Gradient Path Research Articles

A fast spectral conjugate gradient method for solving nonlinear optimization problems

<span>This paper proposes a new spectral conjugate gradient (SCG) approach for solving unregulated nonlinear optimization problems. Our approach proposes Using Wolfe's rapid line scan to adjust the standard conjugate descent (CD) algorithm. A new spectral parameter is a mixture of new gradient and old search path. The path provided by the modified method provides a path of descent for the solution of objective functions. The updated method fits the traditional CD method if the line check is correct. The stability and global convergence properties of the current new SCG are technically obtained from applying certain well-known and recent mild assumptions. We test our approach with eight recently published CD and SCG methods on 55 optimization research issues from the CUTE library. The suggested and all other algorithms included in our experimental research were implemented in FORTRAN language with double precision arithmetic and all experiments were conducted on a PC with 8 GB ram Processor Intel Core i7. The results indicate that our proposed solution outperforms recently reported algorithms by processing and performing fewer iterations in a shorter time.</span>

Joint Multi-Dimension Pruning via Numerical Gradient Update.

We present joint multi-dimension pruning (abbreviated as JointPruning), an effective method of pruning a network on three crucial aspects: spatial, depth and channel simultaneously. To tackle these three naturally different dimensions, we proposed a general framework by defining pruning as seeking the best pruning vector (i.e., the numerical value of layer-wise channel number, spatial size, depth) and construct a unique mapping from the pruning vector to the pruned network structures. Then we optimize the pruning vector with gradient update and model joint pruning as a numerical gradient optimization process. To overcome the challenge that there is no explicit function between the loss and the pruning vectors, we proposed self-adapted stochastic gradient estimation to construct a gradient path through network loss to pruning vectors and enable efficient gradient update. We show that the joint strategy discovers a better status than previous studies that focused on individual dimensions solely, as our method is optimized collaboratively across the three dimensions in a single end-to-end training and it is more efficient than the previous exhaustive methods. Extensive experiments on large-scale ImageNet dataset across a variety of network architectures MobileNet V1&V2&V3 and ResNet demonstrate the effectiveness of our proposed method. For instance, we achieve significant margins of 2.5% and 2.6% improvement over the state-of-the-art approach on the already compact MobileNet V1&V2 under an extremely large compression ratio.

Parametric Analysis of Autopilot Intelligent Robot (PIR) Using Multiple Surface Gradient Path MSGP

Robotic application is taking new dimensions around the globe, of which numerous problems are solved with embedded systems, this research introduces gradient vertices method from 3D geometric to perform data capturing using kinematic effect with aid of autopilot Intelligent Robotic (PIR). The research considered Multiple Surface Gradient Path MSGP using Toyota Camry 200x chases model using DC motor Pulse Wide Modulation (PMW). The discretion only Multiple Surface Gradients, distance values and angular pivots with respect to time. The PIR hardware “Raspberry Pi 3B” as the target board is interface with modular peripherals, using python programming language. Auto pilot is archived using different surface gradients and the digital images obtained during experience are stored for further analysis. The use of Tkinter GUI improved user experience in the extermination of the periodic oscillation, gradient values, proximate distance obtained by the PIR Final implementation. The deployment is completed by improvising a prototype model (PIR) suitable for Toyota Camry 200x. It is important to view it in the context of a larger community policing framework. PIR can be classified as intermission robot that can be used for different activities with the available feature kinematic system which make it relevant for multi-purpose activities.

