Journal articles: 'Linear scale-space'

1

Florack, L. M. J., B. M. ter Haar Romeny, J. J. Koenderink, and M. A. Viergever. "Linear scale-space." Journal of Mathematical Imaging and Vision 4, no. 4 (December 1994): 325–51. http://dx.doi.org/10.1007/bf01262401.

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Lindeberg, Tony. "Generalized Gaussian Scale-Space Axiomatics Comprising Linear Scale-Space, Affine Scale-Space and Spatio-Temporal Scale-Space." Journal of Mathematical Imaging and Vision 40, no. 1 (December 1, 2010): 36–81. http://dx.doi.org/10.1007/s10851-010-0242-2.

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Frisina, Warren. "Linear turbine spacecraft for large-scale space development." Acta Astronautica 35, no. 1 (January 1995): 43–46. http://dx.doi.org/10.1016/0094-5765(94)00129-a.

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Gauthier, Jean Bertrand, Jacques Desrosiers, and Marco E. Lübbecke. "Vector Space Decomposition for Solving Large-Scale Linear Programs." Operations Research 66, no. 5 (October 2018): 1376–89. http://dx.doi.org/10.1287/opre.2018.1728.

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Li, Shaoli, Dejian Li, and Weiqi Yuan. "Wood chip crack detection based on linear scale-space differential." Measurement 175 (April 2021): 109095. http://dx.doi.org/10.1016/j.measurement.2021.109095.

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Qiang, Yi, Seyed H. Chavoshi, Steven Logghe, Philippe De Maeyer, and Nico Van de Weghe. "Multi-scale analysis of linear data in a two-dimensional space." Information Visualization 13, no. 3 (March 25, 2013): 248–65. http://dx.doi.org/10.1177/1473871613477853.

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Many disciplines are faced with the problem of handling time-series data. This study introduces an innovative visual representation for time series, namely the continuous triangular model. In the continuous triangular model, all subintervals of a time series can be represented in a two-dimensional continuous field, where every point represents a subinterval of the time series, and the value at the point is derived through a certain function (e.g. average or summation) of the time series within the subinterval. The continuous triangular model thus provides an explicit overview of time series at all different scales. In addition to time series, the continuous triangular model can be applied to a broader sense of linear data, such as traffic along a road. This study shows how the continuous triangular model can facilitate the visual analysis of different types of linear data. We also show how the coordinate interval space in the continuous triangular model can support the analysis of multiple time series through spatial analysis methods, including map algebra and cartographic modelling. Real-world datasets and scenarios are employed to demonstrate the usefulness of this approach.

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Madrid, Nicolás, Carlos Lopez-Molina, and Petr Hurtik. "Non-linear scale-space based on fuzzy contrast enhancement: Theoretical results." Fuzzy Sets and Systems 421 (September 2021): 133–57. http://dx.doi.org/10.1016/j.fss.2021.02.022.

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GOUZÉ, JEAN-LUC. "POSITIVITY, SPACE SCALE AND CONVERGENCE TOWARDS THE EQUILIBRIUM." Journal of Biological Systems 03, no. 02 (June 1995): 613–20. http://dx.doi.org/10.1142/s0218339095000563.

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All the variables of the biological models are positive. We examine the constraints that one has to put on the model to verify such a property. For a linear (differential) model, it implies that the equilibrium is stable. For the n-dimensional Lotka-Volterra models, the positive orthant is invariant, but we impose stronger constraints to prevent the solutions to go upon or below some given thresholds, that define the space scale of the model. Then we show that, under reasonable hypothesis, this implies the global convergence towards the equilibrium.

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Petrovic, A., O. Divorra Escoda, and P. Vandergheynst. "Multiresolution segmentation of natural images: from linear to nonlinear scale-space representations." IEEE Transactions on Image Processing 13, no. 8 (August 2004): 1104–14. http://dx.doi.org/10.1109/tip.2004.828431.

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Prodanov, Dimiter. "Characterization of strongly non-linear and singular functions by scale space analysis." Chaos, Solitons & Fractals 93 (December 2016): 14–19. http://dx.doi.org/10.1016/j.chaos.2016.08.010.

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Biro, T., and K. Rönnmark. "Phase-space description of plasma waves. Part 1. Linear theory." Journal of Plasma Physics 47, no. 3 (June 1992): 465–77. http://dx.doi.org/10.1017/s0022377800024351.

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We develop an (r, k) phase-space description of waves in plasmas by introducing Gaussian window functions to separate short-scale oscillations from long-scale modulations of the wave fields and variations in the plasma parameters. To obtain a wave equation that unambiguously separates conservative dynamics from dissipation in an inhomogeneous and time-varying background plasma, we first discuss the proper form of the current response function. In analogy with the particle distribution function f(v, r, t), we introduce a wave density N(k, r, t) on phase space. This function is proved to satisfy a simple continuity equation. Dissipation is also included, and this allows us to describe the damping or growth of wave density along rays. Problems involving geometric optics of continuous media often appear simpler when viewed in phase space, since the flow of N in phase space is incompressible.

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Salas, L., and I. Cruz-González. "AN ALTERNATIVE APPROACH TO THE FINGER OF GOD IN LARGE SCALE STRUCTURES." Revista Mexicana de Astronomía y Astrofísica 55, no. 1 (May 31, 2019): 93–104. http://dx.doi.org/10.22201/ia.01851101p.2019.55.01.10.

