Linear Approximation Research Articles

Machine learning-augmented modeling on the formation of Si-dominated Non-β″ early-stage precipitates in Al-Si-Mg alloys with Si supersaturation induced by non-equilibrium solidification

Recent experiments have shown that Al-Si-Mg alloys solidified under high cooling rates may lead to the nucleation of Si-enriched clusters that are remarkably different from the conventional Mg-Si co-clusters (e.g. β″ particles), and yet the responsible mechanism remains to be elucidated. Here we tackle the problem using a multiscale modeling framework that integrates atomistic modeling, energy landscape sampling, and lattice-based kinetic Monte Carlo (kMC) simulation. The migration energy barriers for vacancy-mediated diffusion amid complex local chemical environments are predicted on-the-fly using a surrogate machine learning model. We discover that the actual vacancy-Si migration barriers are much lower than those assumed in the classic linear interpolation approximation. Such a strong deviation from conventional wisdom, in conjunction with differing Si solute composition, can lead to a great variety in the nucleated early-stage precipitates. More specifically, a high-level supersaturation of Si solute (i.e.xSi/(xSi+xMg)>0.75) would lead to an unexpectedly high enrichment of Si in the nucleated clusters with the Si:Mg ratio up to 5∼6; while at a lower-level supply of Si solute the Mg-Si co-clusters (i.e. Si:Mg ratio around 1∼2) are nucleated instead. These findings provide a viable explanation for the diverse types of early-stage precipitates observed in various experiments, from Si-enriched precipitates in high-pressure die cast Al alloys to β″ particles in conventional casting and/or heat-treated alloys. The implications of our findings are also discussed.

"Development of a statistical calculation model for the carbon diffusion parameters in metals and alloys"

Carbon diffusion in metals has received a lot of attention and has been the subject of intensive theoretical investigations in recent years. The purpose of this work is development the statistical calculation model (SCM) on the diffusion of carbon in metals and its application for calculating the diffusion coefficients of carbon in alloys. It includes first-principles calculation of the diffusion coefficient according to a statistical model, physicochemical calculation of activation energies for carbon, and linear approximation of carbon diffusion in alloys. The calculated values of the diffusion coefficient for metals are within the range of the experimental values. For low-melting metals, carbon diffusion coefficients are mainly unknown from experiment, but the statistical model allows us to predict their values. The calculations are compared with known experimental data on the diffusion of carbon atoms in some metals Fe, V, Ta and W at high temperatures with fairly good agreement between the results. The SCM-model allows us to determine the influence of the alloying elements Si, Mo and Cr on the diffusion of carbon in the F – C alloy.

The fly connectome reveals a path to the effectome

A goal of neuroscience is to obtain a causal model of the nervous system. The recently reported whole-brain fly connectome1–3 specifies the synaptic paths by which neurons can affect each other, but not how strongly they do affect each other in vivo. To overcome this limitation, we introduce a combined experimental and statistical strategy for efficiently learning a causal model of the fly brain, which we refer to as the ‘effectome’. Specifically, we propose an estimator for a linear dynamical model of the fly brain that uses stochastic optogenetic perturbation data to estimate causal effects and the connectome as a prior to greatly improve estimation efficiency. We validate our estimator in connectome-based linear simulations and show that it recovers a linear approximation to the nonlinear dynamics of more biophysically realistic simulations. We then analyse the connectome to propose circuits that dominate the dynamics of the fly nervous system. We discover that the dominant circuits involve only relatively small populations of neurons—thus, neuron-level imaging, stimulation and identification are feasible. This approach also re-discovers known circuits and generates testable hypotheses about their dynamics. Overall, we provide evidence that fly whole-brain dynamics are generated by a large collection of small circuits that operate largely independently of each other. This implies that a causal model of a brain can be feasibly obtained in the fly.

