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Kai Jiang

Publications and source records attributed to Kai Jiang.

At least 127 records · Page 7Linked to original sources
arXiv2021

Vertebrate interval graphs

A vertebrate interval graph is an interval graph in which the maximum size of a set of independent vertices equals the number of maximal cliques. For any fixed $v \ge 1$, there is a polynomial-time algorithm for deciding whether a vertebrate interval graph admits a vertex partition into two induced subgraphs with claw number at most $v$. In particular, when $v = 2$, whether a vertebrate interval graph can be partitioned into two proper interval graphs can be decided in polynomial time.

math.CO↗
arXiv2021

Partitioning an interval graph into subgraphs with small claws

The claw number of a graph $G$ is the largest number $v$ such that $K_{1,v}$ is an induced subgraph of $G$. Interval graphs with claw number at most $v$ are cluster graphs when $v = 1$, and are proper interval graphs when $v = 2$. Let $κ(n,v)$ be the smallest number $k$ such that every interval graph with $n$ vertices admits a vertex partition into $k$ induced subgraphs with claw number at most $v$. Let $\checkκ(w,v)$ be the smallest number $k$ such that every interval graph with claw number $w$ admits a vertex partition into $k$ induced subgraphs with claw number at most $v$. We show that $κ(n,v) = \lfloor\log_{v+1} (n v + 1)\rfloor$, and that $\lfloor\log_{v+1} w\rfloor + 1 \le \checkκ(w,v) \le \lfloor\log_{v+1} w\rfloor + 3$. Besides the combinatorial bounds, we also present a simple approximation algorithm for partitioning an interval graph into the minimum number of induced subgraphs with claw number at most $v$, with approximation ratio $3$ when $1 \le v \le 2$, and $2$ when $v \ge 3$.

math.CO↗
arXiv2021

Caterpillars and alternating paths

Let $p(m)$ (respectively, $q(m)$) be the maximum number $k$ such that any tree with $m$ edges can be transformed by contracting edges (respectively, by removing vertices) into a caterpillar with $k$ edges. We derive closed-form expressions for $p(m)$ and $q(m)$ for all $m \ge 1$. The two functions $p(n)$ and $q(n)$ can also be interpreted in terms of alternating paths among $n$ disjoint line segments in the plane, whose $2n$ endpoints are in convex position.

math.CO↗
arXiv2021

Moving intervals for packing and covering

We study several problems on geometric packing and covering with movement. Given a family $\mathcal{I}$ of $n$ intervals of $κ$ distinct lengths, and another interval $B$, can we pack the intervals in $\mathcal{I}$ inside $B$ (respectively, cover $B$ by the intervals in $\mathcal{I}$) by moving $τ$ intervals and keeping the other $σ= n - τ$ intervals unmoved? We show that both packing and covering are W[1]-hard with any one of $κ$, $τ$, and $σ$ as single parameter, but are FPT with combined parameters $κ$ and $τ$. We also obtain improved polynomial-time algorithms for packing and covering, including an $O(n\log^2 n)$ time algorithm for covering, when all intervals in $\mathcal{I}$ have the same length.

cs.CG↗
arXiv2021

An adaptive high-order surface finite element method for the self-consistent field theory on general curved surfaces

In this paper, we develop an adaptive high-order surface finite element method (FEM) incorporating the spectral deferred correction method for chain contour discretization to solve polymeric self-consistent field equations on general curved surfaces. The high-order surface FEM is obtained by the high-order surface geometrical approximation and the high-order function space approximation. Numerical results demonstrate that the precision order of these methods is consistent with the theoretical prediction. In order to describe the sharp interface in the strongly segregated system more accurately, an adaptive FEM equipped with a new Log marking strategy is proposed. Compared with the traditional strategy, the Log marking strategy can not only label the elements that need to be refined or coarsened, but also give the refined or coarsened times, which can make full use of the information of a posterior error estimator and improve the ecciency of the adaptive algorithm. To demonstrate the power of our approach, we investigate the self-assembled patterns of diblock copolymers on several distinct curved surfaces. Numerical results illustrate the ecciency of the proposed method, especially for strongly segregated systems with economical discretization nodes.