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It is generally accepted that linear theory of growth of structure under gravity produces a squashed structure in the two-point correlation function (2PCF) along the line of sight (LoS). The observed radial spread out structure known as Finger of God (FoG) is attributed to non-linear effects. We argue that the squashed structure associated with the redshift-space (s−) linear theory 2PCF is obtained only when this function is displayed in real-space (r−), or when the mapping from r − to s−space is approximated. We solve for the mapping function s(r) that allows us to display thes −space 2PCF in a grid in s−space, by using plane of the sky projections of the r − and s − 2PCFs. Even in the simplest case of a linear Kaiser spectrum with a conservative power-law r−space 2PCF, a structure quite similar to the FoG is observed in the small scale region, while in the large scale the expected squashed structure is obtained. This structure depends on only three parameters.

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SVANSTEDT, NILS. "CONVERGENCE OF QUASI-LINEAR HYPERBOLIC EQUATIONS." Journal of Hyperbolic Differential Equations 04, no. 04 (December 2007): 655–77. http://dx.doi.org/10.1142/s0219891607001306.

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Multiscale stochastic homogenization is studied for quasilinear monotone hyperbolic problems with a linear damping term. It is shown by classical G-convergence methods that the sequence of solutions to a class of multi-scale highly oscillatory (possibly random) hyperbolic problems converges in the appropriate Sobolev space to the solution to a homogenized quasilinear hyperbolic problem.

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Salvati, Luca. "Land Quality, Development and Space: Does Scale Matter?" European Spatial Research and Policy 20, no. 2 (January 22, 2014): 99–112. http://dx.doi.org/10.2478/esrp-2013-0013.

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This study analyzes empirically the relationship between land quality decline and the spatial distribution of per capita income observed in Italy at different spatial scales and geographical divisions. The aim of this contribution is to verify if a decline in land quality has higher probability to occur in economically disadvantaged areas and if scale may influence this relationship. Per capita income was considered a proxy indicator for the level of socio-economic development and life quality in the investigated area. Changes over time (1990–2000) of a composite index of land quality and per capita income in Italy were regressed at four spatial scales: (i) 20 NUTS-2 regions, (ii) 103 NUTS-3 prefectures, (iii) 784 local districts designed as Local Labour Market Areas (LLMAs), and (iv) 8,101 LAU-1 municipalities. Different specifications were tested, including first, second and third order polynomial equations. Linear models allowed the best fit for data examined at all spatial scales. However, elasticity of the dependent variable to per capita income varied considerably according to scale suggesting that developmental policies may have a limited impact on land quality in vulnerable southern Italian areas compared to northern and central Italy. This study suggests that geographically disaggregated data simulating different spatial levels of governance may offer further insights compared to cross-country datasets indicating targets for multi-scale policies possibly preventing a poverty-desertification spiral.

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Griffin, Lewis D., and Alan CF Colchester. "Superficial and deep structure in linear diffusion scale space: isophotes, critical points and separatrices." Image and Vision Computing 13, no. 7 (September 1995): 543–57. http://dx.doi.org/10.1016/0262-8856(95)91145-4.

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Mortensen, Kim Erlend, Fred Godtliebsen, and Arthur Revhaug. "Scale-space analysis of time series in circulatory research." American Journal of Physiology-Heart and Circulatory Physiology 291, no. 6 (December 2006): H3012—H3022. http://dx.doi.org/10.1152/ajpheart.00168.2006.

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Statistical analysis of time series is still inadequate within circulation research. With the advent of increasing computational power and real-time recordings from hemodynamic studies, one is increasingly dealing with vast amounts of data in time series. This paper aims to illustrate how statistical analysis using the significant nonstationarities (SiNoS) method may complement traditional repeated-measures ANOVA and linear mixed models. We applied these methods on a dataset of local hepatic and systemic circulatory changes induced by aortoportal shunting and graded liver resection. We found SiNoS analysis more comprehensive when compared with traditional statistical analysis in the following four ways: 1) the method allows better signal-to-noise detection; 2) including all data points from real time recordings in a statistical analysis permits better detection of significant features in the data; 3) analysis with multiple scales of resolution facilitates a more differentiated observation of the material; and 4) the method affords excellent visual presentation by combining group differences, time trends, and multiscale statistical analysis allowing the observer to quickly view and evaluate the material. It is our opinion that SiNoS analysis of time series is a very powerful statistical tool that may be used to complement conventional statistical methods.

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Jawad, Muhammad, Jens Soltwisch, Klaus Dreisewerd, and Lars Linsen. "Interactive Visual Analysis of Mass Spectrometry Imaging Data Using Linear and Non-Linear Embeddings." Information 11, no. 12 (December 9, 2020): 575. http://dx.doi.org/10.3390/info11120575.

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Mass spectrometry imaging (MSI) is an imaging technique used in analytical chemistry to study the molecular distribution of various compounds at a micro-scale level. For each pixel, MSI stores a mass spectrum obtained by measuring signal intensities of thousands of mass-to-charge ratios (m/z-ratios), each linked to an individual molecular ion species. Traditional analysis tools focus on few individual m/z-ratios, which neglects most of the data. Recently, clustering methods of the spectral information have emerged, but faithful detection of all relevant image regions is not always possible. We propose an interactive visual analysis approach that considers all available information in coordinated views of image and spectral space visualizations, where the spectral space is treated as a multi-dimensional space. We use non-linear embeddings of the spectral information to interactively define clusters and respective image regions. Of particular interest is, then, which of the molecular ion species cause the formation of the clusters. We propose to use linear embeddings of the clustered data, as they allow for relating the projected views to the given dimensions. We document the effectiveness of our approach in analyzing matrix-assisted laser desorption/ionization (MALDI-2) imaging data with ground truth obtained from histological images.

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Suckling, J., M. J. Brammer, A. Lingford-Hughes, and E. T. Bullmore. "Removal of extracerebral tissues in dual-echo magnetic resonance images via linear scale-space features." Magnetic Resonance Imaging 17, no. 2 (February 1999): 247–56. http://dx.doi.org/10.1016/s0730-725x(98)00099-x.

