The Students As Planetary Defenders project launched in September 2023 with a deceptively simple premise: students should not merely read about astronomy but should practice it. Over three years, the initiative engaged more than 2,000 students and nearly 500 teachers across Europe and beyond in STEM activities centered on comets, asteroids, micrometeorites and planetary defence. Rather than relying on simplified textbook exercises, the project connected participating primary and secondary schools directly to professional research infrastructure, including robotic telescope networks, meteor camera arrays and international asteroid search collaborations. The result was a generation of school students who planned observations, retrieved raw data, performed calculations and contributed to genuine scientific workflows, all while their activities were woven into school curricula and astronomy clubs through a student-centred, project-based approach.

The technical scope of what these students accomplished is remarkable for any age group, let alone for secondary school. Working with robotic telescopes from the Las Cumbres Global Observatory network, students learned to plan astronomical observations, retrieve and analyse the resulting data, and produce their own astronomical images from professional-grade instruments. This is not a simulation; the Las Cumbres network operates research-class telescopes distributed across the globe, and the same pipelines used by professional astronomers to monitor transient events were placed at the students’ disposal. Learning to schedule an observation, account for telescope availability and instrument constraints, and then process the returned frames into scientifically meaningful images gave participants a complete end-to-end experience of observational astronomy.

Meteor research formed another pillar of the project. Using the PRISMA/INAF meteor cameras and their data, students calculated meteor trajectories and mapped meteor paths with the PASCAL software, the PRISMA All-Sky Camera Analysis Laboratory, to identify possible landing areas for the recovery of meteorites. The technique relies on triangulation: when a bright meteor is recorded simultaneously by multiple all-sky cameras at known locations, the geometry of the observed paths allows researchers to reconstruct the object’s atmospheric trajectory and, crucially, to narrow down where any surviving fragments might have landed. Students mastered this workflow themselves, transforming raw camera records into candidate fall zones. It is the same methodology that professional networks use to recover freshly fallen meteorites, and it demands genuine competence in geometry, data analysis and error estimation.

The project’s asteroid search component produced tangible discoveries. In collaboration with the International Astronomical Search Collaboration, students analysed astronomical images to search for asteroids, and their efforts resulted in 72 preliminary asteroid discoveries. In this program, participants examine sequences of telescope images taken minutes apart, looking for the faint, slowly moving points of light that betray a previously uncharted object against the fixed background of stars. Each preliminary discovery must pass through confirmation pipelines before an object receives official designation, but the initial detection, the moment a student first spots an unknown worldlet drifting through the solar system, is real science performed by real observers. Seventy-two such detections from school-based teams represents a substantial contribution to the ongoing census of near-Earth and main-belt asteroids.

On the smallest scales, students collected and analysed micrometeorites through hands-on outdoor and laboratory activities. These cosmic dust particles, typically fractions of a millimetre across, rain down continuously onto Earth’s surface and can be extracted from suitable collection sites such as rooftops and gutters, then examined under microscopes and classified by their characteristic features. The work teaches magnetism, microscopy, classification and the physics of atmospheric entry in a single, tangible exercise. One student, Martina Maze, described simulating the collection of a meteorite with her science teacher Giulio Colombo and discovering how much invisible labor the process entails. Before actually doing it, she said, she did not realize all the work that went into it; once done, she realized that behind the search for a stone lies a whole commitment, since one has to recognize the stone and the meteorite itself, among many other things.

The recognition in Florence carried weight precisely because of where it occurred. The COSPAR Scientific Assembly, organized by the International Science Council’s Committee on Space Research, is the world’s premier space research conference, a biennial gathering where thousands of researchers present results across fields ranging from Earth observation and planetary protection to astrophysics and space life sciences. Presenting student achievements at the Opening Reception of such a meeting, and then sharing the StAnD experience with educators from around the world during the sessions of the COSPAR Panel on Education the following day, signaled that the scientific community regards this model of school-based research as genuinely significant. The students’ work also included the creation of a 2027 calendar featuring astronomical images produced through StAnD activities, a small artifact that encapsulates the project’s blend of rigor and accessibility.

