Smoothing Scheme Research Articles

Prototype system for real-time IM/DD MDM transmission based on multiple-ring-core FMF and degenerate-mode-selective reception.

Multiple-input-multiple-output digital signal processing (DSP) has become a severe bottleneck for mode division multiplexing (MDM) because of its huge computational complexity. In this paper, we propose a novel scheme for real-time DSP-free intensity-modulation/direct-detection (IM/DD) MDM transmission, in which the transmission few-mode fiber (FMF) is characterized by multiple-ring-core structure to suppress modal crosstalk among each LP mode, while each pair of non-circularly-symmetric degenerate modes is simultaneously demultiplexed by a degenerate-mode-selective fiber coupler for DSP-free reception. Based on a 10 km ultralow-modal-crosstalk double-ring-core FMF and a pair of all-fiber 4-LP-mode MUX/DEMUX, we demonstrate the first IM/DD MDM prototype system using commercial single-mode (SM) 10 Gbps SFP + modules and 4K video transceivers without any hardware modifications. The temperature and wavelength dependence are evaluated. The stable Q2-factor performance proves that it can be a smooth evolution scheme from conventional SM IM/DD systems. Moreover, the scheme can be further extended to support more modes with improved FMF design adopting more ring areas.

Deep Feature Fusion via Two-Stream Convolutional Neural Network for Hyperspectral Image Classification

The representation power of convolutional neural network (CNN) models for hyperspectral image (HSI) analysis is in practice limited by the available amount of the labeled samples, which is often insufficient to sustain deep networks with many parameters. We propose a novel approach to boost the network representation power with a two-stream 2-D CNN architecture. The proposed method extracts simultaneously, the spectral features and local spatial and global spatial features, with two 2-D CNN networks and makes use of channel correlations to identify the most informative features. Moreover, we propose a layer-specific regularization and a smooth normalization fusion scheme to adaptively learn the fusion weights for the spectral-spatial features from the two parallel streams. An important asset of our model is the simultaneous training of the feature extraction, fusion, and classification processes with the same cost function. Experimental results on several hyperspectral data sets demonstrate the efficacy of the proposed method compared with the state-of-the-art methods in the field.

Derived geometry of the first formal neighbourhood of a smooth analytic cycle

If X is a smooth scheme of characteristic zero or a complex analytic manifold, and S is a locally split infinitesimal thickening of X, we compute explicitly the derived self-intersection of X in S.

Large eddy simulation of turbomachinery flows using a high-order implicit residual smoothing scheme

A recently developed fourth-order accurate implicit residual smoothing scheme (IRS4) is investigated for the large eddy simulation of turbomachinery flows, characterized by moderate to high Reynolds numbers and subject to severe constraints on the maximum allowable time step if an explicit scheme is used. For structured multi-block meshes, the proposed approach leads to the inversion of a scalar pentadiagonal system by mesh direction, which can be done very efficiently. On the other hand, applying IRS4 at each stage of an explicit Runge–Kutta time scheme allows to increase the time step by a factor 5 to 10, leading to substantial savings in terms of overall computational time. With respect to standard second-order fully implicit approaches, the IRS4 does not require approximate linearization and factorization procedures nor inner Newton-Raphson subiterations. As a consequence, it represents a better cost-accuracy compromise for the numerical simulations of turbulent flows where the maximum time step is controlled by the lifetime of the smallest resolved turbulent structures. Numerical results for the well-documented high-pressure VKI LS-89 planar turbine cascade illustrate the potential of IRS4 for significantly reducing the overall cost of turbomachinery large eddy simulations, while preserving an accuracy similar to the explicit solver even for sensitive quantities like the heat transfer coefficient and the turbulent kinetic energy field.

Combined implementation of smoothing technologies for improving illumination uniformity of laser quad in multi-directions

ABSTRACTAzimuthal smoothing (AS) that enables the focal spot of a laser quad to rotate in a period of a few picoseconds can improve the illumination uniformity. However, the smoothing performance of azimuthal smoothing is worse than that of smoothing by spectral dispersion (SSD) due to the low rotation speed in the center area of the focal spot. A combined implementation of the schemes including smoothing by spectral dispersion, radial smoothing (RS) and azimuthal smoothing is discussed to achieve better and faster illumination uniformity. The theoretical models of the combined smoothing scheme have been built up to analyse the smoothing performance. The key parameters affecting the smoothing performance of the combined smoothing scheme are analysed and optimized, including the topological charge and the wavelength difference. The simulation results show that the illumination uniformity of the laser quad can be significantly improved in multi-directions by the combined smoothing scheme.

