Non-uniform Scaling Research Articles

Mechanism analysis for scaling effect on the impact behaviors of RC beam: From material properties to component response

Scaling effects on the resistance response of RC components have been found under impact, penetration, and blast. To investigate the mechanism and origins of the scaling effect on the impact response of RC beams, numerical models of geometrically similar beams were established on the ABAQUS platform by considering the strain rate effect. The influence of material properties such as elasticity, plasticity, and strain rate effect on the similarity of beam impact response was accessed and analyzed. Then, the scaling effects of impact characteristics such as time history, damage, effective mass, and span length of RC beams were discussed and compared from the local and global stages. The numerical findings revealed that material properties influence the scaling effect on the impact response and strain rate distribution. The inhomogeneity of strain rate distribution and the difference in dynamic strength caused by the non-uniform scaling for the strain rate effects (DIFs) contribute to the scaling effect. In addition, the two-stage analysis results indicated that the scaling effects exhibited in the local and global responses of RC beams are not entirely consistent. As the scale factor increases, for the large-sized beams, the normalized deformation profile shrinks, the equivalent mass factor decreases, the effective span length changes slower, and the moving velocity of the plastic hinge slows down. Several impact performance characteristics, such as strain rate distribution within the beam and the damage and deformation curve of the beam, will reflect localization as the scale factor increases. It is expected that the preliminary mechanism analysis of this study could provide a reference for analyzing the impact response of prototype beams.

Enhanced Synaptic Inhibition in the Dorsolateral Geniculate Nucleus in a Mouse Model of Glaucoma.

Elevated intraocular pressure (IOP) triggers glaucoma by damaging the output neurons of the retina called retinal ganglion cells (RGCs). This leads to the loss of RGC signaling to visual centers of the brain such as the dorsolateral geniculate nucleus (dLGN), which is critical for processing and relaying information to the cortex for conscious vision. In response to altered levels of activity or synaptic input, neurons can homeostatically modulate postsynaptic neurotransmitter receptor numbers, allowing them to scale their synaptic responses to stabilize spike output. While prior work has indicated unaltered glutamate receptor properties in the glaucomatous dLGN, it is unknown whether glaucoma impacts dLGN inhibition. Here, using DBA/2J mice, which develop elevated IOP beginning at 6-7 months of age, we tested whether the strength of inhibitory synapses on dLGN thalamocortical relay neurons is altered in response to the disease state. We found an enhancement of feedforward disynaptic inhibition arising from local interneurons along with increased amplitude of quantal inhibitory synaptic currents. A combination of immunofluorescence staining for the γ-aminobutyric acid (GABA)A-α1 receptor subunit, peak-scaled nonstationary fluctuation analysis, and measures of homeostatic synaptic scaling pointed to an ∼1.4-fold increase in GABA receptors at postsynaptic inhibitory synapses, although several pieces of evidence indicate a nonuniform scaling across inhibitory synapses within individual relay neurons. Together, these results indicate an increase in inhibitory synaptic strength in the glaucomatous dLGN, potentially pointing toward homeostatic compensation for disruptions in network and neuronal function triggered by increased IOP.

PerfectTailor: Scale-Preserving 2-D Pattern Adjustment Driven by 3-D Garment Editing.

We address the problem of modifying a given well-designed 2-D sewing pattern to accommodate garment edits in the 3-D space. Existing methods usually adjust the sewing pattern by applying uniform flattening to the 3-D garment. The problems are twofold: first, it ignores local scaling of the 2-D sewing pattern such as shrinking ribs of cuffs; second, it does not respect the implicit design rules and conventions of the industry, such as the use of straight edges for simplicity and precision in sewing. To address those problems, we present a pattern adjustment method that considers the nonuniform local scaling of the 2-D sewing pattern by utilizing the intrinsic scale matrix. In addition, we preserve the original boundary shape by an as-original-as-possible geometric constraint when desirable. We build a prototype with a set of commonly used alteration operations and showcase the capability of our method via a number of alteration examples throughout the article.

