Potential Kernel Research Articles

Two Mechanisms of Kernel Ignition in Shock Tubes

The structure of the flow and temperature field behind a reflected shock wave in a shock tube is studied by numerical modeling. Two possible scenarios of the formation of the regions of elevated temperature, which are the potential ignition kernels of the gaseous mixture under the study, are demonstrated. Both scenarios are assessed as equally probable; however, depending on the parameters of the flow and diameter of the tube, one of the scenarios may be implemented earlier than the other, which is demonstrated by the example of a hydrogen–air mixture. The scenario with the ignition on the axis is the most probable one for the case of high temperatures and narrow channels, while ignition in the region of the boundary layer is implemented with a higher probability at moderate temperatures in wide channels.

Variation in zinc concentration of sweetcorn kernels reflects source-sink dynamics influenced by kernel number.

Grain yield and mineral nutrient concentration in cereal crops are usually inversely correlated, undermining biofortification efforts. Here, sink size, expressed as kernel number per cob, was manipulated by controlling the time when the silks of sweetcorn (Zea mays) cv. Hybrix 5 and var. HiZeax 103146 were exposed to pollen. Twelve other varieties were manually pollinated to achieve the maximum potential kernel number per cob, and kernel Zn concentration was correlated with kernel number and kernel mass. As kernel number increased, kernel Zn concentration decreased, with the decrease occurring to similar extents in the embryo tissue and the rest of the kernel. However, total kernel Zn accumulated per cob increased with increasing kernel number, as the small decreases in individual kernel Zn concentration were more than offset by increases in kernel number. When both kernel number and mass were considered, 90% of the variation in kernel Zn concentration was accounted for. Differential distribution of assimilates and Zn to sweetcorn cobs led to significant decreases in kernel Zn concentration with increasing kernel number. This suggests there will be challenges to achieving high kernel Zn concentrations in modern high-yielding sweetcorn varieties unless genotypes with higher Zn translocation rates into kernels can be identified.

Differential Regulation of Kernel Set and Potential Kernel Weight by Nitrogen Supply and Carbohydrate Availability in Maize Genotypes Contrasting in Nitrogen Use Efficiency.

Sub-optimal nitrogen (N) conditions reduce maize yield due to a decrease in two sink components: kernel set and potential kernel weight. Both components are established during the lag phase, suggesting that they could compete for resources during this critical period. However, whether this competition occurs or whether different genotypic strategies exist to optimize photoassimilate use during the lag phase is not clear and requires further investigation. We have addressed this knowledge gap by conducting a nutrient solution culture experiment that allows abrupt changes in N level and light intensity during the lag phase. We investigated plant growth, dry matter partitioning, non-structural carbohydrate concentration, N concentration, and 15N distribution (applied 4 days before silking) in plant organs at the beginning and the end of the lag phase in two maize hybrids that differ in grain yield under N-limited conditions: one is a nitrogen-use-efficient (EFFI) genotype and the other is a control (GREEN) genotype that does not display high N use efficiency. We found that the two genotypes used different mechanisms to regulate kernel set. The GREEN genotype showed a reduction in kernel set associated with reduced dry matter allocation to the ear during the lag phase, indicating that the reduced kernel set under N-limited conditions was related to sink restrictions. This idea was supported by a negative correlation between kernel set and sucrose/total sugar ratios in the kernels, indicating that the capacity for sucrose cleavage might be a key factor defining kernel set in the GREEN genotype. By contrast, the kernel set of the EFFI genotype was not correlated with dry matter allocation to the ear or to a higher capacity for sucrose cleavage; rather, it showed a relationship with the different EFFI ear morphology with bigger kernels at the apex of the ear than in the GREEN genotype. The potential kernel weight was independent of carbohydrate availability but was related to the N flux per kernel in both genotypes. In conclusion, kernel set and potential kernel weight are regulated independently, suggesting the possibility of simultaneously increasing both sink components in maize.

Large deviation for additive functionals of symmetric Markov processes

In this paper, we establish a large deviation principle for pairs of continuous and purely discontinuous additive functionals of symmetric Borel right processes on Lusin spaces. We also establish compact embedding results for the extended Dirichlet spaces of symmetric Markov processes that possess Green potential kernels.

Green kernel asymptotics for two-dimensional random walks under random conductances

We consider random walks among random conductances on $\mathbb{Z}^2$ and establish precise asymptotics for the associated potential kernel and the Green's function of the walk killed upon exiting balls. The result is proven for random walks on i.i.d. supercritical percolation clusters among ergodic degenerate conductances satisfying a moment condition. We also provide a similar result for the time-dynamic random conductance model. As an application we present a scaling limit for the variances in the Ginzburg-Landau $\nabla \phi$-interface model.

