To date, many interesting subclasses of analytic functions involving symmetrical points and other well celebrated domains have been investigated and studied. The aim of our present investigation is to make use of certain Janowski functions and a Mathieu-type series to define a new subclass of analytic (or invariant) functions. Our defined function class is symmetric under rotation. Some useful results like Fekete-Szegö functional, a number of sufficient conditions, radius problems, and results related to partial sums are derived.

With the extensive use of peer-to-peer applications in recent years, the network traffic becomes more dynamic and less predictable, which leads to the decline of network resource utilization and the degradation of network performance. Aiming towards the above problems, we explore how to strengthen the cooperation between peer-to-peer applications and networks, making the application adjust its own traffic mode according to current network traffic status to enhance the stability of network traffic. We improve two key algorithms of peer selection and choking/unchoking in the protocol and introduce traffic relaxation to characterize traffic state while taking the current most popular peer-to-peer application (bit torrent protocol) as an example. In our improved method, peers are selected probabilistically according their traffic relaxation, and the double-parameter selection problem that simultaneously considers the traffic relaxation and transfer rate of peers is also solved. Finally, we conduct simulation experiments in two real network typologies with real traffic matrix data and different sizes of bit torrent swarms; the experimental results show that our method can significantly improve the stability of the network traffic without sacrificing or even improving the performance of the bit torrent protocol when compared with original BT protocol.

Solving Mathematics Word Problem (MWP) is a basic ability of humanity, which can be mastered by most students at a young age. The existing artificial intelligence system is not good enough in numerical questions, like MWPs. The hard part of this problem is translating natural language sentences in MWP into mathematical expressions or equations. In recent researches, the Transformer network, which proved a great success in machine translation, is applied to automatic mathematic word problem-solving. While previous works have only shown the ability of Transformer model in MWP, how multiple factors such as encoding, decoding, and pre-training affect the performance of Transformer model has not received enough attention. The study is the first to examine the role of these factors experimentally. This paper proposes several methods to improve Transformer network performance in MWPs under the basis of previous studies, achieves higher accuracy compared to the previous state of the art. Pre-training on target tasks dataset improves the translation quality of the Transformer model greatly. Different token encoding and search algorithms also benefit prediction accuracy at the expense of more training and testing time.

Chinese characters are one of the logographic writing systems. There is some association between semantics and structures, shape, phonetic information of Chinese characters. In this work, multi-modal Chinese character-level embeddings are extracted, including visual features, pre-trained embeddings, shapes, and phonetic information. These embedding sequences of Chinese sentences are first fed into individual Bi-LSTM networks to capture context features, and then fused into one vector for sentiment analysis. Experimental results validate that multi-modal character-level can contribute to Chinese sentence sentiment classification. And its effect on the result is analyzed by modal features ablation test.

Reliable methods for localizing functional components in neural networks are essential for interpretability research. Sparse autoencoders (SAEs) have recently emerged as a popular decomposition of neural representations, promising interpretable sub-component granularity for causal intervention: rather than ablating an entire layer, one may ablate individual learned features. However, the measurement discrimination of SAE-based intervention — its ability to reliably distinguish the importance of different components — has not been systematically evaluated. We propose a two-dimensional evaluation framework, Measurement Discrimination Index (MDI) and signal-to-noise ratio (SNR), supported by a five-group controlled experimental design that isolates reconstruction noise (G2), random-feature ablation (G3), and residual-stream baselines (G4). Across three standard circuits (indirect object identification, greater-than comparison, and docstring completion) on GPT-2 Small, we find that SAE intervention effectiveness is highly circuit-dependent: it provides substantial discrimination on IOI (MDI = 0.59, pure effect = +0.50) while failing on Docstring, where reconstruction noise (G2 = 0.76) swamps the intervention signal and the raw MDI (0.54) — comparable to IOI's — is revealed as misleading by the near-zero SNR. We replicate the core finding across architectures with Gemma-2-2B: the IOI sweet spot is recovered (MDI = 0.60 vs. 0.59), but its location shifts from layer 9 to layer 3, demonstrating that layer selection must be data-driven. We also uncover a tokenization portability failure: the greater-than circuit, well-posed under GPT-2 tokenization, becomes ill-posed under Gemma's finer-grained digit tokenization, where multi-token answers share a saturated leading token. We conclude with practical guidelines for reporting reconstruction noise and verifying tokenization portability in SAE intervention studies.