Continual learning (CL) focuses on the ability of models to learn sequentially from a stream of tasks. A major challenge in CL is catastrophic forgetting (CF). CF is a phenomenon where the model experiences significant performance degradation on previously learned tasks after training on new tasks. Although CF is commonly observed in convolutional neural networks (CNNs), the theoretical understanding about CF within CNNs remains limited. To fill the gap, we present a theoretical analysis of CF in a two-layer CNN. By employing a multi-view data model, we analyze the learning dynamics of different features throughout CL and derive theoretical insights. The findings are supported by empirical results from both simulated and real-world datasets.

Sparse ridge regression problems play a significant role across various domains. To solve sparse ridge regression, Liu et al. (2023) recently propose an advanced algorithm, Scalable Optimal $K$-Sparse Ridge Regression (OKRidge), which is both faster and more accurate than existing approaches. However, the absence of theoretical analysis on the error of OKRidge impedes its large-scale applications. In this paper, we reframe the estimation error of OKRidge as a Primary Optimization ($\textbf{PO}$) problem and employ the Convex Gaussian min-max theorem (CGMT) to simplify the $\textbf{PO}$ problem into an Auxiliary Optimization ($\textbf{AO}$) problem. Subsequently, we provide a theoretical error analysis for OKRidge based on the $\textbf{AO}$ problem. This error analysis improves the theoretical reliability of OKRidge. We also conduct experiments to verify our theorems and the results are in excellent agreement with our theoretical findings.

Synthetic aperture radar tomography (TomoSAR) is widely used for 3-D imaging in urban environments. Reference network (RN) technology has emerged as an effective solution in TomoSAR, leveraging a spatially correlated network of persistent scatterers (PSs) to mitigate the atmospheric phase screen (APS), a significant source of error in multipass spaceborne SAR systems. An effective RN should connect sufficient PSs with reliable edges, thereby ensuring comprehensive tomographic imaging of PSs and other scatterers around PSs. However, RN construction faces challenge in simultaneously addressing both network connectivity and quality during RN construction. To resolve this issue, this article introduces an innovative approach for constructing an optimal RN based on the minimum spanning tree (MST-RN). In this approach, the paradigm for determining the optimal RN is transformed into the problem of finding the MST in which the relative elevation estimation quality of the edge in RN is regarded as their weight in MST. Furthermore, standardized metrics are proposed to comprehensively evaluate the effectiveness of RN. The proposed MST-RN method demonstrates superior effectiveness on the metrics including overall connectivity quality, PS candidate (PSC) coverage, and network redundancy, compared to existing methodologies, which underscores the significant progress made in the RN construction. Finally, the effectiveness of the proposed method is validated through experiments conducted on the TerraSAR-X dataset acquired in Shenzhen, China, demonstrating accurate height estimation of PSs in urban areas.

In sub-second stream computing, the answer to a complex query usually depends on operations of aggregation or join on streams, especially multi-way theta join. Some attribute keys are not distributed uniformly, which is called the data intrinsic skew problem, such as taxi car plate in GPS trajectories and transaction records, or stock code in stock quotes and investment portfolios etc. In this paper, we define the concept of key redundancy for single stream as the degree of data intrinsic skew, and joint key redundancy for multi-way streams. We present an execution model for multi-way stream theta joins with a fine-grained cost model to evaluate its performance. We propose a solution named Group Join (GroJoin) to make use of key redundancy during transmission and execution in a cluster. GroJoin is adaptive to data intrinsic skew in the way that it depends on the grouping condition we find out, i.e., the selectivity of theta join results should be smaller than 25%. Experiments are carried out by our MS-Generator to produce multi-way streams, and the simulation results show that GroJoin can decrease at most 45% transmission overheads with different key redundancies and value-key proportionality coefficients, and reduce at most 70% query delay with different key distributions. We further implement GroJoin in Multi-Way Stream Theta Join by Spark Streaming. The experimental results demonstrate that there are about 40%~50% join latency reduced after our optimization with a very small computation cost.

Because phylogenetic inference is an important basis for answering many evolutionary problems, a large number of algorithms have been developed. Some of these algorithms have been improved by integrating gene evolution models with the expectation of accommodating the hierarchy of evolutionary processes. To the best of our knowledge, however, there still is no single unifying model or algorithm that can take all evolutionary processes into account through a stepwise or simultaneous method. On the basis of three existing phylogenetic inference algorithms, we built an integrated pipeline for inferring the evolutionary history of a given gene family; this pipeline can model gene sequence evolution, gene duplication-loss, gene transfer and multispecies coalescent processes. As a case study, we applied this pipeline to the STIMATE (TMEM110) gene family, which has recently been reported to play an important role in store-operated Ca 2+ entry (SOCE) mediated by ORAI and STIM proteins. We inferred their phylogenetic trees in 69 sequenced chordate genomes. By integrating three tree reconstruction algorithms with diverse evolutionary models, a pipeline for inferring the evolutionary history of a gene family was developed, and its application was demonstrated.

In this paper, we develop a framework for the modeling, analysis, and computation of solutions to a supply chain supernetwork with electronic commerce. The association processes between the manufacturers and the consumers are accomplished through the Internet. Manufacturers are assumed to produce homogeneous materiality products, faced with the criteria - the maximum profit. And the demand markets can purchase the products from the manufacturers according to their economic status through Internet. Then, logistics department union is the combination of a manufacturer's order management, inventory, transportation, warehousing, materials handling, and packaging as integrated throughout the supply chain supernetwork. Hereon this base, the optimality conditions for the manufacturers, the logistics department union and the demand markets are established using the variational inequality. Then we describe the win-win situation for the supply chain supernetwork model; get the stationary points for this situation. And an example is illustrated to validate the utility of the model in the last part

In this paper, an effective algorithm is developed to detect and track multiple people in a specific area. It advances a target detecting algorithm based on projection of grayscale image, while specifying a value function uniting the features which are relatively unchanged for target tracking. Based on our algorithms, the result indicates a system that relatively needs less operations while the precision and efficiency are improved. The system has a certain self-adaptive capability.