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Jeong, J., H. Adib-Ramezani, and M. Al-Mukhtar. "Numerical simulation of elastic linear micropolar media based on the pore space length scale assumption." Strength of Materials 40, no. 4 (July 2008): 425–38. http://dx.doi.org/10.1007/s11223-008-9052-9.

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20

Wang, Pei, Xu Sheng Yang, Zhuo Yuan Wang, Lin Gong Li, Ji Chang He, and Qing Jie Wang. "Solving Large-Scale Asymmetric Sparse Linear Equations Based on SuperLU Algorithm." Advanced Materials Research 230-232 (May 2011): 1355–61. http://dx.doi.org/10.4028/www.scientific.net/amr.230-232.1355.

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This article introduces the recent research of SuperLU algorithms and the optimal storage method for [1] the sparse linear equations of coefficient matrix. How to solve large-scale non-symmetric sparse linear equations by SuperLU algorithm is the key part of this article. The advantage of SuperLU algorithm compared to other algorithms is summarized at last. SuperLU algorithm not only saves memory space, but also reduces the computation time. Because of less storage needed by this algorithm, it could solve equation with larger scale, which is much more useful.

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Yao, Shao-Wen. "Variational principle for non-linear fractional wave equation in a fractal space." Thermal Science 25, no. 2 Part B (2021): 1243–47. http://dx.doi.org/10.2298/tsci200301018y.

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The fractal derivative is adopted to describe the non-linear fractional wave equation in a fractal space. A variational principle is successfully established by the semi-inverse method. The two-scale method and He?s exp-function are used to solve the equation, and a good result is obtained.

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Ernesti, Johannes, and Christian Wieners. "Space-Time Discontinuous Petrov–Galerkin Methods for Linear Wave Equations in Heterogeneous Media." Computational Methods in Applied Mathematics 19, no. 3 (July 1, 2019): 465–81. http://dx.doi.org/10.1515/cmam-2018-0190.

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AbstractWe establish an abstract space-time DPG framework for the approximation of linear waves in heterogeneous media. The estimates are based on a suitable variational setting in the energy space. The analysis combines the approaches for acoustic waves of Gopalakrishnan–Sepulveda [J. Gopalakrishnan and P. Sepulveda, A space-time DPG method for the wave equation in multiple dimensions, Space-Time Methods. Applications to Partial Differential Equations, Radon Ser. Comput. Appl. Math. 21, Walter de Gruyter, Berlin 2019, 129–154] and Ernesti–Wieners [J. Ernesti and C. Wieners, A space-time discontinuous Petrov–Galerkin method for acoustic waves, Space-Time Methods. Applications to Partial Differential Equations, Radon Ser. Comput. Appl. Math. 21, Walter de Gruyter, Berlin 2019, 99–127] and is based on the abstract definition of traces on the skeleton of the time-space substructuring. The method is evaluated by large-scale parallel computations motivated from applications in seismic imaging, where the computational domain can be restricted substantially to a subset of the full space-time cylinder.

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Sardorbek, Numonov, Bong-Soo Sohn, and Byung-Woo Hong. "Coherence Enhancement Based on Recursive Anisotropic Scale-Space with Adaptive Kernels." Applied Sciences 10, no. 15 (July 23, 2020): 5079. http://dx.doi.org/10.3390/app10155079.

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The reduction of unnecessary details is important in a variety of imaging tasks. Image denoising can be generally formulated as a diffusion process that iteratively suppresses undesirable image features with high variance. We propose a recursive diffusion process that simultaneously computes the local geometrical property of the image features and determines the size and shape of the diffusion kernel, leading to an anisotropic scale-space. In the construction of the proposed anisotropic scale-space, image features due to undesirable noise are suppressed while significant geometrical image features such as edges and corners are preserved across the scale-space. The diffusion kernels are iteratively determined based on the local geometrical properties of the image features. We demonstrate the effectiveness and robustness of the proposed algorithm in the detection of curvilinear features using simple yet effective synthetic and real images. The algorithm is quantitatively evaluated based on the identification of fissures in lung CT imagery. The experimental results indicate that the proposed algorithm can be used for the detection of linear or curvilinear structures in a variety of images ranging from satellite to medical images.

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Alghamdi, Maryam, Alaa Aljehani, Martin Bohner, and Alaa Hamza. "Hyers-Ulam and Hyers-Ulam-Rassias stability of first-order linear dynamic equations." Publications de l'Institut Math?matique (Belgrade) 109, no. 123 (2021): 83–93. http://dx.doi.org/10.2298/pim2123083a.

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We present several new sufficient conditions for Hyers-Ulam and Hyers-Ulam-Rassias stability of first-order linear dynamic equations for functions defined on a time scale with values in a Banach space.

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Beven, K. J., and S. W. Franks. "Functional similarity in landscape scale SVAT modelling." Hydrology and Earth System Sciences 3, no. 1 (March 31, 1999): 85–93. http://dx.doi.org/10.5194/hess-3-85-1999.

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Abstract. In this study, it is shown that the complexity of Soil Vegetation Atmosphere Transfer (SVAT) models leads to an equifinality of functional behaviour - many parameterizations from many areas of the parameter space lead to very similar responses. Individual parameters derived by calibration (i.e. model inversion) against limited measurements are, therefore, highly uncertain. Due to the non-linear internal behaviour of SVAT models, aggregation of uncertainly known parameter fields to parameterize landscape scale variability in surface fluxes will yield highly uncertain predictions. A disaggregation approach suggested by Beven (1995) requires that the land surface be represented by a linear sum of a number of representative parameterizations or functional types. This study explores the nature of the parameter space in terms of a simple definition of functional behaviour. Parameter interactions producing similar predicted behaviours are investigated through application of Principal Component Analyses. These reveal the lack of a dominant global interaction indicating the presence of highly complex parameter interactions throughout the feasible parameter space.

