Umeå University's logo

Real-world networks have a complex topology comprising many elements often structured into communities. Revealing these communities helps researchers uncover the organizational and functional structure of the system that the network represents. However, detecting community structures in complex networks requires selecting a community detection method among a multitude of alternatives with different network representations, community interpretations, and underlying mechanisms. This tutorial focuses on a popular community detection method called the map equation and its search algorithm Infomap. The map equation framework for community detection describes communities by analyzing dynamic processes on the network. Thanks to its flexibility, the map equation provides extensions that can incorporate various assumptions about network structure and dynamics. To help decide if the map equation is a suitable community detection method for a given complex system and problem at hand - and which variant to choose - we review the map equation's theoretical framework and guide users in applying the map equation to various research problems.

Many real-world systems, from social networks to protein-protein interactions and species distributions, exhibit overlapping flow-based communities that reflect their functional organisation. However, reliably identifying such overlapping flow-based communities requires higher-order relational data, which are often unavailable. To address this challenge, we capitalise on the flow model underpinning the representation-learning algorithm node2vec and model higher-order flows through memory-biased random walks on first-order networks. Instead of simulating these walks, we model their higher-order dynamic constraints with compact models and control model complexity with an information-theoretic approach. Using the map equation framework, we identify overlapping modules in the resulting higher-order networks. Our compact-model approach proves robust across synthetic benchmark networks, reveals interpretable overlapping communities in empirical networks, and scales to large networks.

Deep learning (DL) models require extensive data to achieve strong performance and generalization. Deep generative models (DGMs) offer a solution by synthesizing data. Yet current approaches for tabular data often fail to preserve feature correlations and distributions during training, struggle with multi-metric hyperparameter selection, and lack comprehensive evaluation protocols. We address this gap with a unified framework that integrates training, hyperparameter tuning, and evaluation. First, we introduce a novel correlation- and distribution-aware loss function that regularizes DGMs, enhancing their ability to generate synthetic tabular data that faithfully represents the underlying data distributions. Theoretical analysis establishes stability and consistency guarantees. To enable principled hyper-parameter search via Bayesian optimization (BO), we also propose a new multi-objective aggregation strategy based on iterative objective refinement Bayesian optimization (IORBO), along with a comprehensive statistical testing framework. We validate the proposed approach using a benchmarking framework with twenty real-world datasets and ten established tabular DGM baselines. The correlation-aware loss function significantly improves the synthetic data fidelity and downstream machine learning (ML) performance, while IORBO consistently outperforms standard Bayesian optimization (SBO) in hyper-parameter selection. The unified framework advances tabular generative modeling beyond isolated method improvements. Code is available at: https://github.com/vuhoangminh/TabGen-Framework.

Alternative splicing (AS) enables cells to produce multiple protein isoforms from single genes, fine-tuning protein function across numerous cellular processes. However, despite its biological importance, researchers lack effective tools to compare the domain composition of AS-derived protein isoforms because such comparisons require both structural data and specialized methods. Recent advances in AI-driven protein structure prediction, particularly AlphaFold2, now make accurate structural determination of splicing isoforms accessible, enabling functional AS analysis at the protein structure level. Here, we present IsoformMapper, a web resource that analyzes AS through network community analysis of protein structures. This approach captures 3D physical interactions between protein regions often missed by traditional domain analysis, enabling structural comparisons of isoforms across any biological system. We illustrate our tool by analyzing validated human Bcl-X protein isoforms, revealing how AS creates distinct community structures with antagonistic functional roles. As a proof of concept, we apply our tool to investigate how GENOMES UNCOUPLED1 (GUN1)-dependent retrograde signaling regulates plant de-etiolation through alternative splicing in Arabidopsis. In response to light, gun1 shows alterations in spliceosome component expression, suggesting that GUN1 contributes to AS regulation of genes essential for photosynthetic establishment. The gun1 mutant displays altered splice variant ratios for PNSL2, CHAOS, and SIG5. Our tool reveals that these isoforms form distinct protein community structures, demonstrating how AS impacts protein function and validating IsoformMapper's practical value.

New network models of complex systems use layers, state nodes, or hyperedges to capture higher-order interactions and dynamics. Simplifying how the higher-order networks change over time or depending on the network model would be easy with alluvial diagrams, which visualize community splits and merges between networks. However, alluvial diagrams were developed for networks with regular nodes assigned to non-overlapping flat communities. How should they be defined for nodes in layers, state nodes, or hyperedges? How can they depict multilevel, overlapping communities? Here we generalize alluvial diagrams to map change in higher-order networks and provide an interactive tool for anyone to generate alluvial diagrams. We use the alluvial diagram generator in three case studies to illustrate significant changes in the organization of science, the effect of modeling network flows with memory in a citation network and distinguishing multidisciplinary from field-specific journals, and the effects of multilayer representation of a collaboration hypergraph.

Premise: Cacti are characteristic elements of the Neotropical flora and of major interest for biogeographic, evolutionary, and ecological studies. We tested global biogeographic boundaries for Neotropical Cactaceae using specimen-based occurrences, coupled with data from visual observations, as a means to tackle the known collection biases in the family.

Methods: Species richness and record density were assessed for preserved specimens and human observations, and a bioregional scheme tailored to Cactaceae was produced using the interactive web application Infomap Bioregions, based on data from 261,272 point records cleaned through automated and manual steps.

Results: We found that areas in Mexico and southwestern USA, in eastern Brazil, and along the Andean region have the greatest density of records and the highest species richness. Human observations complement information from preserved specimens substantially, especially along the Andes. We propose 24 cactus bioregions, among which the most species-rich are northern Mexico/southwestern USA, central Mexico, southern central Mexico, Central America, Mexican Pacific coast, central and southern Andes, northwestern Mexico/extreme southwestern USA, southwestern Bolivia, northeastern Brazil, and Mexico/Baja California.

