Smoothing Scheme Research Articles

Syntomic cycle classes and prismatic Poincaré duality

We introduce $F$ -gauges over a prism, construct syntomic cycle classes, and prove the prismatic Poincaré duality for proper smooth schemes.

Mean-motion resonances with interfering density waves

ABSTRACT In this work, we study the dynamics of two less massive objects moving around a central massive object, which are all embedded within a thin accretion disc. In addition to the gravitational interaction between these objects, the disc–object interaction is also crucial for describing the long-term dynamics of the multibody system, especially in the regime of mean-motion resonances. We point out that near the resonance the density waves generated by the two moving objects generally coherently interfere with each other, giving rise to extra angular momentum fluxes. The resulting backreaction on the objects is derived within the thin-disc scenario, which explicitly depends on the resonant angle and sensitively depends on the smoothing scheme used in the two-dimensional theory. We have performed hydrodynamical simulations with planets embedded within a thin accretion disc and have found qualitatively agreement on the signatures of interfering density waves by measuring the torques on the embedded objects, for the cases of $2:1$ and $3:2$ resonance. By including in interference torque and the migration torques in the evolution of a pair of planets, we show that the chance of resonance trapping depends on the sign of the interference torque. For negative interference torques the pairs are more likely located at off-resonance regimes. The negative interference torques may also explain the $1~{{\ \rm per\ cent}}-2~{{\ \rm per\ cent}}$ offset (for the period ratios) from the exact resonance values as observed in Kepler multiplanet systems.

Smoothing and approximation of grassland fire loading data for engineering structures by Capped Extended Support Vector Regression

This research proposes a machine learning-aided data smoothing and approximation scheme to investigate grassland fire loading for engineering structures. The investigations on grassland fire loading have significant impacts on wildfire-resistant design, building codes, regulations, and the like in specific regions. Real-world data collection systems inevitably introduce imperfections, such as noise, outliers, and the like. Furthermore, the collected data are normally discretized on time and location, and thus the information between them is completely absent. Achieving a smooth fit to data and reducing these imperfections are desired to facilitate subsequent analyses. Accordingly, a supervised machine learning algorithm is developed to smooth and approximate grassland fire loading data. Within the proposed algorithm, a convex optimization programming is established, which provides theoretical support to the accuracy of the algorithm. Then, through the proposed scheme, the grassland fire loading data can be approximated into an explicit regression model, which continuously completes the missing information during the observations. Moreover, attributed to the sparsity feature of the developed algorithm, the model can be simplified in its expression to further improve its applicability in engineering. Finally, real-world experimental data and numerical simulation results are separately investigated to demonstrate the effectiveness of the proposed scheme.

A node-based consistent non-conforming gradient smoothing scheme for highly efficient Galerkin meshfree formulation

A node-based consistent non-conforming gradient smoothing scheme for highly efficient Galerkin meshfree formulation

Enhancing Morphological Measurements of the Cosmic Web with Delaunay Tessellation Field Estimation

The density fields constructed by traditional mass assignment methods are susceptible to irritating discreteness, which hinders morphological measurements of cosmic large-scale structure (LSS) through Minkowski functionals (MFs). To alleviate this issue, fixed-kernel smoothing methods are commonly used in the literature, at the expense of losing substantial structural information. In this work, we propose to measure MFs with the Delaunay tessellation field estimation (DTFE) technique, with the goal of maximizing the extraction of morphological information from sparse tracers. We perform our analyses starting from matter fields and progressively extending to halo fields. At the matter-field level, we elucidate how discreteness affects morphological measurements of LSS. Then, by comparing with the traditional Gaussian smoothing scheme, we preliminarily showcase the advantages of DTFE for enhancing measurements of MFs from sparse tracers. At the halo-field level, we first numerically investigate various systematic effects on MFs of DTFE fields, which are induced by finite voxel sizes, halo number densities, halo weightings, and redshift space distortions (RSDs), respectively. Then, we explore the statistical power of MFs measured with DTFE for extracting the cosmological information encoded in RSDs. We find that MFs measured with DTFE exhibit improvements by ∼2 orders of magnitude in discriminative power for RSD effects and by a factor of ∼3–5 in constraining power on the structure growth rate over the MFs measured with Gaussian smoothing. These findings demonstrate the remarkable enhancements in statistical power of MFs achieved by DTFE, showing enormous application potentials for our method in extracting various key cosmological information from galaxy surveys.