math.NA↗
arXiv2021

An adaptive block Bregman proximal gradient method for computing stationary states of multicomponent phase-field crystal model

In this paper, we compute the stationary states of the multicomponent phase-field crystal model by formulating it as a block constrained minimization problem. The original infinite-dimensional non-convex minimization problem is approximated by a finite-dimensional constrained non-convex minimization problem after an appropriate spatial discretization. To efficiently solve the above optimization problem, we propose a so-called adaptive block Bregman proximal gradient (AB-BPG) algorithm that fully exploits the problem's block structure. The proposed method updates each order parameter alternatively, and the update order of blocks can be chosen in a deterministic or random manner. Besides, we choose the step size by developing a practical linear search approach such that the generated sequence either keeps energy dissipation or has a controllable subsequence with energy dissipation. The convergence property of the proposed method is established without the requirement of global Lipschitz continuity of the derivative of the bulk energy part by using the Bregman divergence. The numerical results on computing stationary ordered structures in binary, ternary, and quinary component coupled-mode Swift-Hohenberg models have shown a significant acceleration over many existing methods.

math.NA↗
arXiv2021

An adaptive virtual element method for the polymer self-consistent field theory

In this paper, we develop a high-order adaptive virtual element method (VEM) to simulate the self-consistent field theory (SCFT) model in arbitrary domains. The VEM is very flexible in handling general polygon elements and can treat hanging nodes as polygon vertices without additional processing. Besides, to effectively simulate the phase separation behavior in strong segregation systems, an adaptive method on polygonal mesh equipped with a new marking strategy is developed. This new marking strategy will indicate the times of marked elements to be refined and coarsened, making full use of the information contained in the current numerical results. Using the halfedge data structure, we can apply the adaptive method to the arbitrary polygonal mesh. Numerical results demonstrate that the developed method is efficient in simulating polymers' phase behavior in complex geometric domains. The accuracy is consistent with theoretical results. The adaptive method can greatly reduce computational costs to obtain prescribed numerical accuracy for strong segregation systems.

math.NA↗
arXiv2021

Abnormal Staebler-Wronski effect of amorphous silicon

Great achievements in last five years, such as record-efficient amorphous/crystalline silicon heterojunction (SHJ) solar cells and cutting-edge perovskite/SHJ tandem solar cells, place hydrogenated amorphous silicon (a-Si:H) at the forefront of emerging photovoltaics. Due to the extremely low doping efficiency of trivalent boron (B) in amorphous tetravalent silicon, light harvesting of aforementioned devices are limited by their fill factors (FF), which is a direct metric of the charge carrier transport. It is challenging but crucial to develop highly conductive doped a-Si:H for minimizing the FF losses. Here we report intensive light soaking can efficiently boost the dark conductance of B-doped a-Si:H "thin" films, which is an abnormal Staebler-Wronski effect. By implementing this abnormal effect to SHJ solar cells, we achieve a certificated power conversion efficiency (PCE) of 25.18% (26.05% on designated area) with FF of 85.42% on a 244.63-cm2 wafer. This PCE is one of the highest reported values for total-area "top/rear" contact silicon solar cells. The FF reaches 98.30 per cent of its Shockley-Queisser limit.

physics.app-ph↗
arXiv2020

Efficient numerical methods for computing the stationary states of phase field crystal models

Finding the stationary states of a free energy functional is an important problem in phase field crystal (PFC) models. Many efforts have been devoted for designing numerical schemes with energy dissipation and mass conservation properties. However, most existing approaches are time-consuming due to the requirement of small effective step sizes. In this paper, we discretize the energy functional and propose efficient numerical algorithms for solving the constrained non-convex minimization problem. A class of gradient based approaches, which is the so-called adaptive accelerated Bregman proximal gradient (AA-BPG) methods, is proposed and the convergence property is established without the global Lipschitz constant requirements. A practical Newton method is also designed to further accelerate the local convergence with convergence guarantee. One key feature of our algorithms is that the energy dissipation and mass conservation properties hold during the iteration process. Moreover, we develop a hybrid acceleration framework to accelerate the AA-BPG methods and most of existing approaches through coupling with the practical Newton method. Extensive numerical experiments, including two three dimensional periodic crystals in Landau-Brazovskii (LB) model and a two dimensional quasicrystal in Lifshitz-Petrich (LP) model, demonstrate that our approaches have adaptive step sizes which lead to a significant acceleration over many existing methods when computing complex structures.