A New TVD Scheme for Gradient Smoothing Method Using Unstructured Grids

An improved [Formula: see text]-factor algorithm for implementing total variation diminishing (TVD) scheme has been proposed for the gradient smoothing method (GSM) using unstructured meshes. Different from the methods using structured meshes, for the methods using unstructured meshes, generally the upwind point cannot be clearly defined. In the present algorithm, the value of upwind point has been successfully approximated for unstructured meshes by using the GSM with different gradient smoothing schemes, including node GSM (nGSM) midpoint GSM (mGSM) and centroid GSM (cGSM). The present method has been used to solve hyperbolic partial differential equation discontinuous problems, where three classical flux limiters (Superbee, Van leer and Minmod) were used. Numerical results indicate that the proposed algorithm based on mGSM and cGSM schemes can avoid the numerical oscillation and reduce the numerical diffusion effectively. Generally the scheme based on cGSM leads to the best performance among the three proposed schemes in terms of accuracy and monotonicity.

ON PROFINITE SUBGROUPS OF AN ALGEBRAIC GROUP OVER A LOCAL FIELD

The purpose of this paper is to link anisotropy properties of an algebraic group together with compactness issues in the topological group of its rational points. We nd equivalent conditions on a smooth ane algebraic group scheme over a non-Archimedean local eld for the associated rational points to admit maximal compact subgroups. We use the structure theory of pseudo-reductive groups provided, whatever the characteristic, by Conrad, Gabber and Prasad. We also investigate thoroughly maximal prop subgroups in the semisimple case, using Bruhat-Tits theory.

Motivic periods and Grothendieck arithmetic invariants

We construct a period regulator for motivic cohomology of an algebraic scheme over a subfield of the complex numbers. For the field of algebraic numbers we formulate a period conjecture for motivic cohomology by saying that this period regulator is surjective. Showing that a suitable Betti–de Rham realization of 1-motives is fully faithful we can verify this period conjecture in several cases. The divisibility properties of motivic cohomology imply that our conjecture is a neat generalization of the classical Grothendieck period conjecture for algebraic cycles on smooth and proper schemes. These divisibility properties are treated in an appendix by B. Kahn (extending previous work of Bloch and Colliot-Thélène–Raskind).

Trajectory Tracking of Flexible-Joint Robots Actuated by PMSM via a Novel Smooth Switching Control Strategy

This paper presents the trajectory tracking control of a flexible-joint manipulator driven by permanent magnet synchronous motor (PMSM). Combining the PMSM electrical equation and mechanical equation of robotic manipulators, a novel smooth switching control scheme is proposed. Firstly, the position loop controller of the system is designed, with an improved hierarchical sliding mode control (IHSMC) algorithm proposed to further the response speed of the system, additionally, a robust interconnection and damping assignment passivity-based controller (IDA-PBC) is designed to improve the steady state performance of the system. Then, the IDA-PBC control strategy is leveraged to design the current loop controller of the system, on which basis a hybrid controller with smooth switching is designed. Furthermore, Gaussian function is applied as the smooth switching function of the hybrid controller to promote the switching performance. As a result, the hybrid controller has both good dynamic and steady performance. The simulation results verify the effectiveness of the algorithms.

Towards Robust Direction Invariance in Character Animation

AbstractIn character animation, direction invariance is a desirable property. That is, a pose facing north and the same pose facing south are considered the same; a character that can walk to the north is expected to be able to walk to the south in a similar style. To achieve such direction invariance, the current practice is to remove the facing direction's rotation around the vertical axis before further processing. Such a scheme, however, is not robust for rotational behaviors in the sagittal plane. In search of a smooth scheme to achieve direction invariance, we prove that in general a singularity free scheme does not exist. We further connect the problem with the hairy ball theorem, which is better‐known to the graphics community. Due to the nonexistence of a singularity free scheme, a general solution does not exist and we propose a remedy by using a properly‐chosen motion direction that can avoid singularities for specific motions at hand. We perform comparative studies using two deep‐learning based methods, one builds kinematic motion representations and the other learns physics‐based controls. The results show that with our robust direction invariant features, both methods can achieve better results in terms of learning speed and/or final quality. We hope this paper can not only boost performance for character animation methods, but also help related communities currently not fully aware of the direction invariance problem to achieve more robust results.