Mitigation of laser plasma filamentation by rotating beam smoothing scheme

The propagation of intense laser beams in plasma inevitably gives rise to laser plasma instabilities, which have a significant impact on the illumination uniformity of the focused spot on the target in inertial confinement fusion (ICF) facilities. Here we propose an ultrafast smoothing scheme using a rotating beam (RB) to mitigate the laser plasma filamentation. Using the propagation model of the rotating beam in plasma for the laser-plasma self-focusing (SF) and filamentation, the filamentation characteristics of laser spots were analyzed. The results indicate that the rotating beam smoothing scheme, operating at picosecond timescale, exhibits superior mitigation effect of laser plasma filamentation.

Zero-cycles in families of rationally connected varieties

We study zero-cycles in families of rationally connected varieties. We show that for a smooth projective scheme over a henselian discrete valuation ring the restriction of relative zero cycles to the special fiber induces an isomorphism on Chow groups if the special fiber is separably rationally connected. We further extend this result to certain higher Chow groups and develop conjectures in the non-smooth case. Our main results generalise a result of Kollár (Publ. Res. Inst. Math. Sci. 40(3):689–708, 2004).

METHOD OF THE SERVER HORIZONTAL LOAD BALANCING FOR REDUCING ENERGY CONSUMPTION

Background. Server horizontal load balancing is a crucial aspect of modern computing systems, particularly in cloud computing environments. The efficient management of incoming flows of applications is essential to ensure optimal resource utilization and minimize energy consumption. This study focuses on developing a method for managing the incoming flow of applications to reduce energy consumption in server horizontal load balancing. Objective. The primary objective is to develop a method for managing the incoming flow of applications to reduce energy consumption in server horizontal load balancing. This involves identifying the maximum permissible number of applications that can simultaneously enter the system for service, ensuring that the volume of resources used is close to the total maximum possible amount of resources. The method aims to minimize the variance of the elements of the sequence of maximum allowable numbers of applications and the dispersion of the elements of the sequences of volumes of resources used. Methods. The method involves several key steps: Input Load Smoothing Scheme: A static control method is proposed to smooth the incoming load. This involves developing a scheme for smoothing the incoming load, which is a set of values of the maximum allowable number of requests (sequence {ki}) arriving at the system input for a small time interval ∆ti. The sequence is selected to ensure that the volume of resources used is close to the total maximum possible amount of resources. Genetic Algorithm: The selection of the sequence {ki} is carried out using a genetic algorithm. The algorithm involves crossover, mutation, and selection operations to minimize the variance of the elements of the sequence and the dispersion of the elements of the sequences of volumes of resources used. Resource Allocation: The method involves allocating resources for the maintenance of a given type of service. The parameters of the server, which are characterized as the resources of the system serving the applications, are usually calculated for the average values of the parameters of the input stream. Delay Introduction: To manage the application processing process and prevent resource shortages, a delay is introduced for a part of the applications that coincide with a surge in load. The delay time is determined so that delayed applications do not enter the system until the previous burst of load is successfully serviced in the resource-consuming functional block. Results. The results of the study include the development of a method for managing the incoming flow of applications to reduce energy consumption in server horizontal load balancing. The method involves the use of a genetic algorithm to select the sequence {ki} that minimizes the variance of the elements of the sequence and the dispersion of the elements of the sequences of volumes of resources used. Conclusions. The study concludes that the proposed method for managing the incoming flow of applications can effectively reduce energy consumption in server horizontal load balancing. The method involves the use of a genetic algorithm to select the sequence {ki} that ensures efficient use of system resources and minimizes the variance of the elements of the sequence and the dispersion of the elements of the sequences of volumes of resources used. The method can be applied in various scenarios where efficient use of system resources is crucial, such as in cloud computing environments.