Slippage-Preserving Reshaping of Human-Made 3D Content

Artists often need to reshape 3D models of human-made objects by changing the relative proportions or scales of different model parts or elements while preserving the look and structure of the inputs. Manually reshaping inputs to satisfy these criteria is highly time-consuming; the edit in our teaser took an artist 5 hours to complete. However, existing methods for 3D shape editing are largely designed for other tasks and produce undesirable outputs when repurposed for reshaping. Prior work on 2D curve network reshaping suggests that in 2D settings the user-expected outcome is achieved when the reshaping edit keeps the orientations of the different model elements and when these elements scale as-locally-uniformly-as-possible (ALUP). However, our observations suggest that in 3D viewers are tolerant of non-uniform tangential scaling if and when this scaling preserves slippage and reduces changes in element size, or scale , relative to the input. Slippage preservation requires surfaces which are locally slippable with respect to a given rigid motion to retain this property post-reshaping (a motion is slippable if when applied to the surface, it slides the surface along itself without gaps). We build on these observations by first extending the 2D ALUP framework to 3D and then modifying it to allow non-uniform scaling while promoting slippage and scale preservation. Our 3D ALUP extension produces reshaped outputs better aligned with viewer expectations than prior alternatives; our slippage-aware method further improves the outcome producing results on par with manual reshaping ones. Our method does not require any user input beyond specifying control handles and their target locations. We validate our method by applying it to over one hundred diverse inputs and by comparing our results to those generated by alternative approaches and manually. Comparative study participants preferred our outputs over the best performing traditional deformation method by a 65% margin and over our 3D ALUP extension by a 61% margin; they judged our outputs as at least on par with manually produced ones.

Non-uniform temporal scaling of developmental processes in the mammalian cortex

The time that it takes the brain to develop is highly variable across animals. Although staging systems equate major developmental milestones between mammalian species, it remains unclear how distinct processes of cortical development scale within these timeframes. Here, we compare the timing of cortical development in two mammals of similar size but different developmental pace: eutherian mice and marsupial fat-tailed dunnarts. Our results reveal that the temporal relationship between cell birth and laminar specification aligns to equivalent stages between these species, but that migration and axon extension do not scale uniformly according to the developmental stages, and are relatively more advanced in dunnarts. We identify a lack of basal intermediate progenitor cells in dunnarts that likely contributes in part to this timing difference. These findings demonstrate temporal limitations and differential plasticity of cortical developmental processes between similarly sized Therians and provide insight into subtle temporal changes that may have contributed to the early diversification of the mammalian brain.

A generalized closed-form solution for 3D registration of two-point sets under isotropic and anisotropic scaling

Fitting of two-point sets under non-uniform scaling involves several applications, including ultrasound-guided surgery, where ultrasound images generally show anisotropy between its lateral and depth resolution. However, the current state-of-the-art only accomplishes the closed-form solution under the assumption of isotropic scaling, and only the iterative form of the solution is available for registration regardless of scaling type. A generalized closed-form solution, including anisotropic scaling, could robust the computation in the applications of multi-modality image fusion and surgical navigation based on ultrasound images. In this paper, a generalized closed-form solution (GCFS) that accounts for isotropic scaling and anisotropic scaling is proposed. GCFS finds the least-squares solution of rotation, translation, and scaling based on the singular value decomposition (SVD). The method was demonstrated to 1) register two 3D point sets under the effect of anisotropic scaling and 2) register two coplanar 3D point sets under the effect of anisotropic scaling. This study evaluates 3D registration between the preoperative model and intraoperative ultrasonic scanning of a femur and 2D registration of ultrasound images to the phantom for ultrasound calibration. In addition, the conditions that affect the transformation estimations like estimating reflection and noise degeneracy were also considered in the evaluation.