Experimental validation of Scheil–Gulliver simulations for gradient path planning in additively manufactured functionally graded materials

Additive manufacturing (AM), through directed energy deposition, supports planned composition changes between locations within a single component, allowing for functionally graded materials (FGMs) to be developed and fabricated. The formation of deleterious phases along a particular composition path can cause significant cracking during the AM build process that makes the composition path unviable to produce structurally stable FGMs, but it is challenging to predict which phases will be present in as-built additively manufactured parts by analyzing only equilibrium phase relations. Solute segregation during solidification can lead to the formation of non-equilibrium phases that are stable at compositions far from the nominal composition of the melt, leading to crack formation. In this work, we developed and validated a Scheil–Gulliver simulation tool based on pycalphad. We used this tool to compare the non-equilibrium phases predicted to form during the AM build process using the Scheil–Gulliver model with experimentally measured phases at several locations with different composition in a Ti-6Al-4V to Invar-36 FGM and a commercially pure Ti to Invar-36 FGM. We showed that the phases predicted to form by the Scheil–Gulliver model agree better with the experimental results than the predictions made by assuming equilibrium solidification, proving that the Scheil–Gulliver model can be applied to FGMs. Further, we demonstrated the use of our Scheil–Gulliver simulation tool as a method of designing FGMs through screening potential FGM pathways by calculating the solidification phase fractions along the experimental gradient path in composition space.

Rethinking the Image Fusion: A Fast Unified Image Fusion Network based on Proportional Maintenance of Gradient and Intensity

In this paper, we propose a fast unified image fusion network based on proportional maintenance of gradient and intensity (PMGI), which can end-to-end realize a variety of image fusion tasks, including infrared and visible image fusion, multi-exposure image fusion, medical image fusion, multi-focus image fusion and pan-sharpening. We unify the image fusion problem into the texture and intensity proportional maintenance problem of the source images. On the one hand, the network is divided into gradient path and intensity path for information extraction. We perform feature reuse in the same path to avoid loss of information due to convolution. At the same time, we introduce the pathwise transfer block to exchange information between different paths, which can not only pre-fuse the gradient information and intensity information, but also enhance the information to be processed later. On the other hand, we define a uniform form of loss function based on these two kinds of information, which can adapt to different fusion tasks. Experiments on publicly available datasets demonstrate the superiority of our PMGI over the state-of-the-art in terms of both visual effect and quantitative metric in a variety of fusion tasks. In addition, our method is faster compared with the state-of-the-art.

Gradient Path Labelling method and tracking method for calculation of solar differential rotation using coronal bright points

Abstract With new space missions, such as Solar Dynamics Observatory (SDO), solar images are being produced in unprecedented volumes. To derive, as much as possible, information on evolution of solar activity from those huge datasets, the scientific community needs a new generation of software tools for automatic and efficient data processing. In the last decade, several research teams have been developing tools for obtaining more precise estimations of the solar rotation profile, but more are needed to improve knowledge about solar activity. We applied here a segmentation algorithm called Gradient Path Labelling (GPL), used originally to identify drusens in medical retinal images, to detect and track the coronal bright points (CBPs) using images from the AIA instrument onboard the SDO satellite. The CBPs have a tendency to change shape and size along time, to disappear and reappear at a corresponding heliographic position, therefore, decision trees were also included in the tracking solution. Since our CBP detection algorithm uses an active region mask to filter out the CBPs, whose centroid is inside the active regions, the number of identifications clearly depends on the level of solar activity. Our approach uses the commonly applied fitting relation to the latitudinal dependence of the rotational velocity, which resulted in calculation of the optimum fit parameters as well as the Gegenbauer orthogonal polynomials. Comparison of these parameters with the results presented in recent papers on this topic shows that our rotational velocity profile indicates slightly lower rotational velocities than the profiles obtained with other approaches. We also calculate the meridional motion of the CBPs, but comparison with other authors results, clearly show that a 3-day time interval is too short to estimate the latitudinal dependence of the CBP meridional motion. Distributions of the rotational velocity and meridional motion velocity uncertainties show that 85% of uncertainty values are lower than 1 degree/day. The evaluation of our test results shows that the applied algorithm is a promising tool that can help to refine the solar rotational profile.

