A link invariant from higher-dimensional Heegaard Floer homology

We define a higher-dimensional analogue of symplectic Khovanov homology. Consider the standard Lefschetz fibration $p\colon W\to D\subset\mathbb{C}$ of a $2n$-dimensional Milnor fiber of the $A_{2\kappa-1}$ singularity. We represent a link by a $\kappa$-strand braid, which is expressed as an element $h$ of the symplectic mapping class group $\mathrm{Symp}(W,\partial W)$. We then apply the higher-dimensional Heegaard Floer homology machinery to the pair $(\boldsymbol{a},h(\boldsymbol{a}))$, where $\boldsymbol{a}$ is a collection of $\kappa$ unstable manifolds of $W$ which are Lagrangian spheres. We prove its invariance under arc slides and Markov stabilizations, which shows that it is a link invariant. This work constitutes part of the author's PhD thesis

Heegaard Floer Symplectic homology and Viterbo's isomorphism theorem in the context of multiple particles

Given a Liouville manifold $M$, we introduce an invariant of $M$ that we call the Heegaard Floer symplectic cohomology $SH^*_\kappa(M)$ for any $\kappa \ge 1$ that coincides with the symplectic cohomology for $\kappa=1$. Writing $\hat{M}$ for the completion of $M$, the differential counts pseudoholomorphic curves of arbitrary genus in $\mathbb{R} \times S^1 \times \hat{M}$ that are required to be branched $\kappa$-sheeted covers when projected to the $\mathbb{R} \times S^1$-direction; this resembles the cylindrical reformulation of Heegaard Floer homology by Lipshitz. These cohomology groups provide a closed-string analogue of higher-dimensional Heegaard Floer homology introduced by Colin, Honda, and Tian. When $\hat{M}=T^*Q$ with $Q$ an orientable manifold, we introduce a Morse-theoretic analogue of Heegaard Floer symplectic cohomology, which we call the free multiloop complex of $Q$. When $Q$ has vanishing relative second Stiefel-Whitney class, we prove a generalized version of Viterbo's isomorphism theorem by showing that the cohomology groups $SH^*_\kappa(T^*Q)$ are isomorphic to the cohomology groups of the free multiloop complex of $Q$.Comment: 78 pages, 14 figure

The Memory

Other than the political union by one government, the ultimate peace shall only be achieved by the union of people, friends and families. Due to the Korean War, many families were separated. Due to the DMZ (Demilitarized Zone), those people could never meet familiies in their entire life. With the extremely intense atmosphere, the DMZ creates a harsh physical boundary as well as a spiritual and invisible barrier between the people of two countries

Several Ways of Calculating the Gradient, Curl and Divergence under Orthogonal Curvilinear Coordinate Systems

Calculating gradient, curl and divergence is very important in physics, especially in electrodynam ics and fluid mechanics. To calculate the gradient, curl and divergence under orthogonal curvilin ear coordinate systems, one must consider the Lame coefficients. Also, in many textbooks the calculation of gradient, curl and divergence under orthogonal coordinate systems are not well discussed. In this thesis the concepts such as manifold, tensors, differential forms and Lame coefficients are defined and three different ways-differential form method, covariant derivative method, and Hodge star operator method-of calculating gradient, curl and divergence are discussed. The gra dient, curl and divergence under three different orthogonal curvilinear coordinate systems are obtained

Harnessing Non-Covalent Interactions for Functional Organic Materials

Non‐covalent interactions play a crucial role in developing functional organic materials. As non-covalent interactions are reversible, dynamic and responsive to environment, multifunctional materials with excellent processability and recyclability can be designed and developed utilizing these adaptable forces. In this dissertation, different types of non-covalent interactions were harnessed in developing new functional organic materials which (i) exhibit tunable thermochromism based on the competing charge transfer interactions, (ii) composed of enantiomerically pure macroscopic helices desirable for chiral applications, and (iii) possess conjugated, rigid molecular backbones and regulated intermolecular bonds suitable for extreme operating or processing conditions. The dissertation begins with a brief introduction of different non‐covalent interactions and how they were employed in functional materials. My argument then moves on to examples demonstrating how a variety of non-covalent interactions can be used in developing new functional organic materials. In the first example, a series of donor-acceptor based thermochromic materials were designed and synthesized. These materials can be assembled in water, and solution-processed to form patterns, thin films and aerogels with a reversible thermochromic property. The color transition of donor-acceptor assemblies is resulted from the competing ππ* and n-->π* charge transfer (CT) interactions. To further control the thermochromic properties of these materials, a wide range of -electron rich donors, halogen counterions and -electron poor acceptors have been selected and synthesized. Mechanistic studies to further understand the donor-acceptor self-assembly and color changing processes have also been conducted. Moreover, a facile method to prepare macroscopic helical architectures with controlled handedness was introduced. The feasibility in forming large-scale enantiomerically pure helices and the chiral memory effects of these supramolecular self-assemblies are of great interest for future applications in chiral separation and catalysis. In the last example, conjugated small molecules and a conjugated ladder polymer possessing rigid coplanar backbones and self-complementary intermolecular hydrogen bonds have been developed. The intermolecular π─π interactions and hydrogen bonds of the ladder polymer rendered its excellent resistance to organic solvents, aqueous acids, and thermal treatments. This unique property allows for developments of robust polymer materials for applications associated with extreme operating or processing conditions