Spectral properties of size-invariant shape transformation.

Size-invariant shape transformation is a technique of changing the shape of a domain while preserving its sizes under the Lebesgue measure. In quantum-confined systems, this transformation leads to so-called quantum shape effects in the physical properties of confined particles associated with the Dirichlet spectrum of the confining medium. Here we show that the geometric couplings between levels generated by the size-invariant shape transformations cause nonuniform scaling in the eigenspectra. In particular, the nonuniform level scaling, in the direction of increasing quantum shape effect, is characterized by two distinct spectral features: lowering of the first eigenvalue (ground-state reduction) and changing of the spectral gaps (energy level splitting or degeneracy formation depending on the symmetries). We explain the ground-state reduction by the increase in local breadth (i.e., parts of the domain becoming less confined) that is associated with the sphericity of these local portions of the domain. We accurately quantify the sphericity using two different measures: the radius of the inscribed n-sphere and the Hausdorff distance. Due to Rayleigh-Faber-Krahn inequality, the greater the sphericity, the lower the first eigenvalue. Then level splitting or degeneracy, depending on the symmetries of the initial configuration, becomes a direct consequence of size invariance dictating the eigenvalues to have the same asymptotic behavior due to Weyl law. Such level splittings may be interpreted as geometric analogs of Stark and Zeeman effects. Furthermore, we find that the ground-state reduction causes a quantum thermal avalanche which is the underlying reason for the peculiar effect of spontaneous transitions to lower entropy states in systems exhibiting the quantum shape effect. Unusual spectral characteristics of size-preserving transformations can assist in designing confinement geometries that could lead to classically inconceivable quantum thermal machines.

Efficient anisotropic scaling and translation invariants of Tchebichef moments using image normalization

Anisotropic scaling and translation invariants of Tchebichef moments are commonly used in image analysis to address issues arising from patterns distorted by non-uniform scaling and translation. In this paper, we formulate a new fast computational algorithm and a new normalization scheme based on the properties of Tchebichef moments. The proposed model can correctly resolve the mirror reflection ambiguities caused by the scaling transformations and gives smaller size deviations for various patterns so that the canonical form can easily fit within the normalized space. An empirical study shows that the proposed method significantly improves numerical computation and classification accuracy under non-noisy and noisy conditions when compared with existing methods. The main contribution of this paper is a novel fast computational algorithm for anisotropic scaling and translation invariants of Tchebichef moments and a new normalization scheme that produces features with higher discriminative power. The proposed algorithm is useful for recognizing objects with non-uniform size and displacement deformations. It is also a key component in formulating a better affine invariant algorithm for the image analysis community.

Numerical analysis of anisotropic stiffness and strength for geomaterials

In numerical modelling, selection of the constitutive model is a critical factor in predicting the actual response of a geomaterial. The use of oversimplified or inadequate models may not be sufficient to reproduce the actual geomaterial behaviour. That selection is especially relevant in the case of anisotropic rocks, and particularly for shales and slates, whose behaviour may be affected, e.g. well stability in geothermal or oil and gas production operations. In this paper, an alternative anisotropic constitutive model has been implemented in the finite element method software CODE_BRIGHT, which is able to account for the anisotropy of shales and slates in terms of both deformability and strength. For this purpose, a transversely isotropic version of the generalised Hooke's law is adopted to represent the stiffness anisotropy, while a nonuniform scaling of the stress tensor is introduced in the plastic model to represent the strength anisotropy. Furthermore, a detailed approach has been proposed to determine the model parameters based on the stress–strain results of laboratory tests. Moreover, numerical analyses are performed to model uniaxial and triaxial tests on Vaca Muerta shale, Bossier shale and slate from the northwest of Spain (NW Spain slate). The experimental data have been recovered from the literature in the case of the shale and, in the case of the slate, performed by the authors in terms of stress-strain curves and strengths. A good agreement can be generally observed between numerical and experimental results, hence showing the potential applicability of the approach to actual case studies. Therefore, the presented constitutive model may be a promising approach for analysing the anisotropic behaviour of rocks and its impact on well stability or other relevant geomechanical problems in anisotropic rocks.

