Modelling biological systems depends on the availability of data and components of the system at hand. As our understanding of these systems evolves, the ability to gradually refine models by adding new components of different formalisms covering stochastic, discrete, deterministic, and uncertainty without starting from scratch becomes essential. However, there remains a significant gap in the availability of methodologies and tool support for incrementally modelling and analysing complex biological systems in a flexible and intuitive manner. In this paper, we employ fuzzy hybrid Petri nets as a powerful expressive tool for presenting an incremental modelling and analysis protocol of biological systems. We demonstrate the utility of our protocol through a case study on cholesterol and lipoprotein metabolism and hypercholesterolemia therapy. Our model not only captures the underlying biochemical processes, but also quantitatively analyses how cholesterol levels are regulated, offering insights into potential therapeutic strategies for diseases associated with elevated cholesterol levels. The results confirm the validity and flexibility of our approach in representing complex biological processes and therapeutic interventions.

MOTIVATION: Accurate tumor subtype diagnosis is crucial for precision oncology, yet current methodologies face significant challenges. These include balancing model accuracy with interpretability and the high costs of generating multi-omics data in clinical settings. Moreover, there is a lack of validated models capable of classifying hierarchical tumor subtypes across a comprehensive pan-cancer cohort. RESULTS: We present a graph neural network, HallmarkGraph, the first biologically informed model developed to classify hierarchical tumor subtypes in human cancer. Inspired by cancer hallmarks, the model's architecture integrates transcriptome profiles and gene regulatory interactions to perform multi-label classification. We evaluate the model on a comprehensive pan-cancer cohort comprising 11 476 samples from 26 primary cancers with 405 subtypes up to eight levels. The model demonstrates exceptional performance, achieving 5-fold cross-validation accuracy between 85% and 99% for tumor subtypes labeled with increasing details of genomic information. It also shows good generalizability on a validation dataset of 887 samples, assessed using three metrics that consider tumor subtypes at individual, combined, and sample levels. Benchmarking and ablation experiments show that hallmark-based embeddings slightly influence model performance, while the integrated multilayer perceptron plays a significant role in determining classifier accuracy. Additionally, we use the SHAP method to link cancer hallmarks with genes, identifying key features that influence model decisions. Our findings present a biologically informed machine learning framework capable of tracking tumor transcriptomic trajectories and distinguishing inter- and intra-tumor heterogeneity in pan-cancer. This approach holds promise for enhancing cancer diagnostics. AVAILABILITY AND IMPLEMENTATION: HallmarkGraph is accessible at https://github.com/laixn/HallmarkGraph.

Zero-shot skeleton-based action recognition aims to classify unseen skeleton-based human actions without prior exposure to such categories during training. This task is extremely challenging due to the difficulty in generalizing from known to unknown actions. Previous studies typically use two-stage training: pre-training skeleton encoders on seen action categories using cross-entropy loss and then aligning pre-extracted skeleton and text features, enabling knowledge transfer to unseen classes through skeleton-text alignment and language models' generalization. However, their efficacy is hindered by 1) insufficient discrimination for skeleton features, as the fixed skeleton encoder fails to capture necessary alignment information for effective skeleton-text alignment; 2) the neglect of alignment bias between skeleton and unseen text features during testing. To this end, we propose a prototype-guided feature alignment paradigm for zero-shot skeleton-based action recognition, termed PGFA. Specifically, we develop an end-to-end cross-modal contrastive training framework to improve skeleton-text alignment, ensuring sufficient discrimination for skeleton features. Additionally, we introduce a prototype-guided text feature alignment strategy to mitigate the adverse impact of the distribution discrepancy during testing. We provide a theoretical analysis to support our prototype-guided text feature alignment strategy and empirically evaluate our overall PGFA on three well-known datasets. Compared with the top competitor SMIE method, our PGFA achieves absolute accuracy improvements of 22.96%, 12.53%, and 18.54% on the NTU-60, NTU-120, and PKU-MMD datasets, respectively.

Computational biological models have proven to be an invaluable tool for understanding and predicting the behaviour of many biological systems. While it may not be too challenging for experienced researchers to construct such models from scratch, it is not a straightforward task for early stage researchers. Design patterns are well-known techniques widely applied in software engineering as they provide a set of typical solutions to common problems in software design. In this paper, we collect and discuss common patterns that are usually used during the construction and execution of computational biological models. We adopt Petri nets as a modelling language to provide a visual illustration of each pattern; however, the ideas presented in this paper can also be implemented using other modelling formalisms. We provide two case studies for illustration purposes and show how these models can be built up from the presented smaller modules. We hope that the ideas discussed in this paper will help many researchers in building their own future models.

Text-to-image synthesis aims to generate realistic images conditioned on text descriptions. To fuse text information into synthesized images, conditional affine transformations (CATs), such as conditional batch normalization (CBN) and conditional instance normalization (CIN), are usually used to predict batch statistics of different layers. However, ordinary CAT blocks control the batch statistics independently disregarding the consistency among neighboring layers. To address the above issue, we propose a new fusion approach names recurrent affine transformation (RAT) for synthesizing images conditioned on text information. RAT connects all the CAT blocks with recurrent connections for explicitly fitting the temporal consistency between CAT blocks. To verify the effectiveness of RAT, we propose a novel visualization method to show how generative adversarial network (GAN) fuses conditional information. Our microscopic and macroscopic visualizations not only demonstrate the effectiveness of RAT but also turn out to be a useful perspective to analyze how GAN fuses conditional information. In addition, we propose a more stable spatial attention mechanism for the discriminator, which helps the text description to supervise the generator to synthesize more relevant image contents. Extensive experiments on the CUB, Oxford-102, and COCO datasets demonstrate the proposed model's superiority in comparison to state-of-the-art models. Our code is available onhttps://github.com/senmaoy/RAT-GAN.