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Nguyen, Dung Tien, Xuerong Mao, George Yin, and Chenggui Yuan. "Stability of singular jump-linear systems with a large state space: a two-time-scale approach." ANZIAM Journal 52 (April 4, 2012): 372. http://dx.doi.org/10.21914/anziamj.v52i0.3665.

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NGUYEN, DUNG TIEN, XUERONG MAO, G. YIN, and CHENGGUI YUAN. "STABILITY OF SINGULAR JUMP-LINEAR SYSTEMS WITH A LARGE STATE SPACE: A TWO-TIME-SCALE APPROACH." ANZIAM Journal 52, no. 4 (April 2011): 372–90. http://dx.doi.org/10.1017/s1446181111000745.

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AbstractThis paper considers singular systems that involve both continuous dynamics and discrete events with the coefficients being modulated by a continuous-time Markov chain. The underlying systems have two distinct characteristics. First, the systems are singular, that is, characterized by a singular coefficient matrix. Second, the Markov chain of the modulating force has a large state space. We focus on stability of such hybrid singular systems. To carry out the analysis, we use a two-time-scale formulation, which is based on the rationale that, in a large-scale system, not all components or subsystems change at the same speed. To highlight the different rates of variation, we introduce a small parameter ε>0. Under suitable conditions, the system has a limit. We then use a perturbed Lyapunov function argument to show that if the limit system is stable then so is the original system in a suitable sense for ε small enough. This result presents a perspective on reduction of complexity from a stability point of view.

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Beneda, Károly, Rudolf Andoga, and Ladislav Főző. "Linear Mathematical Model for State-Space Representation of Small Scale Turbojet Engine with Variable Exhaust Nozzle." Periodica Polytechnica Transportation Engineering 46, no. 1 (March 16, 2017): 1. http://dx.doi.org/10.3311/pptr.10605.

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The goal of this article is to develop a linear mathematical model for a small scale turbojet engine with variable convergent nozzle, and validate it on existing laboratory hardware owned by the authors’ Departments.Control of gas turbine engines plays an essential role in the safety of aviation. Although its role is constantly expanding, ranging from pilot workload reduction to detailed diagnostics, the basic competence is to regulate the thrust output of the power plant with maximum available accuracy, rapidity, stability, and robustness. The linear quadratic control is one possible solution for the above mentioned criteria.Although civil aircraft engines include fixed exhaust nozzle geometry, in military applications the exhaust nozzle geometry is also adjustable to reach optimum efficiency due to better matching of individual engine components, etc.In the present article the authors deduce the members of state space governing equations to acquire the basis of the LQ control.The established model is based on the physical laws describing the operational behavior of the engine as well as its complexity should be reduced to an acceptable level where still enough details remain to reflect the nature of the controlled object.

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Wang, Min, Yee Leung, Chenhu Zhou, Tao Pei, and Jiancheng Luo. "A Mathematical Morphology Based Scale Space Method for the Mining of Linear Features in Geographic Data." Data Mining and Knowledge Discovery 12, no. 1 (January 2006): 97–118. http://dx.doi.org/10.1007/s10618-005-0021-7.

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Savenije, Hubert H. G. "HESS Opinions: Linking Darcy's equation to the linear reservoir." Hydrology and Earth System Sciences 22, no. 3 (March 19, 2018): 1911–16. http://dx.doi.org/10.5194/hess-22-1911-2018.

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Abstract. In groundwater hydrology, two simple linear equations exist describing the relation between groundwater flow and the gradient driving it: Darcy's equation and the linear reservoir. Both equations are empirical and straightforward, but work at different scales: Darcy's equation at the laboratory scale and the linear reservoir at the watershed scale. Although at first sight they appear similar, it is not trivial to upscale Darcy's equation to the watershed scale without detailed knowledge of the structure or shape of the underlying aquifers. This paper shows that these two equations, combined by the water balance, are indeed identical provided there is equal resistance in space for water entering the subsurface network. This implies that groundwater systems make use of an efficient drainage network, a mostly invisible pattern that has evolved over geological timescales. This drainage network provides equally distributed resistance for water to access the system, connecting the active groundwater body to the stream, much like a leaf is organized to provide all stomata access to moisture at equal resistance. As a result, the timescale of the linear reservoir appears to be inversely proportional to Darcy's “conductance”, the proportionality being the product of the porosity and the resistance to entering the drainage network. The main question remaining is which physical law lies behind pattern formation in groundwater systems, evolving in a way that resistance to drainage is constant in space. But that is a fundamental question that is equally relevant for understanding the hydraulic properties of leaf veins in plants or of blood veins in animals.

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Mara, Michael, Felix Heide, Michael Zollhöfer, Matthias Nießner, and Pat Hanrahan. "Thallo – Scheduling for High-Performance Large-Scale Non-Linear Least-Squares Solvers." ACM Transactions on Graphics 40, no. 5 (October 31, 2021): 1–14. http://dx.doi.org/10.1145/3453986.