Modified Hamiltonian in FEP Calculations for Reducing the Computational Cost of Electrostatic Interactions.

The free-energy perturbation (FEP) method predicts relative and absolute free-energy changes of biomolecules in solvation and binding with other molecules. FEP is, therefore, one of the most essential tools in in silico drug design. In conventional FEP, to smoothly connect two thermodynamic states, the potential energy is modified as a linear combination of the end-state potential energies by introducing scaling factors. When the particle mesh Ewald is used for electrostatic calculations, conventional FEP requires two reciprocal-space calculations per time step, which largely decreases the computational performance. To overcome this problem, we propose a new FEP scheme by introducing a modified Hamiltonian instead of interpolation of the end-state potential energies. The scheme introduces nonuniform scaling into the electrostatic potential as used in Replica Exchange with Solute Tempering 2 (REST2) and does not require additional reciprocal-space calculations. We tested this modified Hamiltonian in FEP calculations in several biomolecular systems. In all cases, the calculated free-energy changes with the current scheme are in good agreement with those from conventional FEP. The modified Hamiltonian in FEP greatly improves the computational performance, which is particularly marked for large biomolecular systems whose reciprocal-space calculations are the major bottleneck of total computational time.

Multi-Scale Memetic Image Registration

Many technological applications of our time rely on images captured by multiple cameras. Such applications include the detection and recognition of objects in captured images, the tracking of objects and analysis of their motion, and the detection of changes in appearance. The alignment of images captured at different times and/or from different angles is a key processing step in these applications. One of the most challenging tasks is to develop fast algorithms to accurately align images perturbed by various types of transformations. The paper reports a new method used to register images in the case of geometric perturbations that include rotations, translations, and non-uniform scaling. The input images can be monochrome or colored, and they are preprocessed by a noise-insensitive edge detector to obtain binarized versions. Isotropic scaling transformations are used to compute multi-scale representations of the binarized inputs. The algorithm is of memetic type and exploits the fact that the computation carried out in reduced representations usually produces promising initial solutions very fast. The proposed method combines bio-inspired and evolutionary computation techniques with clustered search and implements a procedure specially tailored to address the premature convergence issue in various scaled representations. A long series of tests on perturbed images were performed, evidencing the efficiency of our memetic multi-scale approach. In addition, a comparative analysis has proved that the proposed algorithm outperforms some well-known registration procedures both in terms of accuracy and runtime.

Implications of Non-Uniform Deadline Scaling to Quality of Service Under Single Errors

Fault-tolerant real-time systems for emerging critical applications like wearable electronic healthcare monitors, consumer-grade unmanned aerial vehicles, or environmental monitoring have to tolerate errors during operation. If they fail, the consequences are dire. But often their budgets for error mitigation capabilities are low, which requires to limit mitigation capabilities to the most critical functions of a system. Still, less critical functions of a system should operate as long as possible, but current state-of-the-art scheduling approaches either ignore them or suffer from low acceptance rates. Our fully static and verification friendly mixed-criticality approach guarantees mentioned systems that the most critical system functions are always available, and maximizes the time where less critical system functions are operational: We prove that our approach is feasible, and extends the system operation time while providing full service by a factor of 1.93 with a probability of 0.92. With 1.56 higher acceptance rates compared to similar state-of-the-art approaches, the integration of functionalities of different criticality in one fault-tolerant system succeeds more and more often, which especially benefits emerging critical applications with limited budgets for error mitigation.