Analysis and comparison of high-performance computing solvers for minimisation problems in signal processing

Several physics and engineering applications involve the solution of a minimisation problem to compute an approximation of the input signal. Modern hardware and software use high-performance computing to solve problems and considerably reduce execution time. In this paper, different optimisation methods are compared and analysed for the solution of two classes of non-linear minimisation problems for signal approximation and denoising with different constraints and involving computationally expensive operations, i.e., (i) the global optimisers divide rectangle-local and the improved stochastic ranking evolution strategy, and (ii) the local optimisers principal axis, the Limited-memory Broyden, Fletcher, Goldfarb, Shanno, and the constrained optimisation by linear approximations. The proposed approximation and denoising minimisation problems are attractive due to their numerical and analytical properties, and their analysis is general enough to be extended to most signal-processing problems. As the main contribution and novelty, our analysis combines an efficient implementation of signal approximation and denoising on arbitrary domains, a comparison of the main optimisation methods and their high-performance computing implementations, and a scalability analysis of the main algebraic operations involved in the solution of the problem, such as the solution of linear systems and singular value decomposition. Our analysis is also general regarding the signal processing problem, variables, constraints (e.g., bounded, non-linear), domains (e.g., structured and unstructured grids, dimensionality), high-performance computing hardware (e.g., cloud computing, homogeneous vs. heterogeneous). Experimental tests are performed on the CINECA Marconi100 cluster at the 26th position in the “top500” list and consider several parameters, such as functional computation, convergence, execution time, and scalability. Our experimental tests are discussed on real-case applications, such as the reconstruction of the solution of the fluid flow field equation on an unstructured grid and the denoising of a satellite image affected by speckle noise. The experimental results show that principal axis is the best optimiser in terms of minima computation: the efficiency of the approximation is 38% with 256 processes, while the denoising has 46% with 32 processes.

Classification of high-resolution remote sensing images based on interval type-2 fuzzy logic system

Abstract Aiming at the complexity and uncertainty of remote sensing image classification, this paper proposes a high-resolution remote sensing image classification method based on Interval type-2 Fuzzy Logic Systems for Remote Sensing (IT2FLS-RS), which focuses on dealing with multiple uncertainties and aims to improve the accuracy and reliability of remote sensing image classification. The method establishes a more complex interval two-type fuzzy system covering two types of fuzzifiers, a rule base and an inference machine, and finally uses an integrated algorithm as a defuzzifier to achieve accurate pixel-level classification. In addition, the model uses Constrained Optimization BY Linear Approximations (COBYLA) to optimise the key parameters. In the DLRSD dataset, the accuracy of this model is improved by about 20%, 14%, 24% and 10% compared to the state-of-the-art interval two-type fuzzy neural network algorithm and the benchmark model XGBoost, respectively. On the WHDLD dataset, the accuracy of the proposed method is improved by about 12% and 10% compared to the state-of-the-art interval type-2 fuzzy neural network algorithm and the benchmark model XGBoost, respectively. The experimental results confirm the robustness of the proposed method in processing high-resolution remote sensing image classification, especially the excellent adaptability and scalability in complex feature scenes.

Whittle Index-Based Q-Learning for Wireless Edge Caching With Linear Function Approximation

Whittle Index-Based Q-Learning for Wireless Edge Caching With Linear Function Approximation

An Implementation of the Particle Flow Filter in an Atmospheric Model

Abstract The particle flow filter (PFF) shows promise for fully nonlinear data assimilation (DA) in high-dimensional systems. However, its application in atmospheric models has been relatively unexplored. In this study, we develop a new algorithm, PFF-DART, in order to conduct DA for high-dimensional atmospheric models. PFF-DART combines the PFF and the two-step ensemble filtering algorithm in the Data Assimilation Research Testbed (DART), exploiting the highly parallel structure of DART. To evaluate the performance of PFF-DART, we conduct an observing system simulation experiment (OSSE) in a simplified atmospheric general circulation model and compare the performance of PFF-DART with an existing linear and Gaussian DA method. Using the PFF-DART algorithm, we demonstrate, for the first time, the capability of the PFF to yield stable results in a yearlong cycling DA OSSE. Moreover, PFF-DART retains the important ability of the PFF to improve the assimilation of nonlinear and non-Gaussian observations. Finally, we emphasize that PFF-DART is a versatile algorithm that can be integrated with numerous other non-Gaussian DA techniques. This quality makes it a promising method for further investigation within a more sophisticated numerical weather prediction model in the future. Significance Statement Data assimilation is an important tool in weather forecasting. However, fundamental issues arising from linear and Gaussian approximations still exist, which can limit our utilization of observations. The particle flow filter is a promising method that avoids these approximations, but efficient algorithms for this method have yet to be developed. In this study, we develop an algorithm for the particle flow filter that can be implemented in high-dimensional geophysical models. We have demonstrated, for the first time, that the particle flow filter runs efficiently for a yearlong experiment in an atmospheric model. The new algorithm also improves the results over a commonly used data assimilation method. The results in this work demonstrate the potential usage of the particle flow filter in the weather forecasting and other high-dimensional forecasting problems.