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Large-scale optimization problems at the core of many graphics, vision, and imaging applications are often implemented by hand in tedious and error-prone processes in order to achieve high performance (in particular on GPUs), despite recent developments in libraries and DSLs. At the same time, these hand-crafted solver implementations reveal that the key for high performance is a problem-specific schedule that enables efficient usage of the underlying hardware. In this work, we incorporate this insight into Thallo, a domain-specific language for large-scale non-linear least squares optimization problems. We observe various code reorganizations performed by implementers of high-performance solvers in the literature, and then define a set of basic operations that span these scheduling choices, thereby defining a large scheduling space. Users can either specify code transformations in a scheduling language or use an autoscheduler. Thallo takes as input a compact, shader-like representation of an energy function and a (potentially auto-generated) schedule, translating the combination into high-performance GPU solvers. Since Thallo can generate solvers from a large scheduling space, it can handle a large set of large-scale non-linear and non-smooth problems with various degrees of non-locality and compute-to-memory ratios, including diverse applications such as bundle adjustment, face blendshape fitting, and spatially-varying Poisson deconvolution, as seen in Figure 1. Abstracting schedules from the optimization, we outperform state-of-the-art GPU-based optimization DSLs by an average of 16× across all applications introduced in this work, and even some published hand-written GPU solvers by 30%+.

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Doering, Dionísio, and Adalberto Schuck Junior. "A Novel Method for Generating Scale Space Kernels Based on Wavelet Theory." Revista de Informática Teórica e Aplicada 15, no. 2 (December 12, 2008): 121–38. http://dx.doi.org/10.22456/2175-2745.7024.

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The linear scale-space kernel is a Gaussian or Poisson function. These functions were chosen based on several axioms. This representation creates a good base for visualization when there is no information (in advanced) about which scales are more important. These kernels have some deficiencies, as an example, its support region goes from minus to plus infinite. In order to solve these issues several others scale-space kernels have been proposed. In this paper we present a novel method to create scale-space kernels from one-dimensional wavelet functions. In order to do so, we show the scale-space and wavelet fundamental equations and then the relationship between them. We also describe three different methods to generate two-dimensional functions from one-dimensional functions. Then we show results got from scale-space blob detector using the original and two new scale-space bases (Haar and Bi-ortogonal 4.4), and a comparison between the edges detected using the Gaussian kernel and Haar kernel for a noisy image. Finally we show a comparison between the scale space Haar edge detector and the Canny edge detector for an image with one known square in it, for that case we show the Mean Square Error (MSE) of the edges detected with both algorithms.

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Lucas, Dan, C. P. Caulfield, and Rich R. Kerswell. "Layer formation and relaminarisation in plane Couette flow with spanwise stratification." Journal of Fluid Mechanics 868 (April 10, 2019): 97–118. http://dx.doi.org/10.1017/jfm.2019.192.

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In this paper we investigate the effect of stable stratification on plane Couette flow when gravity is oriented in the spanwise direction. When the flow is turbulent we observe near-wall layering and associated new mean flows in the form of large-scale spanwise-flattened streamwise rolls. The layers exhibit the expected buoyancy scaling $l_{z}\sim U/N$ where $U$ is a typical horizontal velocity scale and $N$ the buoyancy frequency. We associate the new coherent structures with a stratified modification of the well-known large-scale secondary circulation in plane Couette flow. We find that the possibility of the transition to sustained turbulence is controlled by the relative size of this buoyancy scale to the spanwise spacing of the streaks. In parts of parameter space transition can also be initiated by a newly discovered linear instability in this system (Facchini et al., J. Fluid Mech., vol. 853, 2018, pp. 205–234). When wall turbulence can be sustained the linear instability opens up new routes in phase space for infinitesimal disturbances to initiate turbulence. When the buoyancy scale suppresses turbulence the linear instability leads to more ordered nonlinear states, with the possibility for intermittent bursts of secondary shear instability.

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Kim, Youngkyu, Karen Wang, and Youngsoo Choi. "Efficient Space–Time Reduced Order Model for Linear Dynamical Systems in Python Using Less than 120 Lines of Code." Mathematics 9, no. 14 (July 19, 2021): 1690. http://dx.doi.org/10.3390/math9141690.

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A classical reduced order model (ROM) for dynamical problems typically involves only the spatial reduction of a given problem. Recently, a novel space–time ROM for linear dynamical problems has been developed [Choi et al., Space–tume reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems, Journal of Computational Physics, 2020], which further reduces the problem size by introducing a temporal reduction in addition to a spatial reduction without much loss in accuracy. The authors show an order of a thousand speed-up with a relative error of less than 10−5 for a large-scale Boltzmann transport problem. In this work, we present for the first time the derivation of the space–time least-squares Petrov–Galerkin (LSPG) projection for linear dynamical systems and its corresponding block structures. Utilizing these block structures, we demonstrate the ease of construction of the space–time ROM method with two model problems: 2D diffusion and 2D convection diffusion, with and without a linear source term. For each problem, we demonstrate the entire process of generating the full order model (FOM) data, constructing the space–time ROM, and predicting the reduced-order solutions, all in less than 120 lines of Python code. We compare our LSPG method with the traditional Galerkin method and show that the space–time ROMs can achieve O(10−3) to O(10−4) relative errors for these problems. Depending on parameter–separability, online speed-ups may or may not be achieved. For the FOMs with parameter–separability, the space–time ROMs can achieve O(10) online speed-ups. Finally, we present an error analysis for the space–time LSPG projection and derive an error bound, which shows an improvement compared to traditional spatial Galerkin ROM methods.

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Li, Hao. "Edge color difference detection of color image based on artificial intelligence technology." Journal of Computational Methods in Sciences and Engineering 21, no. 3 (August 2, 2021): 787–802. http://dx.doi.org/10.3233/jcm-215189.