Bayesian inference of rock strength anisotropy: Uncertainty analysis of the Hoek–Brown failure criterion

Strength properties of most sedimentary and metamorphic rocks are known to vary with direction. Knowledge of this so-called rock anisotropy is of utmost importance for reliability analysis and engineering design. The purpose of this paper is twofold. First, we propose a formulation of the Hoek–Brown (HB) failure criterion, which calculates strength anisotropy using a non-uniform scaling of the stress tensor. We use two scaling factors, CN and CS, to link the orientation of the anisotropy planes with the loading direction. As we assume isotropic parameters for intact rock, our HB model formulation is relatively easy to use and has the additional advantage that it does not demand any modifications to the HB failure criterion. Second, we embed our HB model formulation in a Bayesian framework and illustrate its power and usefulness using experimental data of anisotropic rock samples published in the literature. Results demonstrate that our HB model formulation predicts accurately measured peak strengths of rocks with different degrees of anisotropy, confining stresses and anisotropy orientations. The uncertainty in peak strength of anisotropic rocks can be quite large, reiterating the need for an explicit treatment of strength anisotropy uncertainty in rock mechanics studies. The Bayesian methodology is general-purpose, and, as such, can help better inform geotechnical engineers, contractors and other professionals about rock conditions and design reliability and assist decision makers in determining the overall risks of engineering structures.

Asymptotic stabilization of nonlinear systems with convex-polytope input constraints by continuous input

In this paper, we propose an asymptotic stabilization controller for a nonlinear system with a convex-polytope input constraint. Moreover, we show that the controller has inverse optimality in the domain of attraction. The controller input is continuous in the set in which the asymptotic stabilization is guaranteed. We consider the asymmetric constraint for zero-input, and this bias is adjusted by using a non-uniform scaling on each vertex point in the neighborhood of the origin. Therefore, the input cost of the inverse optimal performance functional is approximated by a quadratic function near the origin.

Time-Frequency Analysis and Parameterisation of Knee Sounds for Non-Invasive Detection of Osteoarthritis.

In this work the potential of non-invasive detection of knee osteoarthritis is investigated using the sounds generated by the knee joint during walking. The information contained in the time-frequency domain of these signals and its compressed representations is exploited and their discriminant properties are studied. Their efficacy for the task of normal vs abnormal signal classification is evaluated using a comprehensive experimental framework. Based on this, the impact of the feature extraction parameters on the classification performance is investigated using Classification and Regression Trees, Linear Discriminant Analysis and Support Vector Machine classifiers. It is shown that classification is successful with an area under the Receiver Operating Characteristic curve of 0.92. The analysis indicates improvements in classification performance when using non-uniform frequency scaling and identifies specific frequency bands that contain discriminative features. Contrary to other studies that focus on sit-to-stand movements and knee flexion/extension, this study used knee sounds obtained during walking. The analysis of such signals leads to non-invasive detection of knee osteoarthritis with high accuracy and could potentially extend the range of available tools for the assessment of the disease as a more practical and cost effective method without requiring clinical setups.

Perceptual validation of vowel normalization methods for variationist research

AbstractThe evaluation of normalization methods sometimes focuses on the maximization of vowel-space similarity. This focus can lead to the adoption of methods that erase legitimate phonetic variation from our data, that is, overnormalization. First, a production corpus is presented that highlights three types of variation in formant patterns: uniform scaling, nonuniform scaling, and centralization. Then the results of two perceptual experiments are presented, both suggesting that listeners tend to ignore variation according to uniform scaling, while associating nonuniform scaling and centralization with phonetic differences. Overall, results suggest that normalization methods that remove variation not according to uniform scaling can remove legitimate phonetic variation from vowel formant data. As a result, although these methods can provide more similar vowel spaces, they do so by erasing phonetic variation from vowel data that may be socially and linguistically meaningful, including a potential male-female difference in the low vowels in our corpus.