Computational Design of Gradient Paths in Additively Manufactured Functionally Graded Materials

Additive manufacturing (AM) has enabled the creation of a near infinite set of functionally graded materials (FGMs). One limitation on the manufacturability and usefulness of these materials is the presence of undesirable phases along the gradient path. For example, such phases may increase brittleness, diminish corrosion resistance, or severely compromise the printability of the part altogether. In the current work, a design methodology is proposed to plan an FGM gradient path for any number of elements that avoids undesirable phases at a range of temperatures. Gradient paths can also be optimized for a cost function. A case study is shown to demonstrate the effectiveness of the methodology in the Fe–Ni–Cr system. Paths were successfully planned from 316 L Stainless Steel (316 L SS) to pure Cr that either minimize path length or maximize separation from undesirable phases. Examinations on the stochastic variability, parameter dependency, and computational efficiency of the method are also presented. Several avenues of future research are proposed that could improve the manufacturability, utility, and performance of FGMs through gradient path design.

Cell Sequence and Mitosis Affect Fibroblast Directional Decision-Making During Chemotaxis in Microfluidic Mazes.

Directed fibroblast migration is central to highly proliferative processes in regenerative medicine and developmental biology. However, the mechanisms by which single fibroblasts affect each other's directional decisions, while chemotaxing in microscopic pores, are not well understood. We explored effects of cell sequence and mitosis on fibroblast platelet-derived growth factor-BB (PDGF-BB)-induced migration in microfluidic mazes with two possible through paths: short and long. Additionally, image-based modeling of the chemoattractant's diffusion, consumption and decay, was used to explain the experimental observations. It both cases, the cells displayed behavior that is contradictory to expectation based on the global chemoattractant gradient pre-established in the maze. In case of the sequence, the cells tend to alternate when faced with a bifurcation: if a leading cell takes the shorter (steeper gradient) path, the cell following it chooses the longer (weaker gradient) path, and vice versa. Image-based modeling of the process showed that the local PDGF-BB consumption by the individual fibroblasts may be responsible for this phenomenon. Additionally, it was found that when a mother cell divides, its two daughters go in opposite directions (even if it means migrating against the chemoattractant gradient and overcoming on-going cell traffic). It is apparent that micro-confined fibroblasts modify each other's directional decisions in a manner that is counter-intuitive to what is expected from classical chemotaxis theory. Consequently, accounting for these effects could lead to a better understanding of tissue generation in vivo, and result in more advanced engineered tissue products in vitro.

Natural selection for body shape in resource polymorphic Icelandic Arctic charr.

Resource polymorphisms exhibit remarkable intraspecific diversity and in many cases are expected to be maintained by diversifying selection. Phenotypic trade-offs can constrain morphologically intermediate individuals from effectively exploiting both alternate resources, resulting in ecological barriers to gene flow. Determining if and how phenotypic trade-offs cause fitness variation in the wild is challenging because of phenotypic and environmental correlations associated with alternative resource strategies. We investigated multiple pathways through which morphology could affect organismal performance, as measured by growth rate, and whether these effects generate diversifying selection in polymorphic Icelandic Arctic charr (Salvelinus alpinus) populations. We considered direct effects of morphology on growth and indirect effects via trophic resource use, estimated by stable isotopic signatures, and via parasitism associated with trophic resources. We sampled over 3years in (lakes) Thingvallavatn and Vatnshlíðarvatn using the extended selection gradient path analytical approach and estimating size-dependent mortality. We found evidence for diversifying selection only in Thingvallavatn: more streamlined and terminally mouthed planktivore charr experienced greater growth, with the opposite pattern in small benthic charr. However, this effect was mediated by parasitism and nontrophic pathways, rather than trophic performance as often expected. Detection of between-morph differences in the presence (Vatnshlíðarvatn) and direction (Thingvallavatn) of size-dependent mortality, together with nontrophic effects of shape, suggests that a morphological trophic performance explanation for polymorphism is insufficient. This rare insight into selection during early diversification suggests that a complex of interacting local factors must be considered to understand how phenotype influences fitness, despite morphological variation reflecting intuitive trade-off explanations.