Towards Generic Image Manipulation Detection with Weakly-Supervised Self-Consistency Learning

As advanced image manipulation techniques emerge, detecting the manipulation becomes increasingly important. Despite the success of recent learning-based approaches for image manipulation detection, they typically require expensive pixel-level annotations to train, while exhibiting degraded performance when testing on images that are differently manipulated compared with training images. To address these limitations, we propose weakly-supervised image manipulation detection, such that only binary image-level labels (authentic or tampered with) are required for training purpose. Such a weakly-supervised setting can leverage more training images and has the potential to adapt quickly to new manipulation techniques. To improve the generalization ability, we propose weakly-supervised self-consistency learning (WSCL) to leverage the weakly annotated images. Specifically, two consistency properties are learned: multi-source consistency (MSC) and inter-patch consistency (IPC). MSC exploits different content-agnostic information and enables cross-source learning via an online pseudo label generation and refinement process. IPC performs global pair-wise patch-patch relationship reasoning to discover a complete region of manipulation. Extensive experiments validate that our WSCL, even though is weakly supervised, exhibits competitive performance compared with fully-supervised counterpart under both in-distribution and out-of-distribution evaluations, as well as reasonable manipulation localization ability.Comment: Accepted to ICCV 2023, code: https://github.com/yhZhai/WSC

Degradation Mechanisms and Mitigation Strategies of Nickel-Rich NMC-Based Lithium-Ion Batteries

Abstract The demand for lithium-ion batteries (LIBs) with high mass-specific capacities, high rate capabilities and long-term cyclabilities is driving the research and development of LIBs with nickel-rich NMC (LiNixMnyCo1−x−yO2, $$x \geqslant 0.5$$x⩾0.5) cathodes and graphite (LixC6) anodes. Based on this, this review will summarize recently reported and widely recognized studies of the degradation mechanisms of Ni-rich NMC cathodes and graphite anodes. And with a broad collection of proposed mechanisms on both atomic and micrometer scales, this review can supplement previous degradation studies of Ni-rich NMC batteries. In addition, this review will categorize advanced mitigation strategies for both electrodes based on different modifications in which Ni-rich NMC cathode improvement strategies involve dopants, gradient layers, surface coatings, carbon matrixes and advanced synthesis methods, whereas graphite anode improvement strategies involve surface coatings, charge/discharge protocols and electrolyte volume estimations. Electrolyte components that can facilitate the stabilization of anodic solid electrolyte interfaces are also reviewed, and trade-offs between modification techniques as well as controversies are discussed for a deeper understanding of the mitigation strategies of Ni-rich NMC/graphite LIBs. Furthermore, this review will present various physical and electrochemical diagnostic tools that are vital in the elucidation of degradation mechanisms during operation to supplement future degradation studies. Finally, this review will summarize current research focuses and propose future research directions. Graphic Abstract The demand for lithium-ion batteries (LIBs) with high mass specific capacities, high rate capabilities and longterm cyclabilities is driving the research and development of LIBs with nickel-rich NMC (LiNixMnyCo1−x−yO2, x ≥ 0.5) cathodes and graphite (LixC6) anodes. Based on this, this review will summarize recently reported and widely recognized studies of the degradation mechanisms of Ni-rich NMC cathodes and graphite anodes. And with a broad collection of proposed mechanisms on both atomic and micrometer scales, this review can supplement previous degradation studies of Ni-rich NMC batteries. In addition, this review will categorize advanced mitigation strategies for both electrodes based on different modifications in which Ni-rich NMC cathode improvement strategies involve dopants, gradient layers, surface coatings, carbon matrixes and advanced synthesis methods, whereas graphite anode improvement strategies involve surface coatings, charge/discharge protocols and electrolyte volume estimations. Electrolyte components that can facilitate the stabilization of anodic solid-electrolyte interfaces (SEIs) are also reviewed and tradeoffs between modification techniques as well as controversies are discussed for a deeper understanding of the mitigation strategies of Ni-rich NMC/graphite LIBs. Furthermore, this review will present various physical and electrochemical diagnostic tools that are vital in the elucidation of degradation mechanisms during operation to supplement future degradation studies. Finally, this review will summarize current research focuses and propose future research directions