An analytical I-V model of SiC double-gate junctionless MOSFETs

Silicon carbide(SiC) double gate junctionless metal oxide semiconductor field-effect transistors(DG JL MOSFETs) have attracted significant attention due to their ideal high temperature characteristics and radiation resistance. Therefore, it is meaningful to exploit an I-V model for SiC DG JL MOSFETs. In this article, we make a linear approximation to describe the relationship between the surface mobile charge density and the surface electron concentration of the device. Based on this approximation and using the one-dimensional Poisson’s equation, we solve for the potential distribution of a SiC DG JL MOSFET in the subthreshold region. From this solution, we derived a functional relationship between the surface mobile charge density in the channel and the channel quasi-Fermi potential. Then we successfully developed a unified I-V model for the SiC DG JL MOSFETs. Based on the drain to source current calculation formula, the calculation expressions for the device’s transconductance and output conductance are derived. By comparing our model with the results from the two-dimensional numerical simulation software Silvaco Atlas, our model’s calculations closely match the two-dimensional numerical simulation results from the subthreshold region to the accumulation region. This model has reference significance for SiC DG JL MOSFETs in the high temperature electronic circuit application field.

Improved Fast Correlation Attack Using Multiple Linear Approximations and Its Application on SOSEMANUK

Improved Fast Correlation Attack Using Multiple Linear Approximations and Its Application on SOSEMANUK

Perturbing and Oblateness's Impact on the Generalized Photogravitational Restricted Three-Body Problem

In this research work, the effects of perturbing and oblateness on the generalised photogravitational restricted three body problem (RTBP) are examined when the primary are regarded as radiation sources and oblate spheroid. The perturbing forces were included in the equations of motion that we developed for the system. The triangular libration points were derived in terms of the perturbing parameters using linear approximations, and their influence was seen. Applying Murray's criteria, we determined that the triangular libration points remained unstable due to the nature of the characteristics equation matching to the variational equations of motion of the system generated.

LinFa-Q: Accurate Q-learning with linear function approximation

Although Q-learning has achieved remarkable success in some practical cases, it often suffers from the overestimation problem in stochastic environments, which is commonly viewed as a shortcoming of Q-learning. Overestimated values are introduced by estimations on the next state Q value, which is well-known as the maximization bias. In this paper, we propose a more accurate method for estimating the Q value by the Q value decomposition and re-evaluation with similar samples based on linear function approximation. Specifically, we reform the parameterized incremental update formula of Q-learning and also demonstrate that the new formula is equivalent to the original one. Moreover, we propose a new parameterized incremental update formula of Q-learning to address the overestimation problem and present the more accurate computing method, which can be used in problems with continuous state spaces and stochastic environments. Experimentally, when compared with Doubly Bounded Q-learning and other Q-learning based methods, the new algorithm has more than 31% improvement of performance in Mountain Car and Cart Pole. Furthermore, the algorithm is robust to the learning rate and its memory capacity. Finally, the practical applicability of our algorithm is discussed through an analysis of time consumption.

An outcome space algorithm for solving general linear multiplicative programming

The following article presents and corroborates an outcome space branch-and-bound algorithm for solving the general linear multiplicative programming problem (GLMPP). In this new algorithm, GLMPP is transformed into its equivalent problem by introducing auxiliary variables. To compute the tight upper bound for the optimal value of GLMPP, the linear relaxation programming problem is assembled by using bound and hull linear approximations. Furthermore, the global convergence and computational complexity of the algorithm are demonstrated. Finally, the soundness and advantage of the proposed algorithm are validated by solving a demonstrative linear multiplicative problem.