Transience of conditioned walks on the plane: encounters and speed of escape

We consider the two-dimensional simple random walk conditioned on never hitting the origin, which is,formally speaking, the Doob's $h$-transform of the simple random walk with respect to the potential kernel. We then study the behavior of the future minimum distance of the walk to the origin, and also prove that two independent copies of the conditioned walk, although both transient, will nevertheless meet infinitely many times a.s.

An optimizing symbolic algebra approach for generating fast multipole method operators

We have developed a symbolic algebra approach to automatically produce, verify, and optimize computer code for the Fast Multipole Method (FMM) operators. This approach allows for flexibility in choosing a basis set and kernel, and can generate computer code for any expansion order in multiple languages. The procedure is implemented in the publicly available Python program Mosaic. Optimizations performed at the symbolic level through algebraic manipulations significantly reduce the number of mathematical operations compared with a straightforward implementation of the equations. We find that the optimizer is able to eliminate 20%–80% of the floating-point operations and for the expansion orders p≤10 it changes the observed scaling properties. We present our approach using three variants of the operators with the Cartesian basis set for the harmonic potential kernel 1∕r, including the use of totally symmetric and traceless multipole tensors.

Conditioned Two-Dimensional Simple Random Walk: Green’s Function and Harmonic Measure

We study the Doob's $h$-transform of the two-dimensional simple random walk with respect to its potential kernel, which can be thought of as the two-dimensional simple random walk conditioned on never hitting the origin. We derive an explicit formula for the Green's function of this random walk, and also prove a quantitative result on the speed of convergence of the (conditional) entrance measure to the harmonic measure (for the conditioned walk) on a finite set.

On intermediate level sets of two-dimensional discrete Gaussian free field

We consider the discrete Gaussian Free Field (DGFF) in scaled-up (square-lattice) versions of suitably regular continuum domains $D\subset\mathbb C$ and describe the scaling limit, including local structure, of the level sets at heights growing as a $\lambda$-multiple of the height of the absolute maximum, for any $\lambda\in(0,1)$. We prove that, in the scaling limit, the scaled spatial position of a typical point $x$ sampled from this level set is distributed according to a Liouville Quantum Gravity (LQG) measure in $D$ at parameter equal $\lambda$-times its critical value, the field value at $x$ has an exponential intensity measure and the configuration near $x$ reduced by the value at $x$ has the law of a pinned DGFF reduced by a suitable multiple of the potential kernel. In particular, the law of the total size of the level set, properly-normalized, converges that that of the total mass of the LQG measure. This sharpens considerably an earlier conclusion by Daviaud.

Nitrogen applications made close to silking: Implications for yield formation in maize

Given the growing interest in late N applications made at vegetative stages just prior to silking (R1), there is a need to characterize how yield formation in maize responds when a small amount of N is applied early in the season, and the bulk of N fertilizer is delayed to vegetative stages close to R1. To understand how the development of kernel number (KN) and weight (KW) are affected by this shift in fertilizer N availability, a two-year split-plot experiment was conducted. The main plot factor consisted of five pre-plant N rates (in kg N ha−1: 0, 80, 140, 200, 260) and a split-plot factor consisted of an N application at V13, 9 or 11 days before R1. Split-plots either received no in-season N or a non-limiting N rate such that the total N applied equaled 260 kg N ha−1. At 0 kg N ha−1 pre-plant, N stress significantly reduced radiation use efficiency and crop growth rate during the critical period around R1, which in turn reduced potential kernel number (pKN) and potential kernel sink capacity (pKW) by the start of the linear phase of grain-fill. When 80 or 140 kg N ha-1 was applied pre-plant, N stress was not detected at or prior to the start of the linear phase of grain-fill, but reductions in KN and/or KW occurred later, within 30–40 days of R1. The V13 N application increased grain yield at the lower pre-plant N rates by either: i) preventing reductions in pKN and pKW at the start of the linear grain-fill period or by ii) better maintaining KN and KW during the linear phase of grain-fill. At maturity grain yield in the split-N treatments receiving 260 kg N ha−1 at V13 was statistically similar to 260 kg N ha−1 applied pre-plant, but maize N uptake increased in response to the V13 N application only once the crop became N deficient. Overall, these results provide a physiological understanding of the impact of late N applications on yield formation in maize and can assist in the further development of N management strategies that better synchronize fertilizer N supply with crop N demand.

