodology for the generation of synthetic data on both healthy and faulty operation for building heating and air conditioning equipment, which is especially useful for supervision and failure detection in the case of replication and expansion of buildings in tertiary or residential building planning programmes. This work investigates the automatic calibration of a typical air-handling unit hybrid model, composed of the detailed parametric representation of the system components and its control sequence coupled with a simplified thermal load. The model is then extended with fault models that resemble commonly encountered component faults to generate operation data in faulty scenarios. The proposed framework is validated in a real use case with the calibration of an air-handling unit system and its control sequence using 15 days of data gathered from the building management system. The results obtained from the injection of seven typical faults are then compared with the fault-free simulations to highlight and validate their impact on key operating variables. The results prove the capabilities of this methodology to support database generation in the fields of fault detection and advanced maintenance of buildings’ air conditioning systems for building replicas.

Banana diagrams as functions of geodesic distance

We extend the study of banana diagrams in coordinate representation to the case of curved space-times. If the space is harmonic, the Green functions continue to depend on a single variable – the geodesic distance. But now this dependence can be somewhat non-trivial. We demonstrate that, like in the flat case, the coordinate differential equations for powers of Green functions can still be expressed as determinants of certain operators. Therefore, not-surprisingly, the coordinate equations remain straightforward – while their reformulation in terms of momentum integrals and Picard-Fuchs equations can seem problematic. However we show that the Feynman parameter representation can also be generalized, at least for banana diagrams in simple harmonic spaces, so that the Picard-Fuchs equations retain their Euclidean form with just a minor modification. A separate story is the transfer to the case when the Green function essentially depends on several rather than a single argument. In this case, we provide just one example, that the equations are still there, but conceptual issues in the more general case will be discussed elsewhere.

Parameterization of Vertical Turbulent Transport in the Inner Core of Tropical Cyclones and Its Impact on Storm Intensification. Part I: Sensitivity to Turbulent Mixing Length

Abstract In the inner core of a tropical cyclone, turbulence not only exists in the boundary layer (BL) but can also be generated above the BL by eyewall and rainband clouds. Thus, the treatment of vertical turbulent mixing must go beyond the conventional scope of the BL. The turbulence schemes formulated based on the turbulent kinetic energy (TKE) are attractive as they are applicable to both deep and shallow convection regimes in the tropical cyclone (TC) inner core provided that the TKE production and dissipation can be appropriately determined. However, TKE schemes are not self-closed. They must be closed by an empirically prescribed vertical profile of mixing length. This motivates this study to investigate the sensitivity of the simulated TC intensification to the sloping curvature and asymptotic length scale of mixing length, the two parameters that determine the vertical distribution of a prescribed mixing length. To tackle the problem, both idealized and real-case TC simulations are performed. The results show that the simulated TC intensification is sensitive to the sloping curvature of mixing length but only exhibits marginal sensitivity to the asymptotic length scale. The underlying reasons for such sensitivities are explored analytically based on the Mellor and Yamada level-2 turbulence model and the analyses of azimuthal-mean tangential wind budget. The results highlight the uncertainty and importance of mixing length in the numerical prediction of TCs and suggest that future research should focus on searching for physical constraints on mixing length, particularly in the low- to midtroposphere, using observations and large-eddy simulations. Significance Statement The parametric representation of subgrid-scale turbulent mixing is one of the major sources of uncertainty in numerical predictions of tropical cyclones (TCs). This study investigates how the numerical prediction of TC intensification is affected by the turbulent mixing length, a length scale that is required to close a turbulence scheme formulated based on the turbulent kinetic energy (TKE). The research highlights the uncertainty and importance of mixing length in numerical prediction of TCs and suggests that future research should focus on searching for physical constraints on the mixing length, particularly in the low- to midtroposphere, using observations and large-eddy simulations.

A parametric approach for creating finite element models from point clouds for steel superstructure components in steel girder bridges

Finite element (FE) analysis is widely used to evaluate the conditions of existing bridges. However, the creation of high-fidelity FE models (FEM) for existing bridges is often a challenging task. In view of the ability of 3D laser scanning to capture detailed geometrical information, this study proposes a direct scan-to-FEM strategy specifically for steel bridge superstructure and hence to facilitate the creation of high-fidelity FE models for existing steel girder bridges. Parametric representations are proposed to address partial occlusions in the point clouds as well as to reinforce the connectivity and alignment between the superstructure elements. Mesh generation algorithms are developed to automatically convert the parametric representations into all-hexahedron FE mesh assembly that can be used directly for FE analysis without any mesh verification or editing. Experimental validations are carried out to evaluate the effectiveness of proposed method in term of both mesh quality and analysis accuracy.

High-resolution multicomponent LFM parameter estimation based on deep learning

This paper addresses the complex challenge of parameter estimation in multi-component Linear Frequency Modulation (LFM) signals by introducing an innovative approach to high-resolution Fractional Fourier Transform (FrFT) parameter estimation, facilitated by convolutional neural networks. Initially, it analyzes the issues of peak shifts and the masking of weaker components due to spectral overlap in the FrFT domain of multi-component LFM signals. Convolutional neural networks are then employed to train and achieve high-resolution representations of FrFT parameters. Specifically, convolutional modules with residual structures are utilized to learn coarse features, while a weighted attention mechanism refines independent features across both channel and spatial dimensions. This approach effectively addresses the challenges posed by spectral peak overlap and frequency shifts in multi-component LFM signals, thereby enhancing the quality of high-resolution parameter estimation. Experimental results demonstrate that the proposed method significantly outperforms traditional methods in processing multi-component LFM signals. Moreover, it exhibits robust detection capabilities for both weak and compact components, thereby underscoring its potential applicability in the field of complex signal processing.

