In the context of global warming, the accurate prediction of Arctic Sea Ice Concentration (SIC) is crucial for the development of Arctic shipping routes. We have therefore constructed a lightweight, non-recursive spatio-temporal prediction model, the Spatio-Temporal Decomposition Network (STDNet), to predict the daily SIC in the Arctic. The model is based on the Seasonal and Trend decomposition using Loess (STL) decomposition idea to decompose the model into trend and seasonal components. In addition, we have designed the Global Sparse Attention Module (GSAM) to help the model extract global information. STDNet not only extracts seasonal signals and trend information with periodical correspondence from the data but also obtains the spatio-temporal dependence features in the data. The experimental methodology involves predicting the next 10 days based on the first 10 days of data. The prediction results provided the following metrics for the 10-day forecast of STDNet: Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), and coefficient of determination of 1.988%, 3.541%, 5.843%, and 0.979, respectively. The average Binary Accuracy (BACC) at the beginning of September for the period 2018–2022 reached 93.85%. The proposed STDNet model outperforms and is lighter than existing deep-learning-based SIC prediction models.

A universal word for a finite alphabet $A$ and some integer $n\geq 1$ is a word over $A$ such that every word in $A^n$ appears exactly once as a subword (cyclically or linearly). It is well-known and easy to prove that universal words exist for any $A$ and $n$. In this work we initiate the systematic study of universal partial words. These are words that in addition to the letters from $A$ may contain an arbitrary number of occurrences of a special `joker' symbol $\Diamond\notin A$, which can be substituted by any symbol from $A$. For example, $u=0\Diamond 011100$ is a linear partial word for the binary alphabet $A=\{0,1\}$ and for $n=3$ (e.g., the first three letters of $u$ yield the subwords $000$ and $010$). We present results on the existence and non-existence of linear and cyclic universal partial words in different situations (depending on the number of $\Diamond$s and their positions), including various explicit constructions. We also provide numerous examples of universal partial words that we found with the help of a computer.

This paper generalizes the structural Markov properties for undirected decomposable graphs to arbitrary ones. This helps us to exploit the conditional independence properties of joint prior laws to analyze and compare multiple graphical structures, while being able to take advantage of the common conditional independence constraints. This work provides a theoretical support for full Bayesian posterior updating about the structure of a graph using data from a certain distribution. We further investigate the ratio of graph law so as to simplify the acceptance probability of the Metropolis–Hastings sampling algorithms.