Given an annular link $L$, there is a corresponding augmented link $widetilde{L}$ in $S^3$ obtained by adding a meridian unknot component to $L$. In this paper, we construct a spectral sequence with the second page isomorphic to the annular Khovanov
homology of $L$ and it converges to the reduced Khovanov homology of $widetilde{L}$. As an application, we classify all the links with the minimal rank of annular Khovanov homology. We also give a proof that annular Khovanov homology detects unlinks.
Traditional principal component analysis (PCA) is well known in high-dimensional data analysis, but it requires to express data by a matrix with observations to be continuous. To overcome the limitations, a new method called flexible PCA (FPCA) for e
xponential family distributions is proposed. The goal is to ensure that it can be implemented to arbitrary shaped region for either count or continuous observations. The methodology of FPCA is developed under the framework of generalized linear models. It provides statistical models for FPCA not limited to matrix expressions of the data. A maximum likelihood approach is proposed to derive the decomposition when the number of principal components (PCs) is known. This naturally induces a penalized likelihood approach to determine the number of PCs when it is unknown. By modifying it for missing data problems, the proposed method is compared with previous PCA methods for missing data. The simulation study shows that the performance of FPCA is always better than its competitors. The application uses the proposed method to reduce the dimensionality of arbitrary shaped sub-regions of images and the global spread patterns of COVID-19 under normal and Poisson distributions, respectively.
With the rising demand of smart mobility, ride-hailing service is getting popular in the urban regions. These services maintain a system for serving the incoming trip requests by dispatching available vehicles to the pickup points. As the process sho
uld be socially and economically profitable, the task of vehicle dispatching is highly challenging, specially due to the time-varying travel demands and traffic conditions. Due to the uneven distribution of travel demands, many idle vehicles could be generated during the operation in different subareas. Most of the existing works on vehicle dispatching system, designed static relocation centers to relocate idle vehicles. However, as traffic conditions and demand distribution dynamically change over time, the static solution can not fit the evolving situations. In this paper, we propose a dynamic future demand aware vehicle dispatching system. It can dynamically search the relocation centers considering both travel demand and traffic conditions. We evaluate the system on real-world dataset, and compare with the existing state-of-the-art methods in our experiments in terms of several standard evaluation metrics and operation time. Through our experiments, we demonstrate that the proposed system significantly improves the serving ratio and with a very small increase in operation cost.
Coordinated motion control in swarm robotics aims to ensure the coherence of members in space, i.e., the robots in a swarm perform coordinated movements to maintain spatial structures. This problem can be modeled as a tracking control problem, in whi
ch individuals in the swarm follow a target position with the consideration of specific relative distance or orientations. To keep the communication cost low, the PID controller can be utilized to achieve the leader-follower tracking control task without the information of leader velocities. However, the controllers parameters need to be optimized to adapt to situations changing, such as the different swarm population, the changing of the target to be followed, and the anti-collision demands, etc. In this letter, we apply a modified Brain Storm Optimization (BSO) algorithm to an incremental PID tracking controller to get the relatively optimal parameters adaptively for leader-follower formation control for swarm robotics. Simulation results show that the proposed method could reach the optimal parameters during robot movements. The flexibility and scalability are also validated, which ensures that the proposed method can adapt to different situations and be a good candidate for coordinated motion control for swarm robotics in more realistic scenarios.
Swarm intelligence optimization algorithms can be adopted in swarm robotics for target searching tasks in a 2-D or 3-D space by treating the target signal strength as fitness values. Many current works in the literature have achieved good performance
in single-target search problems. However, when there are multiple targets in an environment to be searched, many swarm intelligence-based methods may converge to specific locations prematurely, making it impossible to explore the environment further. The Brain Storm Optimization (BSO) algorithm imitates a group of humans in solving problems collectively. A series of guided searches can finally obtain a relatively optimal solution for particular optimization problems. Furthermore, with a suitable clustering operation, it has better multi-modal optimization performance, i.e., it can find multiple optima in the objective space. By matching the members in a robotic swarm to the individuals in the algorithm under both environments and robots constraints, this paper proposes a BSO-based collaborative searching framework for swarm robotics called Robotic BSO. The simulation results show that the proposed method can simulate the BSOs guided search characteristics and has an excellent prospect for multi-target searching problems for swarm robotics.
Population-based methods are often used to solve multimodal optimization problems. By combining niching or clustering strategy, the state-of-the-art approaches generally divide the population into several subpopulations to find multiple solutions for
a problem at hand. However, these methods only guided by the fitness value during iterations, which are suffering from determining the number of subpopulations, i.e., the number of niche areas or clusters. To compensate for this drawback, this paper presents an Attention-oriented Brain Storm Optimization (ABSO) method that introduces the attention mechanism into a relatively new swarm intelligence algorithm, i.e., Brain Storm Optimization (BSO). By converting the objective space from the fitness space into attention space, the individuals are clustered and updated iteratively according to their salient values. Rather than converge to a single global optimum, the proposed method can guide the search procedure to converge to multiple salient solutions. The preliminary results show that the proposed method can locate multiple global and local optimal solutions of several multimodal benchmark functions. The proposed method needs less prior knowledge of the problem and can automatically converge to multiple optimums guided by the attention mechanism, which has excellent potential for further development.