Discrete Morse Theory for the Barycentric Subdivision

Let $F$ be a discrete Morse function on a simplicial complex $L$. We construct a discrete Morse function $\Delta(F)$ on the barycentric subdivision $\Delta(L)$. The constructed function $\Delta(F)$ "behaves the same way" as $F$, i. e. has the same number of critical simplexes and the same gradient path structure.

Motion planning of particle based microrobots for static obstacle avoidance

Magnetic microrobots have been shown to be effective at navigating microscale environments which has led to many investigations reguarding the motion control of microrobots. To increase the feasibility of using microrobots for microscale tasks and widen the range of potential applications, the use of autonomous navigation systems will be essential. In this work, the magnetic particle based achiral microrobots are controlled wirelessly using a combination of rotating and static magnetic fields generated from electromagnetic coils in an approximate Helmholtz configuration. In previous work, we developed both a kinematic model for particle based microrobots and a feedback controller; once implemented, the controller can guide the microrobots to any goal positions. In the present work, we demonstrate path planning motion control for magnetic particle based microrobots in microfluidic channels formed using patterned static SU-8 microstructures. The microrobots were able to avoid collision with the microstructures, which acted as static obstacles, by using a gradient path method. In experiments, microrobots were able to reach the final goal position by following waypoints of generated path from the gradient path method in a static obstacle laden environment.

Derivative-free restrictively preconditioned conjugate gradient path method without line search technique for solving linear equality constrained optimization

In this paper, we propose a derivative-free restrictively preconditioned conjugate gradient path method without line search technique for solving linear equality constrained optimization. This method originates from the classical conjugate gradient method and its restrictively preconditioned variant. The preconditioned conjugate gradient path is obtained by solving extended system of the preconditioned equation with restrictively preconditioned conjugate gradient method which is a more robust and effective technique to solve large sparse linear system. The global convergence and local superlinear convergence rate of the proposed method are established under some reasonable conditions. Finally, the numerical results are reported to show the effectiveness of the proposed method.

The Gauss-Newton Methods via Conjugate Gradient Path without Line Search Technique for Solving Nonlinear Systems

ABSTRACTIn this article, we propose the Gauss-Newton methods via conjugate gradient path for solving nonlinear systems. By constructing and solving a linearized model of the nonlinear systems, we obtain the iterative direction by employing the conjugate gradient path. In successive iterations, the approximate Jacobian of the nonlinear systems is updated by a Broyden formula to construct the conjugate path. The global convergence and local superlinear convergence rate of the proposed algorithms are established under some reasonable conditions. Finally, the numerical results are reported to show the effectiveness of the proposed algorithms.

How Rivers Get Across Mountains: Transverse Drainages

Although mountains represent a barrier to the flow of liquid water across our planet and an Earth of impenetrable mountains would have produced a very different geography, many rivers do cross mountain ranges. These transverse drainages cross mountains through one of four general mechanisms: antecedence—the river maintains its course during mountain building (orogeny); superimposition—a river erodes across buried bedrock atop erodible sediment or sedimentary rock, providing a route across what later becomes an exhumed mountain range; piracy or capture—where a steeper gradient path captures a lower gradient drainage across a low relief interfluve; and overflow—a basin fills with sediment and water, ultimately breaching the lowest sill to create a new river. This article reviews research that aids in identifying the mechanism responsible for a transverse drainage, notes a major misconception about the power of headward eroding streams that has dogged scholarship, and examines the transverse drainage at the Grand Canyon in Arizona.

Conjugate gradient path method without line search technique for derivative-free unconstrained optimization

In this paper, we propose conjugate gradient path method for solving derivative-free unconstrained optimization. The iterative direction is obtained by constructing and solving quadratic interpolation model of the objective function with conjugate gradient methods. The global convergence and local superlinear convergence rate of the proposed algorithm are established under some reasonable conditions. Finally, the numerical results are reported to show the effectiveness of the proposed algorithm.