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In order to solve the problems of the traditional methods in detecting color image edge chromatic aberration, such as the poor accuracy of detection and the poor detection effect, a color image edge chromatic aberration detection method based on artificial intelligence technology is proposed. The approximate principal component analysis method is used to segment the color image and smooth the image denoising; The linear gray-scale transformation is applied to the color image to enlarge the smaller gray-scale space to the larger gray-scale space according to the linear relationship and obtain the edge information of the color image; The artificial intelligence technology is used to locate the edge sub-pixel of the image to complete the edge color difference detection of the color image. The experimental results show that the detection accuracy of the proposed method is about 98%, and the detection effect is good, which is feasible.

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Nematollahi, N., and M. Jafari Jozani. "Truncated Linear Minimax Estimator of a Power of the Scale Parameter in a Lower- Bounded Parameter Space." Journal of Statistical Research of Iran 1, no. 2 (March 1, 2005): 161–78. http://dx.doi.org/10.18869/acadpub.jsri.1.2.161.

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Choi, Youngsoo, Peter Brown, William Arrighi, Robert Anderson, and Kevin Huynh. "Space–time reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems." Journal of Computational Physics 424 (January 2021): 109845. http://dx.doi.org/10.1016/j.jcp.2020.109845.

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Kreitmeier, F., and P. Lücking. "Demonstration of balance-based space averaging and modelling in view of blading—diffuser interaction." Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 217, no. 4 (January 1, 2003): 461–69. http://dx.doi.org/10.1243/095765003322315522.

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Advanced experimental and numerical methods in the field of fluid dynamics and turbomachinery are increasingly successful in describing real flowfields, i.e. fields that are generally three-dimensional and unsteady. For many purposes, e.g. flow characterization, it is necessary to reduce these flowfields step by step to three-, two- or one-dimensional large-scale unsteady flowfields. This procedure permits a lower-level simulation of the flowfields. However, many averaging approaches are arbitrary or succeed in balancing the flowfields in only a few physical aspects. The first author has already shown the steps of a balance-based procedure that avoids this limitation. Small-scale time averaging of (probabilistically) turbulent inhomogeneities by means of irreversible and reversible small-scale time averaging processes on a threefold infinitesimal control volume element has already been demonstrated. The present paper demonstrates the balance-based procedure of space averaging. It is carried out by averaging generally three-dimensional small-scale time-averaged (deterministic) inhomogeneities using irreversible and reversible space averaging processes on onefold infinitesimal and finite control surfaces. The procedure is, similarly to small-scale time averaging, based on conservative and independent non-conservative small-scale time-averaged integral balance equations. The general concept is to represent all the relevant fluxes through the control surface by appropriate average quantities or numbers. The full use of the vector equations for the linear and angular momentum is important. One of the consequences in space averaging is the introduction of a wrench (parallel linear and angular momentum vectors), which is generally used only in mechanics for the reduction of force systems in space. The flowfield inhomogeneity is described on all dimensional levels via the diffusion intensity of the irreversible averaging process, and, only for space averaging, via the distance vector and the parameter of the wrench. A numerical example on different dimensional levels is presented in detail. The procedure also illustrates the basis of a new and more complete two-and one-dimensional large-scale unsteady theory generally in fluid dynamics and especially in turbomachinery.

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Hunt, G. W., M. K. Wadee, and N. Shiacolas. "Localized Elasticae for the Strut on the Linear Foundation." Journal of Applied Mechanics 60, no. 4 (December 1, 1993): 1033–38. http://dx.doi.org/10.1115/1.2900971.

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Localized solutions, for the classical problem of the nonlinear strut (elastica) on the linear elastic foundation, are predicted from double-scale analysis, and confirmed from nonlinear volume-preserving Runge-Kutta runs. The dynamical phase-space analogy introduces a spatial Lagrangian function, valid over the initial post-buckling range, with kinetic and potential energy components. The indefinite quadratic form of the spatial kinetic energy admits unbounded solutions, corresponding to escape from a potential well. Numerical experimentation demonstrates that there is a fractal edge to the escape boundary, resulting in spatial chaos.

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García-Farieta, Jorge Enrique, Federico Marulli, Lauro Moscardini, Alfonso Veropalumbo, and Rigoberto A. Casas-Miranda. "Validating the methodology for constraining the linear growth rate from clustering anisotropies." Monthly Notices of the Royal Astronomical Society 494, no. 2 (March 20, 2020): 1658–74. http://dx.doi.org/10.1093/mnras/staa791.

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ABSTRACT Redshift-space clustering distortions provide one of the most powerful probes to test the gravity theory on the largest cosmological scales. We perform a systematic validation study of the state-of-the-art statistical methods currently used to constrain the linear growth rate from redshift-space distortions in the galaxy two-point correlation function. The numerical pipelines are tested on mock halo catalogues extracted from large N-body simulations of the standard cosmological framework. We consider both the monopole and quadrupole multipole moments of the redshift-space two-point correlation function, as well as the radial and transverse clustering wedges, in the comoving scale range 10 < r[$h^{-1}\, \mbox{Mpc}$] < 55. Moreover, we investigate the impact of redshift measurement errors on the growth rate and linear bias measurements due to the assumptions in the redshift-space distortion model. Considering both the dispersion model and two widely used models based on perturbation theory, we find that the linear growth rate is underestimated by about $5\!-\! 10\, {\rm {per\ cent}}$ at $z$ < 1, while limiting the analysis at larger scales, r > 30 $h^{-1}\, \mbox{Mpc}$, the discrepancy is reduced below $5\, {\rm {per\ cent}}$. At higher redshifts, we find instead an overall good agreement between measurements and model predictions. Though this accuracy is good enough for clustering analyses in current redshift surveys, the models have to be further improved not to introduce significant systematics in RSD constraints from next-generation galaxy surveys. The effect of redshift errors is degenerate with the one of small-scale random motions, and can be marginalized over in the statistical analysis, not introducing any statistically significant bias in the linear growth constraints, especially at $z$ ≥ 1.