Crystalline comparison isomorphisms in p-adic Hodge theory :the absolutely unramified case

We construct the crystalline comparison isomorphisms for proper smooth formal schemes over an absolutely unramified base. Such isomorphisms hold for \'etale cohomology with nontrivial coefficients, as well as in the relative setting, i.e. for proper smooth morphisms of smooth formal schemes. The proof is formulated in terms of the pro-\'etale topos introduced by Scholze, and uses his primitive comparison theorem for the structure sheaf on the pro-\'etale site. Moreover, we need to prove the Poincar\'e lemma for crystalline period sheaves, for which we adapt the idea of Andreatta and Iovita. Another ingredient for the proof is the geometric acyclicity of crystalline period sheaves, whose computation is due to Andreatta and Brinon.

A note on Grothendieck’s standard conjectures of type 𝐶⁺ and 𝐷 in positive characteristic

Making use of topological periodic cyclic homology, we extend Grothendieck’s standard conjectures of type C + \mathrm {C}^+ and D \mathrm {D} (with respect to crystalline cohomology theory) from smooth projective schemes to smooth proper dg categories in the sense of Kontsevich. As a first application, we prove Grothendieck’s original conjectures in the new cases of linear sections of determinantal varieties. As a second application, we prove Grothendieck’s (generalized) conjectures in the new cases of “low-dimensional” orbifolds. Finally, as a third application, we establish a far-reaching noncommutative generalization of Berthelot’s cohomological interpretation of the classical zeta function and of Grothendieck’s conditional approach to “half” of the Riemann hypothesis. Along the way, following Scholze, we prove that the topological periodic cyclic homology of a smooth proper scheme X X agrees with the crystalline cohomology theory of X X (after inverting the characteristic of the base field).

The -cohomology in the semistable case

For a proper, smooth scheme $X$ over a $p$-adic field $K$, we show that any proper, flat, semistable ${\mathcal{O}}_{K}$-model ${\mathcal{X}}$ of $X$ whose logarithmic de Rham cohomology is torsion free determines the same ${\mathcal{O}}_{K}$-lattice inside $H_{\text{dR}}^{i}(X/K)$ and, moreover, that this lattice is functorial in $X$. For this, we extend the results of Bhatt–Morrow–Scholze on the construction and the analysis of an $A_{\text{inf}}$-valued cohomology theory of $p$-adic formal, proper, smooth ${\mathcal{O}}_{\overline{K}}$-schemes $\mathfrak{X}$ to the semistable case. The relation of the $A_{\text{inf}}$-cohomology to the $p$-adic étale and the logarithmic crystalline cohomologies allows us to reprove the semistable conjecture of Fontaine–Jannsen.

A motivic homotopy theory without $$\mathbb {A}^{1}$$-invariance

In this paper, we continue the program initiated by Kahn-Saito-Yamazaki by constructing and studying an unstable motivic homotopy category with modulus, extending the Morel-Voevodsky construction from smooth schemes over a field $k$ to certain diagrams of schemes. We present this category as a candidate environment for studying representability problems for non $\mathbb{A}^1$-invariant generalized cohomology theories.

Nice triples and moving lemmas for motivic spaces

This paper contains geometric tools developed to solve the finite-field case of the Grothendieck–Serre conjecture in [1]. It turns out that the same machinery can be applied to solve some cohomological questions. In particular, for any presheaf of -spectra on the category of -smooth schemes, all its Nisnevich sheaves of -stable homotopy groups are strictly homotopy invariant. This shows that is -local if and only if all its Nisnevich sheaves of ordinary stable homotopy groups are strictly homotopy invariant. The latter result was obtained by Morel [2] in the case when the field is infinite. However, when is finite, Morel’s proof does not work since it uses Gabber’s presentation lemma and there is no published proof of that lemma. We do not use Gabber’s presentation lemma. Instead, we develop the machinery of nice triples invented in [3]. This machinery is inspired by Voevodsky’s technique of standard triples [4].