Mechanical interactions modeling of inertial wave energy converters

Numerous technological solutions for wave energy converters (WECs), referred as inertial reaction mass (IRM) systems, incorporate a reacting mass within the floater, coupled with a power take-off (PTO) system, to shelter all electronic components from the hostile sea environment. While the overall complexity of the system increases, the current modeling procedures persist in considering only a limited number of modes of motion, neglecting relevant dynamical effects. In this context, this paper proposes a systematic procedure for defining the kinematic characteristics and overall analytical model for the dynamics of IRM WECs. The significance of the proposed procedure lies in the statement of the reaction mass-related dynamic equation, considering the floater’s parametric excitation in six degrees of freedom (DoF). Additionally, it introduces the procedure for defining the reaction forces that the inertial mass exerts on the floater, which are often neglected in the literature for the full simulation of such systems. Furthermore, the proposed analytical modeling procedure allows the definition of approximated models in more simplified nonlinear forms for dynamic analysis and ultimately in fully linear approximations. This enables the application of methodologies and techniques commonly used in the literature for linear systems. The development of the framework is kept generic, in order to introduce a versatile mathematical procedure, that can be easily adjusted, with minor modifications, to accurately capture and represent the mechanical interaction for a wide family of IRM WEC devices. Subsequently, a case study on a vertical-hinged pendulum WEC is analyzed, to showcase the effectiveness of the proposed methodology. Moreover, to test the reliability of the analytical framework, a comparison with the output of a commercial software is conducted.

Nonlinear dynamics of wing-like structures using a momentum subspace-based Koiter-Newton reduction

Cantilevers find a wide range of applications in the design of scientific equipment and large-scale engineering structures such as aircraft wings. Analysis techniques based on linearization approximations are unable to capture the large amplitude oscillation behaviour of such structures and thus, necessitates development of dedicated nonlinear methods. In this work, the recent developments in the Koiter-Newton model reduction method are utilized to obtain nonlinear reduced order models (ROMs) from full finite element structural models in order to simulate large amplitude dynamics of cantilevers. The method describes a nonlinear system of governing equations comprising quadratic and cubic terms which are obtained as higher order derivatives of the in-plane strain energy. To ensure that the large rotations in cantilevers and the resultant foreshortening effect is also accounted for, a ROM updating algorithm is adopted where the ROM parameters are varied with the structural deflections. Linear eigenmodes of the structure are utilized to form the reduction subspace. To validate the methodology, the ROM solution is compared against experimental results and a convergence study is conducted to identify the number of modes needed to replicate the nonlinear response. Finally, a composite wingbox structure is considered for which time domain simulations are conducted and frequency response curves, obtained through a frequency sweep, are presented.

License Plate Recognition Using Three-Dimensional Rotated Character Recognition and Instance Segmentation by Deep Learning

License plate recognition is currently used in various situations, such as parking lot vehicle management and the tracking of wanted vehicles. These applications require recognition from all possible camera angles. Therefore, we propose a method for license plate recognition in images captured from various camera angles. First, the license plate area is detected from the input image using the YOLOv5 object detection method. The subsequent process can be performed in two manners: by rotating the license plate to the front using projective transformation and trapezoidal correction, or by using graph matching. The first method performs Hough transforms or linear approximations as preprocessing, and then calculates the rectangle surrounding the license plate from the YOLOv5 output. After performing trapezoidal correction, the maximally stable extremal regions (MSER) are used to detect character candidates, and characters are recognized using 3D rotated character recognition. The second method performs character candidate detection and recognition without trapezoidal correction, followed by graph matching. These methods are versatile because they do not depend on the layout of license plates, which varies among countries and regions. Two types of datasets were used: a set of images containing Japanese license plates collected by ourselves, and a set of publicly available images containing Taiwanese license plates. Two recognition rates were evaluated: the license plate character recognition rate and license plate recognition rate in which all characters in one plate are recognized. The license plate character recognition rates using graph matching were 91.9% for the Japanese license plates and 89.3% for the Taiwanese license plates. The license plate recognition rates were 84.0% and 84.5%, respectively.

Simulation of gas mixture dynamics in a pipeline network using explicit staggered-grid discretization

We develop an explicit staggered finite difference discretization scheme for simulating the transport of highly heterogeneous gas mixtures through pipeline networks. This study is motivated by the proposed blending of hydrogen into natural gas pipelines to reduce end use carbon emissions while using existing pipeline systems throughout their planned lifetimes. Our computational method accommodates an arbitrary number of constituent gases with very different physical properties that may be injected into a network with significant spatiotemporal variation. In this setting, the gas flow physics are highly location- and time- dependent, so that local composition and nodal mixing must be accounted for. The resulting conservation laws are formulated in terms of pressure, partial densities and flows, and volumetric and mass fractions of the constituents. We include non-ideal equations of state that employ linear approximations of gas compressibility factors, so that the pressure dynamics propagate locally according to a variable wave speed that depends on mixture composition and density. We derive compatibility relationships for network edge boundary values that are more complex than for a homogeneous gas. The simulation method is evaluated on initial boundary value problems for a single pipe and a small network, is cross-validated with a lumped element simulation, and used to demonstrate a local monitoring and control policy for maintaining allowable concentration levels.

