Yuankui Ma

As a task in the digital preservation of calligraphy stone inscriptions, an invaluable cultural heritage, style classification faces prominent challenges: insufficient feature representation of single-channel rubbings, and difficulties in effectively capturing the complex strokes and spatial layouts inherent to calligraphic works. To tackle these issues, an efficient deep learning model integrated with the dual-path attention mechanism of Bottleneck Attention Module (BAM) is proposed in this paper, which is designed to achieve accurate and efficient classification of calligraphy styles. With the lightweight network EfficientNetB2 as its backbone, this model innovatively integrates the BAM. It realizes the channel-spatial collaborative attention in calligraphy analysis, with the weight of stroke structure features increased to over 85%. Through the synergistic effect of channel attention and spatial attention, the model’s ability to extract stroke structure and spatial layout features from calligraphy images is significantly enhanced. The experimental results on the stratified sampling dataset show that the model achieves an accuracy of 98.44% on the test set, a confusion matrix recall rate of 94.80%, an F1-score of 0.9675, a precision of 0.8690, and a macro-averaged Area Under the Curve (AUC) value of 0.9694. To further validate the effectiveness of the BAM module and the necessity of its dual-path design, we conducted a systematic ablation experiment analysis. The experiment used EfficientNet-B2 as the baseline model and sequentially compared the contributions of different attention mechanisms. The experimental results show that the method proposed in this paper balances efficiency and performance, and holds practical significance in fields such as ancient book authentication and calligraphy research.

This paper introduces fully Dowling polynomials of the first and second kinds, which are degenerate versions of the ordinary Dowling polynomials. Then, several important identities for these degenerate polynomials are derived. The relationship between fully degenerate Dowling polynomials and fully degenerate Bell polynomials, degenerate Bernoulli polynomials, degenerate Euler polynomials, and so on is obtained using umbral calculus.

Let [ ] be a random variable whose moment generating function exists in a neighborhood of the origin. The probabilistic central Bell polynomials associated with the random variable [ ] are investigated in this paper, as probabilistic extension of the central Bell polynomials. Furthermore, we consider the probabilistic central Fubini polynomials associated with [ ] and the probabilistic central factorial numbers of the second order associated with [ ]. The aim of this research is to obtain some characteristics, explicit expressions, specific identities, and recurrence relations for those numbers and polynomials.

Let [ ] be a random variable whose moment generating function exists in a neighborhood of the origin. Recently, the degenerate Euler (Bernoulli) polynomials of complex variable have been studied. In this paper, as probabilistic extensions of those polynomials, we study the probabilistic degenerate Euler (Bernoulli) polynomials of complex variable associated with [ ]. In addition, we investigate probabilistic extensions of the degenerate cosine-Euler (sine-Euler) polynomials, the degenerate cosine-Bernoulli (sine-Bernoulli) polynomials and the degenerate cosine (sine) polynomials. The aim of this paper is to derive several fundamental properties, identities and explicit expressions for those probabilistic extensions of special polynomials by using generating functions.

In this paper, we define probabilistic fully degenerate Bell polynomials associated with [ ], which are probabilistic versions of fully degenerate Bell polynomials. Meanwhile, we also derive some combinatorial identities and properties related to probabilistic fully degenerate Bell polynomials, partial Bell polynomials and other special polynomials and numbers.

Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to study the probabilistic degenerate poly-Bell polynomials associated with the random variable Y, arising from the degenerate polyexponential functions, which are probabilistic extensions of degenerate versions of the poly-Bell polynomials. We derive several explicit expressions and some related identities for them. In addition, we consider the special cases that Y is the Bernoulli random variable with probability of success p or the gamma random variable with parameters 1,1.

In this paper, we define the probabilistic degenerate Laguerre polynomials associated with random variables and the probabilistic degenerate generalized Laguerre polynomials associated with random variables. We investigate some expressions, recurrence relations, and properties associated with the probabilistic degenerate Laguerre polynomials, the probabilistic degenerate generalized Laguerre polynomials, the probabilistic Lah numbers, and the partial Bell polynomials. DOI 10.1134/S1061920824040095