Average trapping time on a type of horizontally segmented 3 dimensional Sierpinski gasket network with two types of locally self-similar structures

As a classic self-similar network model, Sierpinski gasket network has been used many times to study the characteristics of self-similar structure and its influence on the dynamic properties of the network. However, the network models studied in these problems only contain a single self-similar structure, which is inconsistent with the structural characteristics of the actual network models. In this paper, a type of horizontally segmented 3 dimensional Sierpinski gasket network is constructed, whose main feature is that it contains the locally self-similar structures of the 2 dimensional Sierpinski gasket network and the 3 dimensional Sierpinski gasket network at the same time, and the scale transformation between the two kinds of self-similar structures can be controlled by adjusting the crosscutting coefficient. The analytical expression of the average trapping time on the network model is solved, which used to analyze the effect of two types of self-similar structures on the properties of random walks. Finally, we conclude that the dominant self-similar structure will exert a greater influence on the random walk process on the network.

Average Trapping time on the 3-dimensional 3-level Sierpinski gasket network with a set of trap nodes

As a basic dynamic feature on complex networks, the property of random walk has received a lot of attention in recent years. In this paper, we first studied the analytical expression of the mean global first passage time (MGFPT) on the 3-dimensional 3-level Sierpinski gasket network. Based on the self-similar structure of the network, the correlation between the MGFPT and the average trapping time (ATT) is found, and then the analytical expression of the ATT is obtained. Finally, by establishing a joint network model, we further give the standard process of solving the analytical expression of the ATT when there is a set of trap nodes in the network. By illustrating examples and numerical simulations, it can be proved that when the trap node sets are different, the ATT will be quite different, but the the super-linear relationship with the number of iterations will not be changed.

Combining Attention with Flow for Person Image Synthesis

Pose-guided person image synthesis aims to synthesize person images by transforming reference images into target poses. In this paper, we observe that the commonly used spatial transformation blocks have complementary advantages. We propose a novel model by combining the attention operation with the flow-based operation. Our model not only takes the advantage of the attention operation to generate accurate target structures but also uses the flow-based operation to sample realistic source textures. Both objective and subjective experiments demonstrate the superiority of our model. Meanwhile, comprehensive ablation studies verify our hypotheses and show the efficacy of the proposed modules. Besides, additional experiments on the portrait image editing task demonstrate the versatility of the proposed combination.

Inferring Economic Condition Uncertainty from Electricity Big Data

Inferring the uncertainties in economic conditions are of significant importance for both decision makers as well as market players. In this paper, we propose a novel method based on Hidden Markov Model (HMM) to construct the Economic Condition Uncertainty (ECU) index that can be used to infer the economic condition uncertainties. The ECU index is a dimensionless index ranges between zero and one, this makes it to be comparable among sectors, regions and periods. We use the daily electricity consumption data of nearly 20 thousand firms in Shanghai from 2018 to 2020 to construct the ECU indexes. Results show that all ECU indexes, no matter at sectoral level or regional level, successfully captured the negative impacts of COVID-19 on Shanghais economic conditions. Besides, the ECU indexes also presented the heterogeneities in different districts as well as in different sectors. This reflects the facts that changes in uncertainties of economic conditions are mainly related to regional economic structures and targeted regulation policies faced by sectors. The ECU index can also be easily extended to measure uncertainties of economic conditions in different fields which has great potentials in the future.

Logarithmic heat kernels: estimates without curvature restrictions

The main results of the article are short time estimates and asymptotic estimates for the first two order derivatives of the logarithmic heat kernel of a complete Riemannian manifold. We remove all curvature restrictions and also develop several techniques. A basic tool developed here is intrinsic stochastic variations with prescribed second order covariant differentials, allowing to obtain a path integration representation for the second order derivatives of the heat semigroup $P_t$ on a complete Riemannian manifold, again without any assumptions on the curvature. The novelty is the introduction of an $varepsilon^2$ term in the variation allowing greater control. We also construct a family of cut-off stochastic processes adapted to an exhaustion by compact subsets with smooth boundaries, each process is constructed path by path and differentiable in time, furthermore the differentials have locally uniformly bounded moments with respect to the Brownian motion measures, allowing to bypass the lack of continuity of the exit time of the Brownian motions on its initial position.