On the relative Gersten conjecture for Milnor K-theory in the smooth case

We show that the Gersten complex for the (improved) Milnor K-sheaf on a smooth scheme over an excellent discrete valuation ring is exact except at the first place and that exactness at the first place may be checked at the discrete valuation ring associated to the generic point of the special fibre. This complements results of Gillet-Levine for K-theory, Geisser for motivic cohomology and Schmidt-Strunk and the author for étale cohomology.

LSTM network optimization and task network construction based on heuristic algorithm

This work aims to advance the security management of complex networks to better align with evolving societal needs. The work employs the Ant Colony Optimization algorithm in conjunction with Long Short-Term Memory neural networks to reconstruct and optimize task networks derived from time series data. Additionally, a trend-based noise smoothing scheme is introduced to mitigate data noise effectively. The approach entails a thorough analysis of historical data, followed by applying trend-based noise smoothing, rendering the processed data more scientifically robust. Subsequently, the network reconstruction problem for time series data originating from one-dimensional dynamic equations is addressed using an algorithm based on the principles of Stochastic Gradient Descent (SGD). This algorithm decomposes time series data into smaller samples and yields optimal learning outcomes in conjunction with an adaptive learning rate SGD approach. Experimental results corroborate the remarkable fidelity of the weight matrix reconstructed by this algorithm to the true weight matrix. Moreover, the algorithm exhibits efficient convergence with increasing data volume, manifesting shorter time requirements per iteration while ensuring the attainment of optimal solutions. When the sample size remains constant, the algorithm’s execution time is directly proportional to the square of the number of nodes. Conversely, as the sample size scales, the SGD algorithm capitalizes on the availability of more information, resulting in improved learning outcomes. Notably, when the noise standard deviation is 0.01, models predicated on SGD and the Least-Squares Method (LSM) demonstrate reduced errors compared to instances with a noise standard deviation of 0.1, highlighting the sensitivity of LSM to noise. The proposed methodology offers valuable insights for advancing research in complex network studies.

Filtrations on the globalization of twisted D-modules over Dedekind schemes

In [11], we established the theory of twisted D-modules over general base schemes. In this short note, we construct a K-invariant positive exhaustive filtration on the globalization of the twisted D-module on a smooth quasi-compact K-scheme over a Dedekind scheme S obtained by the direct image of a K-equivariant twisted integrable connection along a K-equivariant closed immersion from a smooth proper K-scheme Y with K a smooth S-affine group scheme, whose pth associated graded OS-module is locally free of finite rank for every integer p. In particular, the k-module of its global sections is projective if S is affine with coordinate ring k.

A linear smoothed quadratic finite element for buckling analysis of laminated composite plates

In this paper, a linear smoothing scheme over eight-node Reissner-Mindlin plate element under the framework of the CS-FEM is employed to buckling analysis of laminated composite plates based on the first-order shear deformation theory. The modified stain matrix is computed by the divergence theorem between the nodal shape functions and their derivatives using Taylor's expansion. Isoparametric mapping and the computation of interior derivatives of shape function is not required in the proposed method, furthermore, all the computation are based on the global Cartesian coordinates. Some numerical examples are given at the end to demonstrate that the present method has good performance to alleviate the shear-locking phenomenon and improve the quality of the solutions with distorted meshes.

Ultrafast random polarization beam smoothing driven by counter-rotating wavefronts via the optical Kerr effect

We propose an ultrafast random polarization smoothing scheme to achieve ultrafast speckle movement and polarization randomization of the focal spot. In the scheme, each beamlet in a laser quad is driven by a rotating petal-like wavefront, giving rise to the ultrafast redistribution of the speckles within the focal spot. The rotating wavefront is induced by an optical Kerr medium pumped by a laser beam with rotating intensity distribution that is generated by the superposition of two Laguerre–Gaussian beams carrying conjugate vortex phase and frequency shift. In addition, by properly selecting the topological charges of the pump beams and polarization states of the beamlets, the beamlets in a quad can be divided into two sets with counter-rotating wavefronts and orthogonal polarizations, which further randomizes the polarization of the focal spot. Results indicate that the proposed scheme can reduce the contrast by more than 70% and the degree of polarization by more than 75% within several picoseconds, by utilizing the rotating phase pumped by two Laguerre-Gaussian beams with a peak intensity of 0.18GW/cm2 and a frequency shift of 1 THz. The ultrafast random polarization smoothing scheme is expected to suppress the growth of Laser Plasma Instabilities (LPIs) including the filamentation and backscatter in indirect-drive inertial confinement fusion (ICF) facilities.

