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This article investigates the pseudo transitions of the Blume-Capel model on two-dimensional finite-size lattices. By employing the Wang-Landau sampling method and microcanonical inflection point analysis, we identified the positions of phase transitions as well as higher-order phase transitions. Through Metropolis sampling and canonical ensemble analysis, we obtained the corresponding geometric characteristics of the system at these transition points. The results indicate the presence of a third-order independent phase transition in the system. However, when the crystal field parameter $D$ exceeds 1.965, crossing the tricritical point, no third-order dependent phase transition is observed. Furthermore, the positions of the third-order phase transition obtained from both microcanonical and canonical analyses are consistent and mutually corroborative. We speculate that third-order dependent transitions may only occur in second-order phase transitions and not in first-order transitions., Comment: 15 pages, 9 figures

Within the canonical ensemble framework, this paper investigates the presence of higher-order transition signals in the q-state Potts model (for q>3), using two geometric order parameters: isolated spins number and the average perimeter of clusters. Our results confirm that higher-order transitions exist in the Potts model, where the number of isolated spins reliably indicates third-order independent transitions. This signal persists regardless of the system's phase transition order, even at higher values of q. In contrast, the average perimeter of clusters, used as an order parameter for detecting third-order dependent transitions, shows that for q = 6 and q = 8, the signal for third-order dependent transitions disappears, indicating its absence in systems undergoing first-order transitions. These findings are consistent with results from microcanonical inflection-point analysis, further validating the robustness of this approach., Comment: 12 pages, 8 figures

In the domain of language-based fashion image retrieval, pinpointing the desired fashion item using both a reference image and its accompanying textual description is an intriguing challenge. Existing approaches lean heavily on static fusion techniques, intertwining image and text. Despite their commendable advancements, these approaches are still limited by a deficiency in flexibility. In response, we propose a Self-distilled Dynamic Fusion Network to compose the multi-granularity features dynamically by considering the consistency of routing path and modality-specific information simultaneously. Two new modules are included in our proposed method: (1) Dynamic Fusion Network with Modality Specific Routers. The dynamic network enables a flexible determination of the routing for each reference image and modification text, taking into account their distinct semantics and distributions. (2) Self Path Distillation Loss. A stable path decision for queries benefits the optimization of feature extraction as well as routing, and we approach this by progressively refine the path decision with previous path information. Extensive experiments demonstrate the effectiveness of our proposed model compared to existing methods., Comment: ICASSP 2024

In this paper, we investigate phase transitions in the Majority-Vote model coupled with noise layers of different structures. We examine the Square lattice and Random-regular networks, as well as their combinations, for both vote layers and noise layers. Our findings reveal the presence of independent third-order transitions in all cases and dependent third-order transitions when critical transitions occur. This suggests that dependent third-order transitions may serve as precursors to critical transitions in non-equilibrium systems. Furthermore, we observe that when the structure of vote layers is local, the coupling between the vote layer and the noise layer leads to the absence of critical phenomena., Comment: 16 pages, 10 figures

In this work, we propose a deep learning-based method to perform semiparametric regression analysis for spatially dependent data. To be specific, we use a sparsely connected deep neural network with rectified linear unit (ReLU) activation function to estimate the unknown regression function that describes the relationship between response and covariates in the presence of spatial dependence. Under some mild conditions, the estimator is proven to be consistent, and the rate of convergence is determined by three factors: (1) the architecture of neural network class, (2) the smoothness and (intrinsic) dimension of true mean function, and (3) the magnitude of spatial dependence. Our method can handle well large data set owing to the stochastic gradient descent optimization algorithm. Simulation studies on synthetic data are conducted to assess the finite sample performance, the results of which indicate that the proposed method is capable of picking up the intricate relationship between response and covariates. Finally, a real data analysis is provided to demonstrate the validity and effectiveness of the proposed method.