Entropy Maximization for Partially Observable Markov Decision Processes

We study the problem of synthesizing a controller that maximizes the entropy of a partially observable Markov decision process (POMDP) subject to a constraint on the expected total reward. Such a controller minimizes the predictability of an agents trajectories to an outside observer while guaranteeing the completion of a task expressed by a reward function. We first prove that an agent with partial observations can achieve an entropy at most as well as an agent with perfect observations. Then, focusing on finite-state controllers (FSCs) with deterministic memory transitions, we show that the maximum entropy of a POMDP is lower bounded by the maximum entropy of the parametric Markov chain (pMC) induced by such FSCs. This relationship allows us to recast the entropy maximization problem as a so-called parameter synthesis problem for the induced pMC. We then present an algorithm to synthesize an FSC that locally maximizes the entropy of a POMDP over FSCs with the same number of memory states. In numerical examples, we illustrate the relationship between the maximum entropy, the number of memory states in the FSC, and the expected reward.

Low Complexity Joint Impairment Mitigation of I/Q Modulator and PA Using Neural Networks

Neural networks (NNs) for multiple hardware impairments mitigation of a realistic direct conversion transmitter are impractical due to high computational complexity. We propose two methods to reduce complexity without significant performance penalty. We first propose a novel attention residual learning NN, referred to as attention residual real-valued time-delay neural network (ARDEN), where trainable neuron-wise shortcut connections between the input and output layers allow to keep the attention always active. Furthermore, we implement a NN pruning algorithm that gradually removes connections corresponding to minimal weight magnitudes in each layer. Simulation and experimental results show that ARDEN with pruning achieves better performance for compensating frequency-dependent quadrature imbalance and power amplifier nonlinearity than other NN-based and Volterra-based models, while requiring less or similar complexity.

Efficient Mining of Frequent Subgraphs with Two-Vertex Exploration

Frequent Subgraph Mining (FSM) is the key task in many graph mining and machine learning applications. Numerous systems have been proposed for FSM in the past decade. Although these systems show good performance for small patterns (with no more than four vertices), we found that they have difficulty in mining larger patterns. In this work, we propose a novel two-vertex exploration strategy to accelerate the mining process. Compared with the single-vertex exploration adopted by previous systems, our two-vertex exploration avoids the large memory consumption issue and significantly reduces the memory access overhead. We further enhance the performance through an index-based quick pattern technique that reduces the overhead of isomorphism checks, and a subgraph sampling technique that mitigates the issue of subgraph explosion. The experimental results show that our system achieves significant speedups against the state-of-the-art graph pattern mining systems and supports larger pattern mining tasks that none of the existing systems can handle.

MG-SAGC: A multiscale graph and its self-adaptive graph convolution network for 3D point clouds

To enhance the ability of neural networks to extract local point cloud features and improve their quality, in this paper, we propose a multiscale graph generation method and a self-adaptive graph convolution method. First, we propose a multiscale graph generation method for point clouds. This approach transforms point clouds into a structured multiscale graph form that supports multiscale analysis of point clouds in the scale space and can obtain the dimensional features of point cloud data at different scales, thus making it easier to obtain the best point cloud features. Because traditional convolutional neural networks are not applicable to graph data with irregular vertex neighborhoods, this paper presents an sef-adaptive graph convolution kernel that uses the Chebyshev polynomial to fit an irregular convolution filter based on the theory of optimal approximation. In this paper, we adopt max pooling to synthesize the features of different scale maps and generate the point cloud features. In experiments conducted on three widely used public datasets, the proposed method significantly outperforms other state-of-the-art models, demonstrating its effectiveness and generalizability.

Constrained Active Classification Using Partially Observable Markov Decision Processes

In this work, we study the problem of actively classifying the attributes of dynamical systems characterized as a finite set of Markov decision process (MDP) models. We are interested in finding strategies that actively interact with the dynamical system and observe its reactions so that the attribute of interest is classified efficiently with high confidence. We present a decision-theoretic framework based on partially observable Markov decision processes (POMDPs). The proposed framework relies on assigning a classification belief (a probability distribution) to the attributes of interest. Given an initial belief, confidence level over which a classification decision can be made, a cost bound, safe belief sets, and a finite time horizon, we compute POMDP strategies leading to classification decisions. We present two different algorithms to compute such strategies. The first algorithm computes the optimal strategy exactly by value iteration. To overcome the computational complexity of computing the exact solutions, we propose a second algorithm is based on adaptive sampling to approximate the optimal probability of reaching a classification decision. We illustrate the proposed methodology using examples from medical diagnosis and privacy-preserving advertising.