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Comişel, Horia, Yasuhiro Nariyuki, Yasuhito Narita, and Uwe Motschmann. "On the role of ion-scale whistler waves in space and astrophysical plasma turbulence." Annales Geophysicae 34, no. 11 (November 9, 2016): 975–84. http://dx.doi.org/10.5194/angeo-34-975-2016.

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Abstract. Competition of linear mode waves is studied numerically to understand the energy cascade mechanism in plasma turbulence on ion-kinetic scales. Hybrid plasma simulations are performed in a 3-D simulation box by pumping large-scale Alfvén waves on the fluid scale. The result is compared with that from our earlier 2-D simulations. We find that the whistler mode is persistently present both in the 2-D and 3-D simulations irrespective of the initial setup, e.g., the amplitude of the initial pumping waves, while all the other modes are excited and damped such that the energy is efficiently transported to thermal energy over non-whistler mode. The simulation results suggest that the whistler mode could transfer the fluctuation energy smoothly from the fluid scale down to the electron-kinetic scale, and justifies the notion of whistler turbulence.

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Lindeberg, Tony. "Provably Scale-Covariant Continuous Hierarchical Networks Based on Scale-Normalized Differential Expressions Coupled in Cascade." Journal of Mathematical Imaging and Vision 62, no. 1 (October 25, 2019): 120–48. http://dx.doi.org/10.1007/s10851-019-00915-x.

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Abstract This article presents a theory for constructing hierarchical networks in such a way that the networks are guaranteed to be provably scale covariant. We first present a general sufficiency argument for obtaining scale covariance, which holds for a wide class of networks defined from linear and nonlinear differential expressions expressed in terms of scale-normalized scale-space derivatives. Then, we present a more detailed development of one example of such a network constructed from a combination of mathematically derived models of receptive fields and biologically inspired computations. Based on a functional model of complex cells in terms of an oriented quasi quadrature combination of first- and second-order directional Gaussian derivatives, we couple such primitive computations in cascade over combinatorial expansions over image orientations. Scale-space properties of the computational primitives are analysed, and we give explicit proofs of how the resulting representation allows for scale and rotation covariance. A prototype application to texture analysis is developed, and it is demonstrated that a simplified mean-reduced representation of the resulting QuasiQuadNet leads to promising experimental results on three texture datasets.

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Yu, Xiaoyan, and Li Chen. "Observer-based two-time scale robust control of free-flying flexible-joint space manipulators with external disturbances." Robotica 35, no. 11 (March 21, 2017): 2201–17. http://dx.doi.org/10.1017/s0263574716000801.

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SUMMARYObserver-based two-time scale robust control is proposed for free-flying flexible-joint space manipulators with unknown payload parameters and bounded disturbances. The dynamic equations of a free-flying space manipulator with two flexible revolute joints were derived by the momentum conservation law and the Lagrange equations. A flexibility compensator was introduced to make the equivalent joint stiffness large enough, which made traditional singular perturbation approach applicable. Then, a singular perturbation model was formulated and a reduced-order controller is proposed. This controller consisted of a slow sub-controller and a fast flexible-joint sub-controller. To the slow subsystem, a sliding observer based robust slow sub-controller was proposed. By optimal linear quadratic regulator method, the fast sub-controller was designed with the estimated velocity by linear observer. This fast sub-controller could stabilize the fast subsystem around the equilibrium trajectory created by the slow subsystem under the effect of the slow control. Finally the numerical simulations were carried out, which showed that elastic joint vibrations had been stabilized effectively and good tracking performances had been achieved.

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Čermák, Jan, Tomáš Kisela, and Luděk Nechvátal. "Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations." Abstract and Applied Analysis 2011 (2011): 1–21. http://dx.doi.org/10.1155/2011/565067.

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This paper investigates some initial value problems in discrete fractional calculus. We introduce a linear difference equation of fractional order along with suitable initial conditions of fractional type and prove the existence and uniqueness of the solution. Then the structure of the solutions space is discussed, and, in a particular case, an explicit form of the general solution involving discrete analogues of Mittag-Leffler functions is presented. All our observations are performed on a special time scale which unifies and generalizes ordinary difference calculus andq-difference calculus. Some of our results are new also in these particular discrete settings.

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Lin, C. Y., and W. H. Ip. "Observation of Comet C/1999 S4 (LINEAR)." International Astronomical Union Colloquium 183 (2001): 277–78. http://dx.doi.org/10.1017/s0252921100079069.

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AbstractComet C/1999 S4 (LINEAR) with a maximum magnitude of 6 mag was the brightest comet in 2000. The 24” telescope on NCU campus was used to observe its coma behavior in June and July of 2000 as it approached perihelion. The observations were carried out using the comet filters designed by the European Space Agency for the ground-based observational program of Comet Wirtanen (target comet of the Rosetta mission). Comet C/1999 S4 (LINEAR) ended up disrupting into many small fragments near perihelion. We are in the process of analyzing the time variations of the cometary dust coma and dust tail to examine the physical condition prior to the destruction of the nucleus of this intriguing comet. An image processing method will be developed to trace small-scale structures in the dust tail.

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Elbers, Willem, Carlos S. Frenk, Adrian Jenkins, Baojiu Li, and Silvia Pascoli. "An optimal non-linear method for simulating relic neutrinos." Monthly Notices of the Royal Astronomical Society 507, no. 2 (August 6, 2021): 2614–31. http://dx.doi.org/10.1093/mnras/stab2260.