Numerical simulation of surface diffusion motion and its application in MEMS fabrication

Surface diffusion motion has been proposed as a new technique, called Silicon Migration Technology (SiMiT) for the fabrication of Micro-Electro-Mechanical System (MEMS) devices. Using this new technology, the integration of MEMS-CMOS can be achieved without the “sacrificial-structural” layers and “release-etch” procedure, which are necessary in traditional approaches. However, numerical simulation of surface diffusion process is still a challenging task due to the stiffness nature and the topological changes during the process. In this paper, we adopted a high-order explicit level-set method based on the total variation diminishing Runge-Kutta (TVD-RK) method, a high-order scheme for distance computation. An efficient smoothing scheme is proposed to increase the numerical stability and an adaptive time marching scheme is developed to accelerate the simulation. Experimental investigation of shape transformation of silicon trenches is carried out to verify the accuracy of the numerical scheme. Results show that numerical simulation results match quite well with experimental ones, which suggests the accuracy and reliability of the numerical simulation in the application of MEMS design.

A remark on the Hochschild-Kostant-Rosenberg theorem in characteristic p

We prove a Hochschild-Kostant-Rosenberg decomposition theorem for smooth proper schemes $X$ in characteristic $p$ when $\dim X\leq p$. The best known previous result of this kind, due to Yekutieli, required $\dim X<p$. Yekutieli's result follows from the observation that the denominators appearing in the classical proof of HKR do not divide $p$ when $\dim X<p$. Our extension to $\dim X=p$ requires a homological fact: the Hochschild homology of a smooth proper scheme is self-dual.

Motivic spectral sequence for relative homotopy K-theory

We construct a motivic spectral sequence for the relative homotopy invariant K-theory of a closed immersion of schemes $D \subset X$. The $E_2$-terms of this spectral sequence are the cdh-hypercohomology of a complex of equi-dimensional cycles. Using this spectral sequence, we obtain a cycle class map from the relative motivic cohomology group of 0-cycles to the relative homotopy invariant K-theory. For a smooth scheme $X$ and a divisor $D \subset X$, we construct a canonical homomorphism from the Chow groups with modulus $\CH^i(X|D)$ to the relative motivic cohomology groups $H^{2i}(X|D, \Z(i))$ appearing in the above spectral sequence. This map is shown to be an isomorphism when $X$ is affine and $i = \dim(X)$.

A Robust Statistical Approach to Distributed Power System State Estimation With Bad Data

This paper presents a robust statistical approach to distributed power system state estimation (DPSSE) under bad data based on iterative reweight least squares (IRWLS) method and an improved alternating direction method of multipliers (ADMM) framework. In particular, the Hampel’s redescending and the Schweppe–Huber generalized M-estimators (SHGM) are studied for mitigating the adverse effect of outliers with large magnitude. Moreover, a new robust weight smoothing scheme is proposed for improving the numerical stability and convergence speed of the algorithm. The proposed approach is further extended to recursive monitoring of measurement devices and inpainting of missing data by utilizing prior information provided in previous state estimation. The resultant algorithm is solved using the Levenberg–Marquardt (LM) solver, which helps to maintain numerical stability under unexpected adverse situations. Experimental results show that the proposed approach outperforms conventional approaches using the ADMM with L1 outlier detection in state estimation accuracy and convergence speed. Moreover, it maintains numerical stability and good performance under missing data. As state estimation will be performed more frequently in future smart grid due to the increased penetration of renewables, the proposed methods and investigations offer much insight in addressing the missing data and outlier problems in DPSSE.

Semistable Higgs bundles, periodic Higgs bundles and representations of algebraic fundamental groups

Let k be the algebraic closure of a finite field of odd characteristic p and X a smooth projective scheme over the Witt ring W(k) which is geometrically connected in characteristic zero. We introduce the notion of Higgs–de Rham flow and prove that the category of periodic Higgs–de Rham flows over X/W(k) is equivalent to the category of Fontaine modules, hence further equivalent to the category of crystalline representations of the étale fundamental group \pi_1(X_K) of the generic fiber of X , after Fontaine–Laffaille and Faltings. Moreover, we prove that every semistable Higgs bundle over the special fiber X_k of X of rank \leq p initiates a semistable Higgs–de Rham flow and thus those of rank \leq p-1 with trivial Chern classes induce k -representations of \pi_1(X_K) . A fundamental construction in this paper is the inverse Cartier transform over a truncated Witt ring. In characteristic p , it was constructed by Ogus–Vologodsky in the nonabelian Hodge theory in positive characteristic; in the affine local case, our construction is related to the local Ogus–Vologodsky correspondence of Shiho.