Annealing evolutionary parallel algorithm analysis of optimization arrangement on mistuned blades with non-linear friction

This paper sets up a lumped parameter model of engine bladed disk system when considering the nonlinear friction damping based on mistuned parameters which is obtained from the blade modal experiment. A bladed arrangement optimization method, namely annealing evolutionary algorithm with tabu list is presented which combines the local search ability of SA (simulated annealing) and the global searching ability of GA (genetic algorithm) introducing tabu list as the search memory list. Parallel TAEA (tabu annealing evolutionary algorithm) is presented based on CUDA (Compute Unified Device Architecture) combining GPU (Graphics Processing Unit) and its performance is analyzed. The results show that optimization based on CUDA framework can improve computing speed. At the same time using optimization results can reduce the amplitude of forced vibration response of bladed disk system and make it in the range of allowable engineering

Effects of stator-rotor interaction on unsteady aerodynamic load of compressor rotor blades

In compressor working, unsteady aerodynamic load induced by the interaction of stator-rotor blade rows is the main vibration source of blade high cycle fatigue. It has a direct influence on fatigue strength of compressor blades. Further research on unsteady aerodynamic load has very important significance for improving the service life and reliability of compressor blades. Based on an aero-engine compressor rotor system, three-dimensional flow field model of former stator and downstream rotor is established. With the method of numerical simulation, compressor flow characteristics are solved at different moments. Then the paper analyzes the process of stator-rotor interaction and the distribution law of rotor blade aerodynamic load. In addition, the effects on rotor blade aerodynamic load are discussed at different pressure ratios, rotational speeds and ratios of stator-rotor blade number. The results show unsteady flow field area with lower speed is induced by stator-rotor interaction at rotor blade leading edge. When the overlap space between stator and rotor channels is the maximum, mass flow and static pressure around rotor blade will appear jumping fluctuations. Unsteady aerodynamic load fluctuates periodically, and dominant frequencies are manly at frequency doubling of stator-rotor interaction, especially at one time frequency (1×f0). In the interaction period T, variations of aerodynamic load on pressure and suction surfaces take the contrary trend, magnitude and pulsation amplitude on pressure surface are far greater than that on suction surface. Effects of pressure ratio on pressure and suction surfaces are consistent, and the magnitude of aerodynamic load increases with pressure ratio. Rotational speed and stator-rotor blade number ratio affect the magnitude of aerodynamic load on suction surface more heavily than that on pressure surface. With the increasing of rotational speed, unsteady characteristics of aerodynamic load are enhanced. Besides, pulsation amplitude and peak value of unsteady aerodynamic load reach the maximum when stator-rotor blade number ratio λ=1. This research provides the theoretical basis for dynamics design of aero-engine compressor rotor syste

MoEC: Mixture of Expert Clusters

Sparsely Mixture of Experts (MoE) has received great interest due to its promising scaling capability with affordable computational overhead. MoE converts dense layers into sparse experts, and utilizes a gated routing network to make experts conditionally activated. However, as the number of experts grows, MoE with outrageous parameters suffers from overfitting and sparse data allocation. Such problems are especially severe on tasks with limited data, thus hindering the progress for MoE models to improve performance by scaling up. In this work, we propose Mixture of Expert Clusters - a general approach to enable expert layers to learn more diverse and appropriate knowledge by imposing variance-based constraints on the routing stage. We further propose a cluster-level expert dropout strategy specifically designed for the expert cluster structure. Our experiments reveal that MoEC could improve performance on machine translation and natural language understanding tasks, and raise the performance upper bound for scaling up experts under limited data. We also verify that MoEC plays a positive role in mitigating overfitting and sparse data allocation