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ABSTRACT Cosmology places the strongest current limits on the sum of neutrino masses. Future observations will further improve the sensitivity and this will require accurate cosmological simulations to quantify possible systematic uncertainties and to make predictions for non-linear scales, where much information resides. However, shot noise arising from neutrino thermal motions limits the accuracy of simulations. In this paper, we introduce a new method for simulating large-scale structure formation with neutrinos that accurately resolves the neutrinos down to small scales and significantly reduces the shot noise. The method works by tracking perturbations to the neutrino phase-space distribution with particles and reduces shot noise in the power spectrum by a factor of $\mathcal {O}\left(10^2\right)$ at z = 0 for minimal neutrino masses and significantly more at higher redshifts, without neglecting the back-reaction caused by neutrino clustering. We prove that the method is part of a family of optimal methods that minimize shot noise subject to a maximum deviation from the non-linear solution. Compared to other methods, we find per mille level agreement in the matter power spectrum and per cent level agreement in the large-scale neutrino bias, but large differences in the neutrino component on small scales. A basic version of the method can easily be implemented in existing N-body codes and allows neutrino simulations with significantly reduced particle load. Further gains are possible by constructing background models based on perturbation theory. A major advantage of this technique is that it works well for all masses, enabling a consistent exploration of the full neutrino parameter space.

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CĂRPUȘ, Eftalea, and Angela DOROGAN. "SPACE OPERATIONAL SCALE OF THE TEXTILE-CLOTHING SECTOR BASED ON CREATIVITY, INNOVATION AND FUTURE." TEXTEH Proceedings 2019 (November 5, 2019): 228–32. http://dx.doi.org/10.35530/tt.2019.04.

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The textile industry is one of the most important polluters of the environment. The linear economic system, which dominates the sector, puts pressure on resources, pollutes and degrades the natural environment and its ecosystems and creates significant negative societal impacts on a local scale, regional and global. Given the multitude of technologies, which are growing exponentially, the complexity of current economic processes and society and the need to respond to growing environmental risk challenges, it is necessary to operationalize the textile sector through convergent solutions: disruptive innovation, circular economy, education for sustainable development. The article outlines the benchmarks of the spatial operational scale for creativity, innovation in the context of the textile field, from fiber to textiles, in the succession of (un)conventional, processing processes, on traditional production chains, finalized by specific activities for clothing production, respectively on multidisciplinary production chains, completed by activities specific to obtaining textile systems.

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Pan, Xiaoda, Hengliang Zhu, Fan Yang, and Xuan Zeng. "Subspace Trajectory Piecewise-Linear Model Order Reduction for Nonlinear Circuits." Communications in Computational Physics 14, no. 3 (September 2013): 639–63. http://dx.doi.org/10.4208/cicp.070512.051112a.

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AbstractDespite the efficiency of trajectory piecewise-linear (TPWL) model order reduction (MOR) for nonlinear circuits, it needs large amount of expansion points for large-scale nonlinear circuits. This will inevitably increase the model size as well as the simulation time of the resulting reduced macromodels. In this paper, subspace TPWL-MOR approach is developed for the model order reduction of nonlinear circuits. By breaking the high-dimensional state space into several subspaces with much lower dimensions, the subspace TPWL-MOR has very promising advantages of reducing the number of expansion points as well as increasing the effective region of the reduced-order model in the state space. As a result, the model size and the accuracy of the TWPL model can be greatly improved. The numerical results have shown dramatic reduction in the model size as well as the improvement in accuracy by using the subspace TPWL-MOR compared with the conventional TPWL-MOR approach.

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Rybas, O. V., and G. Z. Gilmanova. "The application of the scale-space theory for medium-resolution DTM in geological and geotectonic studies." Geomorphology RAS, no. 2 (April 26, 2019): 68–78. http://dx.doi.org/10.31857/s0435-42812019268-78.

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The article presents a technique for identifying structural elements and details of the geological structure in digital terrain models (DTM) based on the theory of scale spaces. With its help, linear, dome-shaped and textural features are singled out from medium-resolution DTM (for example, SRTM03, GMTED2010), allowing to significantly improve the quality of studies related to tectonic and geological mapping and zoning. In general, the theory of scale — spaces is described in application to the solution of these problems and illustarted on the examples of a number of case studies.

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TARTAGLIA, ANGELO. "A STRAINED SPACE-TIME TO EXPLAIN THE LARGE SCALE PROPERTIES OF THE UNIVERSE." International Journal of Modern Physics: Conference Series 03 (January 2011): 303–11. http://dx.doi.org/10.1142/s2010194511001401.

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Space-time can be treated as a four-dimensional material continuum. The corresponding generally curved manifold can be thought of as having been obtained, by continuous deformation, from a flat four-dimensional Euclidean manifold. In a three-dimensional ordinary situation such a deformation process would lead to strain in the manifold. Strain in turn may be read as half the difference between the actual metric tensor and the Euclidean metric tensor of the initial unstrained manifold. On the other side we know that an ordinary material would react to the attempt to introduce strain giving rise to internal stresses and one would have correspondingly a deformation energy term. Assuming the conditions of linear elasticity hold, the deformation energy is easily written in terms of the strain tensor. The Einstein-Hilbert action is generalized to include the new deformation energy term. The new action for space-time has been applied to a Friedmann-Lemaître-Robertson-Walker universe filled with dust and radiation. The accelerated expansion is recovered, then the theory has been put through four cosmological tests: primordial isotopic abundances from Big Bang Nucleosynthesis; Acoustic Scale of the CMB; Large Scale Structure formation; luminosity/redshift relation for type Ia supernovae. The result is satisfying and has allowed to evaluate the parameters of the theory.

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Journal articles on the topic 'Linear scale-space'

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