Climatic and landscape controls on water transit times and silicate mineral weathering in the critical zone

AbstractThe critical zone (CZ) can be conceptualized as an open system reactor that is continually transforming energy and water fluxes into an internal structural organization and dissipative products. In this study, we test a controlling factor on water transit times (WTT) and mineral weathering called Effective Energy and Mass Transfer (EEMT). We hypothesize that EEMT, quantified based on local climatic variables, can effectively predict WTT within—and mineral weathering products from—the CZ. This study tests whether EEMT or static landscape characteristics are good predictors of WTT, aqueous phase solutes, and silicate weathering products. Our study site is located around Redondo Peak, a rhyolitic volcanic resurgent dome, in northern New Mexico. At Redondo Peak, springs drain slopes along an energy gradient created by differences in terrain aspect. This investigation uses major solute concentrations, the calculated mineral mass undergoing dissolution, and the age tracer tritium and relates them quantitatively to EEMT and landscape characteristics. We found significant correlations between EEMT, WTT, and mineral weathering products. Significant correlations were observed between dissolved weathering products (Na+ and DIC), 3H concentrations, and maximum EEMT. In contrast, landscape characteristics such as contributing area of spring, slope gradient, elevation, and flow path length were not as effective predictive variables of WTT, solute concentrations, and mineral weathering products. These results highlight the interrelationship between landscape, hydrological, and biogeochemical processes and suggest that basic climatic data embodied in EEMT can be used to scale hydrological and hydrochemical responses in other sites.

Responses of soil erosion processes to land cover changes in the Loess Plateau of China: A case study on the Beiluo River basin

Understanding the responses of soil erosion processes to land cover changes would benefit catchment ecological management. Landsat thematic mapper images in 1987, 1995, and 2007 were collected to obtain the historical normalized difference vegetation index and land cover data of the Beiluo River basin, one of the catchments in the Loess Plateau. The sediment load data of five subcatchments were collected in the corresponding periods. A set of location-weighted landscape contrast indices was used to analyze the effect of land cover changes on soil erosion processes, as specified by the following indices: slope gradient, flow path length, relative altitude, and relative distance. Results showed that vegetation cover (VC) notably increased from 41.12% to 63.43% in the basin from 1987 to 2007. The increased VC was mainly concentrated in the hilly-gully area from 18.40% in 1987 and 20.21% in 1995 to 41.65% in 2007. The mean annual sediment load modulus in the region over the same periods significantly decreased by 90%. All the indices for each subcatchment exhibited a decreasing trend. The change extent of the indices revealed a significantly positive correlation with that of sediment load modulus. Slope gradient and flow path length were the most important influential factors on soil erosion. Results implied that the improvement in land cover in the Beiluo River basin from 1987 to 2007 led to sediment entrapment in the sink area and changed the soil erosion processes, especially the slope gradient and flow length of the soil erosion source area. This study contributed to improving catchment ecological management and evaluating erosion control practices in the Loess Plateau.

Analysis of Micro/Mesoscale Sheet Forming Process by Strain Gradient Plasticity and Its Characterization of Tool Feature Size Effects

Conventional material models cannot describe material behaviors precisely in micro/mesoscale due to the size/scale effects. In micro/mesoscale forming process, the reaction force, localized stress concentration, and formability are not only dependent on the strain distribution and strain path but also on the strain gradient and strain gradient path caused by decreased scale. This study presented an analytical model based on the conventional mechanism of strain gradient (CMSG) plasticity. Finite element (FE) simulations were performed to study the effects of the width of microchannel features. Die sets were fabricated and micro/mesoscale sheet forming experiments were conducted. The results indicated that the CMSG plastic theory achieves better agreements compared to the conventional plastic theory. It was also found that the influence of strain gradient on the forming process increases with the decrease of the geometrical parameters of tools. Furthermore, the feature size effects in the forming process were evaluated and quantitated by the similarity difference and the similarity accuracy. Various tool geometrical parameters were designed based on the Taguchi method to explore the influence of the strain gradient caused by the decrease of tool dimension. According to the scale law, the difference and accuracy of similarity were calculated. Greater equivalent strain gradient was revealed with the decrease of tool dimension, which led to the greater maximum reaction force error due to the increasing size effects. The main effect plots for equivalent strain gradient and reaction force indicated that the influence of tools clearance is greater than those of punch radius, die radius, and die width.