Drinfeld’s Lemma for F-isocrystals, I

Abstract We prove that in either the convergent or overconvergent setting, an absolutely irreducible $F$-isocrystal on the absolute product of two or more smooth schemes over perfect fields of characteristic $p$, further equipped with actions of the partial Frobenius maps, is an external product of $F$-isocrystals over the multiplicands. The corresponding statement for lisse $\overline{{\mathbb{Q}}}_{\ell }$-sheaves, for $\ell \neq p$ a prime, is a consequence of Drinfeld’s lemma on the fundamental groups of absolute products of schemes in characteristic $p$. The latter plays a key role in V. Lafforgue’s approach to the Langlands correspondence for reductive groups with $\ell $-adic coefficients; the $p$-adic analogue will be considered in subsequent work with Daxin Xu.

Spectral equivalence of smooth group schemes over principal ideal local rings

Let G be a smooth linear group scheme of finite type. For any positive integer k and a finite field F, let Wk(F) be the ring of Witt vectors of length k over F. We show that the group algebras of G(F[t]/(tk)) and G(Wk(F)) are isomorphic (i.e. the multi-sets of the dimensions of the irreducible representations are equal) for any positive integer k and finite field F with large enough characteristic. We also prove that if charF is large enough, then the cardinality of the set {dim⁡ρ|ρ∈irr(G(F))} is bounded uniformly in F.

Formation and evolution of vortex breakdown consequent to post design flow increase in a Francis turbine

Draft tube flow instability encountered under off-design operating conditions in hydraulic turbines significantly limits their operational flexibility. The instability arises consequent to a higher than threshold swirl content in the runner outflow and leads to vortex breakdown phenomenon in the draft tube cone. At high load condition, the phenomenon presents as an enlarged vortex core counter-rotating with respect to the runner. The flow situation is known to compromise the turbine efficiency besides the generation of unwanted effects such as power swings and large-scale pressure fluctuations. The present paper is the first to encapsulate a thorough numerical investigation on the formation and evolution of the enlarged vortex core alongside the consequent effects. A transient operating sequence between best efficiency and high load operating points in a model Francis turbine is simulated. Turbulence closure has been attained using the shear stress transport-scale adaptive simulations turbulence model. Dynamic meshing based on a Laplacian smoothing scheme has been used to account for mesh deformation arising from guide vane motion during load change. The pressure and velocity fields have been determined and analyzed to elucidate the physics of vortex breakdown, the phenomenon underlying the formation of the enlarged vortex core. Furthermore, pressure fluctuations at salient points in the domain have been analyzed using Fourier and short-time Fourier transforms. Finally, the enlarged vortex core formed in the draft tube has been visualized through the λ2 criterion. The core takes the shape of a cork-screw like compactly wound spiral structure extending up to the draft tube elbow.

Iterative ensemble smoothing scheme for reservoir history matching with unknown observation error covariance

Ensemble-based smoothers are well-known data assimilation tools in reservoir applications, including history matching and geophysical inversion. They entail the knowledge of the covariance of observation errors, which, however, is often poorly known in real applications and commonly estimated subjectively on the basis of a diagonal structure. This neglects the correlations within the observation errors, which may deteriorate the quality of the model estimates. Herein, we relaxed the independent observational error assumption by considering a nondiagonal structure for the covariance. Given that all the elements in the covariance matrix could not be estimated given a limited amount of data, which is typically the case in practice, we reduced the number of degrees of freedom by parameterizing this covariance with two scalar parameters, one for error variance and the other for error correlation length–scale. We then estimated these parameters together with the model variables using a hybrid algorithm that combined a variational Bayesian approach with particle filters and an ensemble-based smoother. The proposed approach was validated with a linear Gaussian model and a nonlinear reservoir flow model. The results clearly demonstrate the potential of the proposed method in effectively addressing the uncertainty of observations in the history-matching process.