Development of a generalized scaling law for underwater explosions using a numerical and experimental parametric study

In order to reduce enormous cost of real-scale underwater explosion experiments on ships, the mechanical response of the ships have been analyzed by combining scaled-down experiments and Hopkinson's scaling law. However, the Hopkinson's scaling law is applicable only if all variables vary in an identical ratio; for example, thickness of ship, size of explosive, and distance between the explosive and the ship should vary with same ratio. Unfortunately, it is infeasible to meet such uniform scaling requirement because of environmental conditions and limitations in manufacturing scaled model systems. For the facile application of the scaling analysis, we propose a generalized scaling law that is applicable for non-uniform scaling cases in which different parts of the experiments are scaled in different ratios compared to the real-scale experiments. In order to establish such a generalized scaling law, we conducted a parametric study based on numerical simulations, and validated it with experiments and simulations. This study confirms that the initial peak value of response variables in a real-scale experiment can be predicted even when we perform a scaled experiment composed of different scaling ratios for each experimental variable.

Critique of “Planetary Normal Mode Computation: Parallel Algorithms, Performance, and Reproducibility” by SCC Team From University of Washington

One of the tasks for the SC19 Student Cluster Competition is to reproduce the results in the reproducibility challenge article “Computing Planetary Interior Normal Modes with a Highly Parallel Polynomial Filtering Eigensolver”, by J. Shi et al., which describes a highly parallel algorithm for computing planetary normal modes. In running experiments from the article, we study the weak and strong scalability of the algorithm, as well as the relationship between model size, degree of polynomial filter, and execution time. We investigate these findings on a two-node, 64-core Intel Skylake-based Xeon cluster. Unfortunately, we are able to confirm some, but not all, of the original findings, with discrepancies possibly due to a low number of experimental runs due to competition time limits as well as nonuniform scaling of compute resources.

On the Topological Structure and Properties of Multidimensional (C, R) Space

Generally, the linear topological spaces successfully generate Tychonoff product topology in lower dimensions. This paper proposes the construction and analysis of a multidimensional topological space based on the Cartesian product of complex and real spaces in continua. The geometry of the resulting space includes a real plane with planar rotational symmetry. The basis of topological space contains cylindrical open sets. The projection of a cylindrically symmetric continuous function in the topological space onto a complex planar subspace maintains surjectivity. The proposed construction shows that there are two projective topological subspaces admitting non-uniform scaling, where the complex subspace scales at a higher order than the real subspace generating a quasinormed space. Furthermore, the space can be equipped with commutative and finite translations on complex and real subspaces. The complex subspace containing the origin of real subspace supports associativity under finite translation and multiplication operations in a combination. The analysis of the formation of a multidimensional topological group in the space requires first-order translation in complex subspace, where the identity element is located on real plane in the space. Moreover, the complex translation of identity element is restricted within the corresponding real plane. The topological projections support additive group structures in real one-dimensional as well as two-dimensional complex subspaces. Furthermore, a multiplicative group is formed in the real projective space. The topological properties, such as the compactness and homeomorphism of subspaces under various combinations of projections and translations, are analyzed. It is considered that the complex subspace is holomorphic in nature.

Fractal Correlation Dimensions Analysis of Al–Si Dendrites

Solidification dendrites in metal alloys have intricate shapes with fractal elements, making fractal dimension an attractive potential method for more completely quantifying these important shapes. However, fractal analysis as usually applied to dendrites has some pitfalls, which we demonstrate here on micrographs of dendrites from two different aluminum–silicon alloys with different solidification velocities. Box dimension and a more rigorous analysis of correlation dimension were calculated for each sample, but both measures exhibited non-uniform scaling. Further analysis using the Takens–Theiler estimator of correlation dimension revealed a transition between two distinct scaling regimes: a small-scale exponent associated with dendrite boundary texture and the large-scale with overall dendrite morphology. The scaling transition between regimes may prove useful as an automated alternative to secondary dendrite arm spacing. Overall, the investigations give further insight into the quantitative description of complex dendritic structures and clarify the ability of fractal analysis to describe this important solidification morphology.