The spin rotations and lattice rotations are locked in the Shubnikov magnetic space groups in describing magnetically ordered materials. However, real materials may contain symmetry elements whose spin and lattice operations are partially unlocked. T
hese groups are called spin space groups and may give rise to new band structures for itinerant electrons. In the present work, we focus on potential magnetic materials in which the intrinsic electronic spin-orbit coupling is negligible. We theoretically predict many new fermionic quasiparticles at the high symmetry points (HSPs) or high symmetry lines (HSLs) in the Brillouin zone (BZ), which can neither be realized in non-magnetic systems nor in magnetic ones with Shubnikov magnetic space group symmetries. These new quasiparticles are characterized by the symmetry invariants of the little co-group, which are more essential than the representations (Reps) themselves. We also provide the dispersion around the high-symmetry points/lines, and predict a large class of nodal-point or nodal-line semimetals.
The paper is concerned with the exponential attractors for the viscoelastic wave model in $Omegasubset mathbb R^3$: $$u_{tt}-h_t(0)Delta u-int_0^inftypartial_sh_t(s)Delta u(t-s)mathrm ds+f(u)=h,$$ with time-dependent memory kernel $h_t(cdot)$ which
is used to model aging phenomena of the material. Conti et al [Amer. J. Math., 2018] recently provided the correct mathematical setting for the model and a well-posedness result within the novel theory of dynamical systems acting on. time-dependent spaces, recently established by Conti, Pata and Temam [J. Differential Equations, 2013], and proved the existence and the regularity of the time-dependent global attractor. In this work, we further study the existence of the time-dependent exponential attractors as well as their regularity. We establish an abstract existence criterion via quasi-stability method introduced originally by Chueshov and Lasiecka [J. Dynam. Diff.Eqs.,2004], and on the basis of the theory and technique developed in [Amer. J. Math., 2018] we further provide a new method to overcome the difficulty of the lack of further regularity to show the existence of the time-dependent exponential attractor. And these techniques can be used to tackle other hyperbolic models.
Cross-resolution face recognition (CRFR), which is important in intelligent surveillance and biometric forensics, refers to the problem of matching a low-resolution (LR) probe face image against high-resolution (HR) gallery face images. Existing shal
low learning-based and deep learning-based methods focus on mapping the HR-LR face pairs into a joint feature space where the resolution discrepancy is mitigated. However, little works consider how to extract and utilize the intermediate discriminative features from the noisy LR query faces to further mitigate the resolution discrepancy due to the resolution limitations. In this study, we desire to fully exploit the multi-level deep convolutional neural network (CNN) feature set for robust CRFR. In particular, our contributions are threefold. (i) To learn more robust and discriminative features, we desire to adaptively fuse the contextual features from different layers. (ii) To fully exploit these contextual features, we design a feature set-based representation learning (FSRL) scheme to collaboratively represent the hierarchical features for more accurate recognition. Moreover, FSRL utilizes the primitive form of feature maps to keep the latent structural information, especially in noisy cases. (iii) To further promote the recognition performance, we desire to fuse the hierarchical recognition outputs from different stages. Meanwhile, the discriminability from different scales can also be fully integrated. By exploiting these advantages, the efficiency of the proposed method can be delivered. Experimental results on several face datasets have verified the superiority of the presented algorithm to the other competitive CRFR approaches.
Heterogeneity of brain diseases is a challenge for precision diagnosis/prognosis. We describe and validate Smile-GAN (SeMI-supervised cLustEring-Generative Adversarial Network), a novel semi-supervised deep-clustering method, which dissects neuroanat
omical heterogeneity, enabling identification of disease subtypes via their imaging signatures relative to controls. When applied to MRIs (2 studies; 2,832 participants; 8,146 scans) including cognitively normal individuals and those with cognitive impairment and dementia, Smile-GAN identified 4 neurodegenerative patterns/axes: P1, normal anatomy and highest cognitive performance; P2, mild/diffuse atrophy and more prominent executive dysfunction; P3, focal medial temporal atrophy and relatively greater memory impairment; P4, advanced neurodegeneration. Further application to longitudinal data revealed two distinct progression pathways: P1$rightarrow$P2$rightarrow$P4 and P1$rightarrow$P3$rightarrow$P4. Baseline expression of these patterns predicted the pathway and rate of future neurodegeneration. Pattern expression offered better yet complementary performance in predicting clinical progression, compared to amyloid/tau. These deep-learning derived biomarkers offer promise for precision diagnostics and targeted clinical trial recruitment.