The role of the exponential and linear phases of maize (Zea mays L.) ear growth for determination of kernel number and kernel weight

Abstract Although the importance of the critical period for establishing the maize (Zea mays L.) yield components of kernel number (KN) and kernel weight (KW) is well known, there is little detailed information on how early ear development during the critical period and lag phase are influenced by hybrid improvement or N stress. Seven hybrids commercialized between 1946 and 2015 were compared under a range of N stress created by five N fertilizer treatments: no N applied or a total of 220 kg N ha−1 where N was applied either at the four-leaf stage (V4), at flowering, or a combination of these two times. Ears (cobs plus kernels) were sampled five times at weekly intervals, from approximately 14 days before until 14 days after flowering, to determine dry weight, N concentration, and N content. The dynamics of these traits were modeled using an expolinear function and parameters estimated using a non-linear mixed model. Hybrid and N treatment influences on the exponential and linear phases of ear growth were determined by comparing parameters. The greatest impact of genotype or plant N status was realized in the linear phase when modern hybrids exhibited higher linear growth rates and ears accumulated progressively more N with increasing V4 stage N rate. Neither genotype nor N stress resulted in different ear growth or N accumulation rates during the exponential phase; however, modern hybrids exhibited a longer exponential phase duration. Use of expolinear function with parameters estimated within the non-linear mixed models enabled us to gain insight on development phases modified as the result of genetic improvement or affected by N stress. During the exponential phase, which overlaps with the lag phase when cell division is a key determinant of potential kernel weight and sink strength, neither hybrid era nor N treatments substantially impacted ear growth. Instead, the most important early ear growth characteristics to differentially impact final KN and KW at maturity were the duration of the lag phase and ear growth rates during the linear phase. Future research is suggested to unravel how the duration of the exponential phase is related to cell number and kernel size determination, and how these in turn affect kernel growth rate during the linear phase.

Medical Image Segmentation with Adjustable Computational Complexity Using Data Density Functionals

Techniques of automatic medical image segmentation are the most important methods for clinical investigation, anatomic research, and modern medicine. Various image structures constructed from imaging apparatus achieve a diversity of medical applications. However, the diversified structures are also a burden of contemporary techniques. Performing an image segmentation with a tremendously small size (<25 pixels by 25 pixels) or tremendously large size (>1024 pixels by 1024 pixels) becomes a challenge in perspectives of both technical feasibility and theoretical development. Noise and pixel pollution caused by the imaging apparatus even aggravate the difficulty of image segmentation. To simultaneously overcome the mentioned predicaments, we propose a new method of medical image segmentation with adjustable computational complexity by introducing data density functionals. Under this theoretical framework, several kernels can be assigned to conquer specific predicaments. A square-root potential kernel is used to smoothen the featured components of employed images, while a Yukawa potential kernel is applied to enhance local featured properties. Besides, the characteristic of global density functional estimation also allows image compression without losing the main image feature structures. Experiments on image segmentation showed successful results with various compression ratios. The computational complexity was significantly improved, and the score of accuracy estimated by the Jaccard index had a great outcome. Moreover, noise and regions of light pollution were mostly filtered out in the procedure of image compression.

Endoscopy image restoration: A study of the kernel estimation from specular highlights

Endoscopy images show part of the gastrointestinal tract or other parts of the human body. Due to the complex environment in which this tract is located in the human body and the limitations of the image acquisition equipment, endoscopy images may present blur and specular highlights that are common types of degradation. In this paper, we present a blind deblurring approach for endoscopy images that estimate the blur kernel from the fusion of the specular highlights. The proposed method can be divided into two phases. First, the specular highlights are precisely extracted from the original image using a sparse and low-rank image decomposition approach. Then, these highlights are automatically clustered and fused according to the spatial and intensity features. In this way, potential kernels are generated and used for the deblurring process. The experimental results show that the proposed method presents an improved and comparable performance when considered other state-of-the-art methods that use highlights segmentation and image deblurring.

Potential kernel, hitting probabilities and distributional asymptotics

$\mathbb{Z}^{d}$-extensions of probability-preserving dynamical systems are themselves dynamical systems preserving an infinite measure, and generalize random walks. Using the method of moments, we prove a generalized central limit theorem for additive functionals of the extension of integral zero, under spectral assumptions. As a corollary, we get the fact that Green–Kubo’s formula is invariant under induction. This allows us to relate the hitting probability of sites with the symmetrized potential kernel, giving an alternative proof and generalizing a theorem of Spitzer. Finally, this relation is used to improve, in turn, the assumptions of the generalized central limit theorem. Applications to Lorentz gases in finite horizon and to the geodesic flow on Abelian covers of compact manifolds of negative curvature are discussed.

Skip-free Markov chains

The aim of this paper is to develop a general theory for the class of skip-free Markov chains on denumerable state space. This encompasses their potential theory via an explicit characterization of their potential kernel expressed in terms of family of fundamental excessive functions, which are defined by means of the theory of Martin boundary. We also describe their fluctuation theory generalizing the celebrated fluctuations identities that were obtained by using the Wiener-Hopf factorization for the specific skip-free random walks. We proceed by resorting to the concept of similarity to identify the class of skip-free Markov chains whose transition operator has only real and simple eigenvalues. We manage to find a set of sufficient and easy-to-check conditions on the one-step transition probability for a Markov chain to belong to this class. We also study several properties of this class including their spectral expansions given in terms of Riesz basis, derive a necessary and sufficient condition for this class to exhibit a separation cutoff, and give a tighter bound on its convergence rate to stationarity than existing results.