As a revolutionary auction mechanism for display advertising, real-time bidding (RTB) allows advertisers to purchase individual ad impressions through real-time auctions. In RTB, the demand-side platform (DSP) acts as advertisers' bidding agent and aims at developing appropriate bidding strategies to maximize their specific key performance indicators (KPIs). Existing bidding strategies perform well for optimizing profits when the ad budget severely limited. However, when there is sufficient budget, their performance deteriorates. This results in added complexity for advertisers when applying these approaches in practice, hindering wider adoption. To address this challenging limitation, we propose the Adaptive ROI-Aware Bidding (ARAB) approach. It intelligently analyzes the budget setting and auction market conditions, and adjusts the bidding function accordingly to optimize profits. Different from previous studies that only bid based on the ad revenue, our proposed ROI-aware bidding function also takes into account the ad cost at impression-level. By doing so, ARAB dynamically allocates the budget on more cost-effective impressions to increase profits. Through extensive offline experiments on two real-world public datasets, we demonstrate that the proposed ARAB has achieved significant improvements in terms of both profit and ROI compared to state-of-the-art approaches.

Integrated modelling of biological systems is becoming a necessity for constructing models containing the major biochemical processes of such systems in order to obtain a holistic understanding of their dynamics and to elucidate emergent behaviours. Hybrid modelling methods are crucial to achieve integrated modelling of biological systems. This paper reviews currently popular hybrid modelling methods, developed for systems biology, mainly revealing why they are proposed, how they are formed from single modelling formalisms and how to simulate them. By doing this, we identify future research requirements regarding hybrid approaches for further promoting integrated modelling of biological systems.

Modeling and simulation are becoming indispensable tools for studying multicellular events such as pattern formation during embryonic development. In this paper, we propose a new approach for analyzing multicellular biological phenomena by combining colored hybrid Petri nets (ColHPNs) with newly devised biological experiments that can control level of a gene quantitatively. With this approach, we analyzed patterning of the boundary cells in the Drosophila large intestine, where one-cell-wide domain of boundary cells differentiate through Delta-Notch signaling. Biological experiments regulating the level of Delta resulted in six distinct patterns of boundary cells correlating with the level of Delta. All these patterns were successfully reproduced by simulation based on ColHPN modeling only by changing the parameter related to the level of Delta. By monitoring the concentration of the active form of Notch in each cell during simulation, it was revealed that these distinct modes of patterning correlate with the fluctuation range of active Notch. Combination of simulation and quantitative manipulation of a gene activity described here is a reliable and powerful approach for analyzing and understanding the patterning process regulated by Notch signaling. This approach can be easily adapted to address other similar pattern formation issues in the systems biology area.

Integrated modelling of biological systems is challenged by composing components with sufficient kinetic data and components with insufficient kinetic data or components built only using experts' experience and knowledge. Fuzzy continuous Petri nets (FCPNs) combine continuous Petri nets with fuzzy inference systems, and thus offer an hybrid uncertain/certain approach to integrated modelling of such biological systems with uncertainties. In this paper, we give a formal definition and a corresponding simulation algorithm of FCPNs, and briefly introduce the FCPN tool that we have developed for implementing FCPNs. We then present a methodology and workflow utilizing FCPNs to achieve hybrid (uncertain/certain) modelling of biological systems illustrated with a case study of the Mercaptopurine metabolic pathway. We hope this research will promote the wider application of FCPNs and address the uncertain/certain integrated modelling challenge in the systems biology area.

The modelling of biological systems is accompanied with epistemic uncertainties that range from structural uncertainty to parametric uncertainty due to such limitations as insufficient understanding of the underlying mechanism and incomplete measurement data of a system. Fuzzy logic approaches such as fuzzy Petri nets (FPNs) are effective in addressing these issues. In this paper, we review FPNs that have been used for modelling uncertain biological systems, which we classify in three categories: basic fuzzy Petri nets, fuzzy quantitative Petri nets and Petri nets with fuzzy kinetic parameters. For each category of these FPNs, we summarize its modelling capabilities and current applications, discuss its merits and drawbacks and give suggestions for further research. This understanding on how to use FPNs for modelling uncertain biological systems will assist readers in selecting appropriate FPN classes for specific modelling circumstances. This review may also promote the extensive research and application of FPNs in the systems biology area.

Owing to the availability of data of one biological phenomenon at different levels/scales, modelling of biological systems is moving from single level/scale to multiple levels/scales, which introduces a number of challenges. Coloured Petri nets (ColPNs) have been successfully applied to multilevel, multiscale and multidimensional modelling of some biological systems, addressing many of these challenges. In this article, we first review the basics of ColPNs and some popular extensions, and then their applications for multilevel, multiscale and multidimensional modelling of biological systems. This understanding of how to use ColPNs for modelling biological systems will assist readers in selecting appropriate ColPN classes for specific modelling circumstances.

Modeling across multiple scales is a current challenge in Systems Biology, especially when applied to multicellular organisms. In this paper, we present an approach to model at different spatial scales, using the new concept of Hierarchically Colored Petri Nets (HCPN). We apply HCPN to model a tissue comprising multiple cells hexagonally packed in a honeycomb formation in order to describe the phenomenon of Planar Cell Polarity (PCP) signaling in Drosophila wing. We have constructed a family of related models, permitting different hypotheses to be explored regarding the mechanisms underlying PCP. In addition our models include the effect of well-studied genetic mutations. We have applied a set of analytical techniques including clustering and model checking over time series of primary and secondary data. Our models support the interpretation of biological observations reported in the literature.