math.NA↗
arXiv2020

2nd Place Solution to Instance Segmentation of IJCAI 3D AI Challenge 2020

Compared with MS-COCO, the dataset for the competition has a larger proportion of large objects which area is greater than 96x96 pixels. As getting fine boundaries is vitally important for large object segmentation, Mask R-CNN with PointRend is selected as the base segmentation framework to output high-quality object boundaries. Besides, a better engine that integrates ResNeSt, FPN and DCNv2, and a range of effective tricks that including multi-scale training and test time augmentation are applied to improve segmentation performance. Our best performance is an ensemble of four models (three PointRend-based models and SOLOv2), which won the 2nd place in IJCAI-PRICAI 3D AI Challenge 2020: Instance Segmentation.

cs.CV↗
arXiv2020

High-order energy stable schemes of incommensurate phase-field crystal model

This article focuses on the development of high-order energy stable schemes for the multi-length-scale incommensurate phase-field crystal model which is able to study the phase behavior of aperiodic structures. These high-order schemes based on the scalar auxiliary variable (SAV) and spectral deferred correction (SDC) approaches are suitable for the L 2 gradient flow equation, i.e., the Allen-Cahn dynamic equation. Concretely, we propose a second-order Crank-Nicolson (CN) scheme of the SAV system, prove the energy dissipation law, and give the error estimate in the almost periodic function sense. Moreover, we use the SDC method to improve the computational accuracy of the SAV/CN scheme. Numerical results demonstrate the advantages of high-order numerical methods in numerical computations and show the influence of length-scales on the formation of ordered structures.

math.NA↗
arXiv2020

Complete integrability of diffeomorphisms and their local normal forms

In this paper, we consider the normal form problem of a commutative family of germs of diffeomorphisms at a fixed point, say the origin, of $\mathbb{K}^n$ ($\mathbb{K}=\mathbb{C}$ or $\mathbb{R}$). We define a notion of integrability of such a family. We give sufficient conditions which ensure that such an integrable family can be transformed into a normal form by an analytic (resp. a smooth) transformation if the initial diffeomorphisms are analytic (resp. smooth).

math.DS↗
arXiv2020

High-order energy stable schemes of incommensurate phase-field crystal model

This article focuses on the development of high-order energy stable schemes for the multi-length-scale incommensurate phase-field crystal model which is able to study the phase behavior of aperiodic structures. These high-order schemes based on the scalar auxiliary variable (SAV) and spectral deferred correction (SDC) approaches are suitable for the L 2 gradient flow equation, i.e., the Allen-Cahn dynamic equation. Concretely, we propose a second-order Crank-Nicolson (CN) scheme of the SAV system, prove the energy dissipation law, and give the error estimate in the almost periodic function sense. Moreover, we use the SDC method to improve the computational accuracy of the SAV/CN scheme. Numerical results demonstrate the advantages of high-order numerical methods in numerical computations and show the influence of length-scales on the formation of ordered structures.

math.NA↗
arXiv2020

Reinforcement Learning with Goal-Distance Gradient

Reinforcement learning usually uses the feedback rewards of environmental to train agents. But the rewards in the actual environment are sparse, and even some environments will not rewards. Most of the current methods are difficult to get good performance in sparse reward or non-reward environments. Although using shaped rewards is effective when solving sparse reward tasks, it is limited to specific problems and learning is also susceptible to local optima. We propose a model-free method that does not rely on environmental rewards to solve the problem of sparse rewards in the general environment. Our method use the minimum number of transitions between states as the distance to replace the rewards of environmental, and proposes a goal-distance gradient to achieve policy improvement. We also introduce a bridge point planning method based on the characteristics of our method to improve exploration efficiency, thereby solving more complex tasks. Experiments show that our method performs better on sparse reward and local optimal problems in complex environments than previous work.

cs.LG↗