Immune checkpoint blockade lowers the threshold of naïve T-cell priming to drug-associated antigens in a dose-dependent fashion.

A growing body of clinical and experimental evidence indicates that immune checkpoint blockade enhances patient susceptibility to hypersensitivity reactions to co-administered medications. In this study, we utilized an in vitro T-cell priming assay to demonstrate one of the mechanistic hypotheses on how this occurs; through lowering of the threshold in patients to elicit aberrant T-cell responses. We outline the dependency of de novo T-cell priming responses to drug-associated antigens on dose at initial exposure. Findings support the aforementioned hypothesis and offer an experimental representation of fundamental parameters at play in hypersensitivity reactions to low molecular weight compounds.

Developing MATLAB graphical user interface for acquiring single star SCIDAR data

To enhance operational efficiency and meet experimental demands, we have developed a graphical user interface (GUI) using MATLAB for Acquiring Single Star SCIDAR Data, leveraging the software’s integrated GUI Development Environment (GUIDE) tool. This interface streamlines the preprocessing and numerical computation of the power spectrum of atmospheric speckles while providing real-time graphical representations of atmospheric parameters, including the vertical profile of the refractive index structure function Cn2(h). It also incorporates parameters related to adaptive optics and high angular resolution, such as seeing, enabling immediate and instantaneous visual assessment of observational conditions. Furthermore, the novelty of this GUI lies in the ease of acquiring and processing data from various atmospheric parameters. The Single Star SCIDAR (Scintillation Detection and Ranging) method relies on analyzing the scintillation of light from single stars to assess the turbulent characteristics of the atmosphere. This assessment is based on the description provided by Cn2(h) derived from minimizing an objective function determined using the power spectrum of atmospheric speckles from single stars. For this purpose, a minimization algorithm called active-set is used.

Parametric approximations of fast close encounters of the planar three-body problem as arcs of a focus-focus dynamics

Abstract A gravitational close encounter of a small body with a planet may produce a substantial change of its orbital parameters which can be studied using the circular restricted three-body problem. In this paper we provide parametric representations of the fast close encounters with the secondary body of the planar CRTBP as arcs of non-linear focus-focus dynamics. The result is the consequence of a remarkable factorisation of the Birkhoff normal forms of the Hamiltonian of the problem represented with the Levi–Civita regularisation. The parameterisations are computed using two different sequences of Birkhoff normalisations of given order N. For each value of N, the Birkhoff normalisations and the parameters of the focus-focus dynamics are represented by polynomials whose coefficients can be computed iteratively with a computer algebra system; no quadratures, such as those needed to compute action-angle variables of resonant normal forms, are needed. We also provide some numerical demonstrations of the method for values of the mass parameter representative of the Sun–Earth and the Sun–Jupiter cases.

Revisiting the time-ordering issue of TMD soft factors: causality, coordinate space analyticity and new equalities

We show that as a result of causality-constrained coordinate space analyticity, the Drell-Yan-shape transverse-momentum dependent soft factor in the exponential regulator allows Euclidean-type parametric representations without cuts, to all orders in perturbation theory. Moreover, it is identical to another soft factor defined with a single time-ordering that has a natural interpretation as a space-like form factor. Furthermore, this relation continues to hold for a larger class of TMD soft factors that interpolate between three different rapidity regulators: the off-light-cone regulator, the finite light-front length regulator, and the exponential regulator.

Improved Parametric Representation of IM From FEM for More Accurate Torque Predictions: Simulations and Experimental Validations

Improved Parametric Representation of IM From FEM for More Accurate Torque Predictions: Simulations and Experimental Validations

Acanthus ornament generation using layout subdivisions with parameterized motifs

AbstractAcanthus ornaments frequently adorn Western architectural designs. The placement of these motifs varies according to the decorative object, with some having motifs arranged in a grid pattern. In this study, we propose a procedural modeling system aimed at generating acanthus ornaments on a planar surface. The proposed approach initially establishes the layout of boundary grids for acanthus motifs by subdividing the target surface into nonuniform grids. Subsequently, the medial axis line of the acanthus motif is generated to optimally conform to each boundary grid, employing a parameterized representation of deformable motifs. The three‐dimensional motif shapes are ultimately constructed from the medial axis, with the shape parameters adjusted to improve aesthetic appeal. The proposed system generates various acanthus ornaments through rule‐based layout subdivisions, offering users the option to select their preferred design while adjusting the motif shapes with a few manual parameters.

Retrieving compressive sea ice strength in the Beaufort Sea using the inverse visco-plastic model

We apply a simplified 2d Visco-Plastic (VP) sea ice model with a spatially variable representation of the sea ice rheological parameters for retrieving maximum compressive sea ice strength from satellite and in situ observations. A set of Observing System Simulation Experiments (OSSEs) demonstrates feasibility of optimizing rheological parameter of the VP sea ice model through the variational data assimilation approach during the periods of strong sea ice convergence if accurate sea ice observations are available. Following this strategy, the developed variational data assimilation VP model was applied to the sea ice velocity (https://nsidc.org/data/nsidc-0116/versions/4), sea ice concentration (https://nsidc.org/data/) and CryoSat-2 sea ice thickness observations collected in the vicinity of three moorings in the Beaufort Sea during periods of intensive sea ice convergence. Ice velocities from moorings and atmospheric wind speed (NCEP-NCAR) were used as well. Our results show that conventional maximum compressive sea ice strength (Hibler, 1979) may depend on sea ice thickness or other parameters partly controlled by the sea ice thickness, which is driven by the seasonal cycle.