Conclusions: The bioregionalization proposed shows biogeographic boundaries specific to cacti and can thereby aid further evolutionary, biogeographic, and ecological studies by providing a validated framework for further analyses. This classification builds upon, and is distinctive from, other expert-derived regionalization schemes for other taxa. Our results showcase how observation data, including citizen-science records, can complement traditional specimen-based data for biogeographic research, particularly for taxa with specific specimen collection and preservation challenges and those that are threatened or internationally protected.

Madagascar's biota is hyperdiverse and includes exceptional levels of endemicity. We review the current state of knowledge on Madagascar's past and current terrestrial and freshwater biodiversity by compiling and presenting comprehensive data on species diversity, endemism, and rates of species description and human uses, in addition to presenting an updated and simplified map of vegetation types. We report a substantial increase of records and species new to science in recent years; however, the diversity and evolution of many groups remain practically unknown (e.g., fungi and most invertebrates). Digitization efforts are increasing the resolution of species richness patterns and we highlight the crucial role of field- and collections-based research for advancing biodiversity knowledge and identifying gaps in our understanding, particularly as species richness corresponds closely to collection effort. Phylogenetic diversity patterns mirror that of species richness and endemism in most of the analyzed groups. We highlight humid forests as centers of diversity and endemism because of their role as refugia and centers of recent and rapid radiations. However, the distinct endemism of other areas, such as the grassland-woodland mosaic of the Central Highlands and the spiny forest of the southwest, is also biologically important despite lower species richness. The documented uses of Malagasy biodiversity are manifold, with much potential for the uncovering of new useful traits for food, medicine, and climate mitigation. The data presented here showcase Madagascar as a unique "living laboratory" for our understanding of evolution and the complex interactions between people and nature. The gathering and analysis of biodiversity data must continue and accelerate if we are to fully understand and safeguard this unique subset of Earth's biodiversity.

Madagascar's unique biota is heavily affected by human activity and is under intense threat. Here, we review the current state of knowledge on the conservation status of Madagascar's terrestrial and freshwater biodiversity by presenting data and analyses on documented and predicted species-level conservation statuses, the most prevalent and relevant threats, ex situ collections and programs, and the coverage and comprehensiveness of protected areas. The existing terrestrial protected area network in Madagascar covers 10.4% of its land area and includes at least part of the range of the majority of described native species of vertebrates with known distributions (97.1% of freshwater fishes, amphibians, reptiles, birds, and mammals combined) and plants (67.7%). The overall figures are higher for threatened species (97.7% of threatened vertebrates and 79.6% of threatened plants occurring within at least one protected area). International Union for Conservation of Nature (IUCN) Red List assessments and Bayesian neural network analyses for plants identify overexploitation of biological resources and unsustainable agriculture as the most prominent threats to biodiversity. We highlight five opportunities for action at multiple levels to ensure that conservation and ecological restoration objectives, programs, and activities take account of complex underlying and interacting factors and produce tangible benefits for the biodiversity and people of Madagascar.

We live in an interconnected world full of complex systems that cannot be understood simply by analyzing their components. From how genes regulate biological functions to the distribution of life on Earth, we need methods that can analyze systems as a whole.

Networks are abstractions of complex systems, helping capture properties that emerge from patterns of interactions rather than from the individual parts. To understand the patterns of interactions in large networks, we need to simplify them by discovering their modular structure that often characterizes complex systems. A hierarchical modular structure functions as a map that lets us navigate relational data efficiently and helps us see the general patterns. But how reliable is the map if it is based on incomplete data?

This thesis applies and builds upon the map equation, which is an information-theoretic method for detecting modular regularities in the flow patterns on networks. To robustly map incomplete data, we have developed three general approaches: (1) Adaptive resolution in both sampling of and dynamics on networks better fits the data. (2) Regularization avoids overfitting to random patterns. (3) Richer data can be included into the network for a more complete map. Methods that can include evolutionary relationships and handle incomplete data provide more powerful tools for mapping biodiversity in space and time.

Vi lever i en sammankopplad värld full av komplexa system som inte låter sig förstås enbart genom att analysera dess komponenter. Från hur gener reglerar biologiska funktioner till livets utbredning på jorden behöver vi metoder som kan analysera system som en helhet.

Nätverk är abstraktioner av komplexa system som hjälper till att fånga egenskaper som uppstår genom interaktionsmönster snarare än hos de enskilda delarna. För att förstå dessa mönster i stora nätverk måste vi förenkla dem genom att upptäcka dess modulära stuktur som präglar komplexa system. En hierarkisk modulär struktur fungerar som en karta som låter oss navigera effektivt i relationsdata och hjälper oss att se de allmänna mönstren. Men hur tillförlitlig är kartan om den baseras på inkompletta data?

Den här avhandlingen applicerar och bygger vidare på kartekvationen som är en informationsteoretisk metod för att upptäcka modulära regelbundenheter i flödesmönstren på nätverk.För att robust kartlägga inkompletta data har vi utvecklat tre övergripande tillvägagångssätt: (1) Adaptiv upplösning i båda sampling av och dynamik på nätverk ger bättre anpassning till data. (2) Regularisering undviker överanpassning till slumpmässiga mönster. (3) Rikare data kan inkluderas i nätverket för en mer komplett karta. Metoder som kan inkludera evolutionära relationer och hantera inkompletta data ger kraftfullare verktyg för att kartlägga den biologiska mångfalden i rum och tid.