To safely and rationally participate in dense and heterogeneous traffic, autonomous vehicles require to sufficiently analyze the motion patterns of surrounding traffic-agents and accurately predict their future trajectories. This is challenging because the trajectories of traffic-agents are not only influenced by the traffic-agents themselves but also by spatial interaction with each other. Previous methods usually rely on the sequential step-by-step processing of Long Short-Term Memory networks (LSTMs) and merely extract the interactions between spatial neighbors for single type traffic-agents. We propose the Spatio-Temporal Transformer Networks (S2TNet), which models the spatio-temporal interactions by spatio-temporal Transformer and deals with the temporel sequences by temporal Transformer. We input additional category, shape and heading information into our networks to handle the heterogeneity of traffic-agents. The proposed methods outperforms state-of-the-art methods on ApolloScape Trajectory dataset by more than 7\% on both the weighted sum of Average and Final Displacement Error. Our code is available at https://github.com/chenghuang66/s2tnet., Comment: Accepted by ACML2021

The applications of traditional statistical feature selection methods to high-dimension, low sample-size data often struggle and encounter challenging problems, such as overfitting, curse of dimensionality, computational infeasibility, and strong model assumption. In this paper, we propose a novel two-step nonparametric approach called Deep Feature Screening (DeepFS) that can overcome these problems and identify significant features with high precision for ultra high-dimensional, low-sample-size data. This approach first extracts a low-dimensional representation of input data and then applies feature screening based on multivariate rank distance correlation recently developed by Deb and Sen (2021). This approach combines the strengths of both deep neural networks and feature screening, and thereby has the following appealing features in addition to its ability of handling ultra high-dimensional data with small number of samples: (1) it is model free and distribution free; (2) it can be used for both supervised and unsupervised feature selection; and (3) it is capable of recovering the original input data. The superiority of DeepFS is demonstrated via extensive simulation studies and real data analyses.

This article offers a detailed analysis of pseudo-phase transitions of Ising and Baxter-Wu models in two-dimensional finite-size lattices. We carry out Wang Landau sampling to obtain the density of states. Using microcanonical inflection point analysis with microcanonical entropy, we obtain the order of the psuedo-phase transitions in the models. The microcanonical analysis results of the second-order transition for the Ising model and the first-order transition for the Baxter-Wu model are consistent with the traditional canonical results. In addition, the third-order transitions are found in both models, implying the universality of higher-order phase transitions., Comment: 13 pages, 5 figures

Recently, there is growing attention on one-stage panoptic segmentation methods which aim to segment instances and stuff jointly within a fully convolutional pipeline efficiently. However, most of the existing works directly feed the backbone features to various segmentation heads ignoring the demands for semantic and instance segmentation are different: The former needs semantic-level discriminative features, while the latter requires features to be distinguishable across instances. To alleviate this, we propose to first predict semantic-level and instance-level correlations among different locations that are utilized to enhance the backbone features, and then feed the improved discriminative features into the corresponding segmentation heads, respectively. Specifically, we organize the correlations between a given location and all locations as a continuous sequence and predict it as a whole. Considering that such a sequence can be extremely complicated, we adopt Discrete Fourier Transform (DFT), a tool that can approximate an arbitrary sequence parameterized by amplitudes and phrases. For different tasks, we generate these parameters from the backbone features in a fully convolutional way which is optimized implicitly by corresponding tasks. As a result, these accurate and consistent correlations contribute to producing plausible discriminative features which meet the requirements of the complicated panoptic segmentation task. To verify the effectiveness of our methods, we conduct experiments on several challenging panoptic segmentation datasets and achieve state-of-the-art performance on MS COCO with $45.1$\% PQ and ADE20k with $32.6$\% PQ., Comment: Tech report

With the rapid advances of data acquisition techniques, spatio-temporal data are becoming increasingly abundant in a diverse array of disciplines. Here we develop spatio-temporal regression methodology for analyzing large amounts of spatially referenced data collected over time, motivated by environmental studies utilizing remotely sensed satellite data. In particular, we specify a semiparametric autoregressive model without the usual Gaussian assumption and devise a computationally scalable procedure that enables the regression analysis of large datasets. We estimate the model parameters by quasi maximum likelihood and show that the computational complexity can be reduced from cubic to linear of the sample size. Asymptotic properties under suitable regularity conditions are further established that inform the computational procedure to be efficient and scalable. A simulation study is conducted to evaluate the finite-sample properties of the parameter estimation and statistical inference. We illustrate our methodology by a dataset with over 2.96 million observations of annual land surface temperature and the comparison with an existing state-of-the-art approach highlights the advantages of our method.