Porównanie metod sterowania adaptacyjnego dla stołu balansującego kulą

The purpose of this paper is to present and compare adaptive control algorithms: Model Identification Adaptive Control (MIAC) and Model Reference Adaptive Control (MRAC), with their modifications that allow to improve quality of control in specific cases. The ball balancing (BBT) table physical stand, which is an example of a ball on plate system, was used, and the balancing problem that occurs could potentially lead to work on stabilizing a boat or a drone. This paper presents a non-linear model of the object and its linear approximation in the vicinity of the operating point, additionally demonstrating the process of parameters identification with the Recursive Least Square (RLS) method. The quality of the adaptive control algorithms was compared during transients and in steady state. The research showed the possibilities of both indirect and direct adaptation of the controller parameters, depending on the selected method. Quality indices, such as the cost of control and the integral of absolute error, were utilized for the comparative analysis. The advantages of the compared algorithms and their modifications, that can enhance the system performance in special cases, were also demonstrated. The tested adaptive control algorithms made the system robust to modeling errors (lack of knowledge of parameters) or other internal disturbances.

Multidimensional zero-correlation linear cryptanalysis on uBlock and RAIN

uBlock and RAIN are both SPN structure lightweight block ciphers with sufficient security against traditional attacks. This article mainly focuses on the zero-correlation linear cryptanalysis of uBlock-128/128 and RAIN-64 without considering the whitening key for the first time. On the one hand, combining the linear mask propagation rules of S-box with matrix method, a large number of 4-round zero-correlation linear approximations for uBlock-128/128 are obtained. Therefore, a 6-round key recovery attack is carried out with partial-compression technique, which can recover 48-bit subkeys with data complexity 2 126.41 known plaintexts, time complexity 2 122.82 times of 6-round of algorithm encryptions, and memory complexity 2 48 nibbles. On the other hand, a similar method is used on RAIN-64, thus a 10-round attack is performed, which recovers 64-bit subkeys with data complexity 2 61.95 known plaintexts, time complexity 2 74.26 times of 10-round algorithm encryptions, and memory complexity 2 64 nibbles. The results show that both uBlock and RAIN are safe enough to resist zero-correlation linear cryptanalysis.

A new quasi-finite-rank approximation of compression operators on [formula omitted] with applications to sampled-data and time-delay systems: Piecewise linear kernel approximation approach

This paper provides a new quasi-finite-rank approximation (QFRA) of infinite-rank compression operators defined on the Banach space L∞[0,H), which are associated with tractable representations of infinite-dimensional systems such as time-delay and sampled-data systems. We first formulate the QFRA by an optimization problem with a matrix-valued parameter X to minimize the associated error in terms of the L∞[0,H)-induced norm. To facilitate solving the optimization problem, we next employ the piecewise linear kernel approximation (PLKA) technique, by which the optimization problem is then converted to a linear programming (LP) problem. The solution of the LP problem is shown to converge to the optimal solution of the original QFRA with the order of 1/M, where M is the PLKA parameter. The PLKA-based QFRA is shown to lead to practical methods of the stability analysis for time-delay systems and the L1 optimal controller synthesis for sampled-data systems. Finally, the overall arguments developed in this paper are demonstrated through some numerical and experimental studies.

Generalized hydrodynamics for the volterra lattice: ballistic and non-ballistic behavior of correlation functions

Abstract In recent years, a lot of effort has been put in describing the hydrodynamic behavior of in- tegrable systems. In this paper, we describe such picture for the Volterra lattice. Specifically, we are able to explicitly compute the susceptibility matrix and the current-field correlation matrix in terms of the density of states of the Volterra lattice endowed with a Generalized Gibbs ensemble. Furthermore, we apply the theory of linear Generalized Hydrodynamics to describe the Euler scale behavior of the correlation functions. We anticipate that the solution to the Generalized Hydrodynamics equations develops shocks at ξ0=x/t ; so this linear approximation does not fully describe the behavior of correlation functions. Intrigued but this fact, we performed several numerical investigations which show that, exactly when the solution to the hydrodynamic equations develops shock, the correlation functions show an highly oscillatory behavior. In view of this empirical observation, we believe that at this point ξ0 the diffusive contribution are not sub-leading corrections to the ballistic transport, but they are of the same order.