Flow over submerged energy storage balloons in closely and widely spaced floral configurations

Water flow past the accumulator unit of an underwater compressed air energy storage plant was studied numerically. The accumulator unit consists of three underwater balloons arranged in a floral configuration. The numerical simulation was conducted at a Reynolds number of 2.3×105 using URANS k–ω and LES Dyna-SM turbulence models of the ANSYS-Fluent CFD software. The URANS mean values are compatible with those of LES; however, LES appeared to better predict the turbulent nature of the studied flow. The flow pattern was illustrated through iso-surfaces of the second invariant of the velocity gradient (Q criterion) and three-dimensional path lines. Several swirling tube flows were found to shed downstream of the balloons. The turbulence dynamic of the flow was illustrated through time-series snapshots of the vorticity contours on planes perpendicular to the flow direction; revealing the swinging movements of the observed swirling tube flows. The force coefficients of the hydrodynamic loading on these underwater structures were also investigated. The drag coefficient of the upstream balloon was found to be larger than the downstream one; the difference is more significant for the closely spaced configuration. It is noteworthy to mention that the total drag coefficient of the wide unit was larger than that of the closed one. A Fast Fourier transform of the time history of the force coefficients was used to find the Strouhal number. Strouhal numbers of approximately 0.52 and 0.18 were found for the widely spaced and closely spaced configurations respectively.

The spatial density gradient of galactic cosmic rays and its solar cycle variation observed with the Global Muon Detector Network

We derive the long-term variation of the three-dimensional (3D) anisotropy of approximately 60 GV galactic cosmic rays (GCRs) from the data observed with the Global Muon Detector Network (GMDN) on an hourly basis and compare it with the variation deduced from a conventional analysis of the data recorded by a single muon detector at Nagoya in Japan. The conventional analysis uses a north-south (NS) component responsive to slightly higher rigidity (approximately 80 GV) GCRs and an ecliptic component responsive to the same rigidity as the GMDN. In contrast, the GMDN provides all components at the same rigidity simultaneously. It is confirmed that the temporal variations of the 3D anisotropy vectors including the NS component derived from two analyses are fairly consistent with each other as far as the yearly mean value is concerned. We particularly compare the NS anisotropies deduced from two analyses statistically by analyzing the distributions of the NS anisotropy on hourly and daily bases. It is found that the hourly mean NS anisotropy observed by Nagoya shows a larger spread than the daily mean due to the local time-dependent contribution from the ecliptic anisotropy. The NS anisotropy derived from the GMDN, on the other hand, shows similar distribution on both the daily and hourly bases, indicating that the NS anisotropy is successfully observed by the GMDN, free from the contribution of the ecliptic anisotropy. By analyzing the NS anisotropy deduced from neutron monitor (NM) data responding to lower rigidity (approximately 17 GV) GCRs, we qualitatively confirm the rigidity dependence of the NS anisotropy in which the GMDN has an intermediate rigidity response between NMs and Nagoya. From the 3D anisotropy vector (corrected for the solar wind convection and the Compton-Getting effect arising from the Earth’s orbital motion around the Sun), we deduce the variation of each modulation parameter, i.e., the radial and latitudinal density gradients and the parallel mean free path for the pitch angle scattering of GCRs in the turbulent interplanetary magnetic field. We show the derived density gradient and mean free path varying with the solar activity and magnetic cycles.