Cogroupoid structures on the circle and the Hodge degeneration

Abstract We exhibit the Hodge degeneration from nonabelian Hodge theory as a $2$ -fold delooping of the filtered loop space $E_2$ -groupoid in formal moduli problems. This is an iterated groupoid object which in degree $1$ recovers the filtered circle $S^1_{fil}$ of [MRT22]. This exploits a hitherto unstudied additional piece of structure on the topological circle, that of an $E_2$ -cogroupoid object in the $\infty $ -category of spaces. We relate this cogroupoid structure with the more commonly studied ‘pinch map’ on $S^1$ , as well as the Todd class of the Lie algebroid $\mathbb {T}_{X}$ ; this is an invariant of a smooth and proper scheme X that arises, for example, in the Grothendieck-Riemann-Roch theorem. In particular, we relate the existence of nontrivial Todd classes for schemes to the failure of the pinch map to be formal in the sense of rational homotopy theory. Finally, we record some consequences of this bit of structure at the level of Hochschild cohomology.

Near forward scattering light of planar film target driven by broadband laser

Laser plasma interaction (LPI) has always been an important research topic in the ignition phase of inertial confinement fusion (ICF). Over the years, researchers have attempted to use various laser beam smoothing schemes and optimized light source solutions to suppress the development of LPI. Among them, low-coherence laser drivers have attracted widespread attention in the fields of laser-plasma physics and laser technology in recent years. Recently, a broadband second harmonic laser facility named “Kunwu” has provided a reliable experimental research platform for the LPI process driven by broadband lasers. Aiming at the strong stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS) in the LPI process of large-scale low-density plasma, forward scattering experiment and near-forward scattering experiment on C<sub>8</sub>H<sub>8</sub> planar film targets driven by broadband laser and narrowband laser under the same conditions are carried out. Based on the “Kunwu” laser facility, two sets of measurement systems are designed, one is centered around fiber-heads and spectrometer, and the other around phototubes and oscilloscope. These systems enable multi-directional precise measurements of scattered lightand a comprehensive analysis of LPI. The main focus is on the comparison of the components and spectral information of the scattering beams between broadband laser and narrowband laser, and it is found that the LPI processes driven by broadband laser and narrowband laser are greatly different. Additionally, preliminary results indicate that broadband laser exhibits a stronger penetration capability than narrowband laser. The time to ablation the target and penetrate the plasma are both nearly 1 ns ahead, with the transmitted energy increased by nearly an order of magnitude. And after penetrating the plasma, there is a smaller spatial divergence angle. These results provide good reference value for better understanding the effect of broadband laser on LPI.

A comparison of three algorithms in the filtering of a Markov-modulated non-homogeneous Poisson process

ABSTRACT A Markov-modulated non-homogeneous Poisson process (MMNPP), whose intensity process is designed to capture both the cyclical and nonrecurring trends, is considered for modelling the total count of cyber incidents. Extending the Expectation-Maximisation (EM) algorithm for the current MMPP literature, we derive the filters and smoothers to support the MMNPP online parameter estimation. A scaling transformation is introduced to address the numerical issue for large data sizes whilst maintaining accuracy. The filter- and smoother-based EM algorithms are then benchmarked to the maximum likelihood-based EM algorithm at the theoretical level. The differences emerge in the E-step of the EM procedure. Both the filtering and smoothing schemes, in conjunction with the change-of-measure technique, avoid the computing complication caused by the hidden regimes. In contrast to the usual EM algorithm, the said two algorithms could be implemented given only the incident counts data without the specific times of jumps. Within the data compiled by the U.S. Department of Health and Human Services, the filter-based algorithm performs better than the algorithm involving smoothers. The benchmarked algorithm may do well in calibration under the presence of extreme incident counts with an extremely low frequency; however, overfitting may occur. For most practical applications involving 2 or 3 regimes, both algorithms are superior when it comes to efficiency, real-time update, and low computational cost. The benchmarked algorithm is better when there are more regimes under relatively closer intensities. Overall, the filter-based algorithm gives better estimation, especially if there is a low-frequency regime and the flexible binning of the data set is an important consideration.