Multivariate Time Series (MTS) forecasting entails the intricate process of modeling temporal dependencies within historical data records. Transformers have demonstrated remarkable performance in MTS forecasting due to their capability to capture long-term dependencies. However, prior work has been confined to modeling temporal dependencies at either a fixed scale or multiple scales that exponentially increase (most with base 2). This limitation impedes their capacity to effectively capture diverse seasonalities. In our study, we present a dimension-invariant embedding technique designed to capture short-term temporal dependencies. This procedure projects MTS data into a higher-dimensional space while preserving the original time steps and variable dimensions. Furthermore, we present a novel Multi-scale Transformer Pyramid Network (MTPNet), specifically designed to capture temporal dependencies at multiple unconstrained scales effectively. The predictions are inferred from multi-scale latent representations obtained from transformers at various scales. Extensive experiments on nine benchmark datasets demonstrate that the proposed MTPNet outperforms recent state-of-the-art methods. This enhancement in performance is particularly pronounced in datasets rich in fine-scale information, as it enables MTPNet to effectively capture a wide spectrum of temporal dependencies, ranging from fine to coarse scales. This finding highlights MTPNet’s notable potential in analyzing MTS data sampled at the minute level. Code is available at github.com/MTPNet.

Networks provide effective models to study complex biological systems, such as gene and protein interaction networks. With the advent of new sequencing technologies, many life scientists are grasping for user-friendly methods and tools to examine biological components at the whole-systems level. Gene co-expression network analysis approaches are frequently used to successfully associate genes with biological processes and demonstrate great potential to gain further insights into the functionality of genes, thus becoming a standard approach in Systems Biology. Here the objective is to construct biologically meaningful and statistically strong co-expression networks, the identification of research dependent subnetworks, and the presentation of self-contained results. We introduce petal, a novel approach to generate gene co-expression network models based on experimental gene expression measures. petal focuses on statistical, mathematical, and biological characteristics of both, input data and output network models. Often over-looked issues of current co-expression analysis tools include the assumption of data normality, which is seldom the case for hight-throughput expression data obtained from RNA-seq technologies. petal does not assume data normality, making it a statistically appropriate method for RNA-seq data. Also, network models are rarely tested for their known typical architecture: scale-free and small-world. petal explicitly constructs networks based on both these characteristics, thereby generating biologically meaningful models. Furthermore, many network analysis tools require a number of user-defined input variables, these often require tuning and/or an understanding of the underlying algorithm; petal requires no user input other than experimental data. This allows for reproducible results, and simplifies the use of petal. Lastly, this approach is specifically designed for very large high-throughput datasets; this way, petal’s network models represent as much of the entire system as possible to provide a whole-system approach. petal is a novel tool for generating co-expression network models of whole-genomics experiments. It is implemented in R and available as a library. Its application to several whole-genome experiments has generated novel meaningful results and has lead the way to new testing hypothesizes for further biological investigation.