A revisited proof of the Seneta-Heyde norming for branching random walks under optimal assumptions

We introduce a set of tools which simplify and streamline the proofs of limit theorems concerning near-critical particles in branching random walks under optimal assumptions. We exemplify our method by giving another proof of the Seneta-Heyde norming for the critical additive martingale, initially due to A\"id\'ekon and Shi. The method involves in particular the replacement of certain second moment estimates by truncated first moment bounds, and the replacement of ballot-type theorems for random walks by estimates coming from an explicit expression for the potential kernel of random walks killed below the origin. Of independent interest might be a short, self-contained proof of this expression, as well as a criterion for convergence in probability of non-negative random variables in terms of conditional Laplace transforms.

On the range of a two-dimensional conditioned simple random walk

We consider the two-dimensional simple random walk conditioned on never hitting the origin. This process is a Markov chain, namely it is the Doob $h$-transform of the simple random walk with respect to the potential kernel. It is known to be transient and we show that it is recurrent in the sense that each infinite set is visited infinitely often, almost surely. We prove that, for a large set, the proportion of its sites visited by the conditioned walk is approximately a Uniform$[0,1]$ random variable. Also, given a set $G\subset\mathbb{R}^2$ that does not surround the origin, we prove that a.s. there is an infinite number of $k$'s such that $kG\cap \mathbb{Z}^2$ is unvisited. These results suggest that the range of the conditioned walk has fractal behavior.

Source-sink relations and kernel weight in maize inbred lines and hybrids: Responses to contrasting nitrogen supply levels

Maize (Zea mays, L.) kernel weight (KW) is regulated by the source-sink relationship at the early grain-filling period, when potential kernel size is defined, and at the effective grain-filling period, when final KW is established. The relative importance of each period is expected to depend upon the occurrence or not of environmental restrictions to plant growth. The objective of this study was to analyze the effect of nitrogen (N) availability on KW determination in two different groups of genotypes (inbreds and hybrids) when it is caused by changes in the source-sink relationship at mentioned periods. Six inbred lines of different genetic background and their F1 derived hybrids were tested in the field under two contrasting soil N levels (N0: low; N1: high). Almost all evaluated traits had greater mean values (P < 0.001) at N1 than at N0 level, except the plant growth rate per kernel during the critical period for kernel set (PGRCP kernel−1). However, the magnitude of the response to increased N was considerably higher for hybrids than for inbreds. Under contrasting N availability, plant growth during grain filling (PGGF) was the main determinant of increments registered in the source-sink ratio during this stage (i.e. PGGF kernel−1), and KW was chiefly associated with this ratio (r2 ≥ 0.50, P < 0.001). By contrast, the association between KW and PGRCP kernel-1 was important only at N1, and more robust for hybrids (r2 = 0.61, P < 0.001) than for inbreds (r2 = 0.34, P < 0.001). The uncoupling between both source-sink ratios observed at N0, as a result of a decreased post-flowering growth in this treatment, was responsible for differences in KW response to the PGRCP kernel−1 detected between N levels. The KW of inbreds was almost unaffected by mentioned N effects on the analyzed source-sink ratios, a trend attributed to negative inbreeding depression effects on traits controlling seed expansion. These differential responses between genotypic groups should be considered in breeding programs targeting KW increase.

On Compactness of Regular Integral Operators in the Space L1

In this paper we obtain a sufficient condition for quite continuity of Fredholm type integral operators in the space L1(a, b). Uniform approximations by operators with degenerate kernels of horizontally striped structures are constructed. A quantitative error estimate is obtained. We point out the possibility of application of the obtained results to second kind integral equations, including convolution equations on a finite interval, equations with polar kernels, one-dimensional equations with potential type kernels, and some transport equations in non-homogeneous layers.

Student cluster competition 2017, Team University of Texas at Austin/Texas State University: Reproducing vectorization of the Tersoff multi-body potential on the Intel Skylake and NVIDIA V100 architectures

This paper satisfies the reproducibility challenge of the Student Cluster Competition at Supercomputing 2017. We attempted to reproduce the results of H\"{o}hnerbach et al. (2016) for an implementation of a vectorized code for the Tersoff multi-body potential kernel of the molecular dynamics code Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). We investigated accuracy, optimization performance, and scaling with our Intel CPU and NVIDIA GPU based cluster.