Teachers were central to the project’s design, and StAnD invested heavily in building lasting capacity in schools. Educators were supported through a purpose-built Teacher’s Manual, an online MOOC and two summer schools, resources intended to equip them to deliver STEM topics through inclusive and interdisciplinary approaches long after the project’s formal conclusion. Tabea Mann, an accompanying teacher from Germany, highlighted how the project’s many components interlock: students can observe meteorites or asteroids with the robotic telescopes, then calculate through triangulation where they fall, and then search that area to see whether meteorites can actually be found. Giulio Colombo, Martina’s teacher, said the project gave him the opportunity to put knowledge acquired through the PRISMA project into practice at school, adding that he hopes some seeds have been planted and that meteorite researchers may emerge in the future thanks to this work.

Leaders of the space research community framed the students’ achievements in generational terms. Dr. Jean-Claude Worms, Executive Director of COSPAR, said that StAnD has shown that when students are given real scientific tools and mentorship, they become not just learners but contributors to the global space science endeavour. Rosa Doran, Chair of the COSPAR Panel on Education and President of NUCLIO, a partner in the project, said the students celebrated in Florence represent the future of space science, having demonstrated remarkable curiosity, dedication and scientific ability throughout the project. She expressed the hope that this recognition marks the beginning of their scientific journeys, and that one day the assembly might welcome them back, not as students but as researchers presenting discoveries of their own.

Behind the celebration stands a broad European partnership. StAnD was led by the Istituto Nazionale di Astrofisica in Italy, with INAF’s Osservatorio Astrofisico di Torino serving as leading partner, and brought together organizations working in astronomy, education and science outreach from Italy, France, Portugal, Greece and Germany: COSPAR, NUCLIO, Ellinogermaniki Agogi and FTP-Europlanet. Over three years the collaboration developed educational resources, teacher-training materials and practical activities designed to remain available to schools beyond the project’s lifetime, funded under Erasmus+, the European Union’s education, training, youth and sport program. As the project formally concludes, its legacy rests on a simple but powerful demonstration: space science is not merely something to read about. For more than 2,000 young people and their teachers, it became something they could actively do, and 72 preliminary asteroid discoveries, along with a cohort of students now visible on the world stage, stand as evidence that the approach works.

Subject of Research: Student participation in planetary defence research through the Erasmus+ StAnD education project

Article Title: Europe's young planetary defenders recognized on world stage as Erasmus+ StAnD Project concludes

Article References: Europe's young planetary defenders recognized on world stage as Erasmus+ StAnD Project concludes. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: planetary defence, StAnD project, Erasmus+, COSPAR, asteroid discovery, meteorites, micrometeorites, STEM education, robotic telescopes, PRISMA, INAF, space science education

The core problem the team set out to solve is one of biological interpretation. Standard trajectory inference methods frequently produce trees with multifurcations, meaning nodes where three, four, or more branches radiate from a single point. Mathematically, such high-degree branching is often the cheapest way to connect all the cells in a dataset, which is why minimum spanning tree approaches favor it. Biologically, however, a node with five simultaneous outgoing branches is hard to defend. Cell fate decisions, as conceptualized in Waddington’s famous epigenetic landscape, are typically depicted as a ball rolling down a valley that splits into two channels, not five. A binary structure, where each decision point offers at most two alternatives, aligns far more naturally with this classical picture of progressive restriction of cell potential.

To impose this binary discipline, the researchers turned to integer programming, a branch of discrete optimization in which decisions are encoded as variables restricted to whole-number values. In their formulation, the choice of which edges to include in the spanning tree becomes a set of binary variables, each indicating whether a particular connection between two cell cluster representatives is selected. The objective function minimizes the total edge weight, preserving the spirit of the minimum spanning tree, while additional constraints enforce that no node in the resulting tree exceeds a degree of two in the branching sense appropriate for trajectory topology. This transforms a problem that classical greedy algorithms such as Kruskal’s or Prim’s can solve efficiently into a harder combinatorial optimization problem, but one whose solutions carry direct biological meaning.

The degree restriction is not merely cosmetic. When an unconstrained minimum spanning tree is built over cluster centroids in a high-dimensional gene expression space, the algorithm has no incentive to respect the sequential nature of cell differentiation. It may connect a mature cell type directly to a primitive progenitor population through a shortcut that skips intermediate states, or it may hang several distinct lineages off a single hub. By capping the degree, the integer programming formulation forces the tree to route connections through intermediate nodes, producing a hierarchy in which each branching event represents a discrete, interpretable fate choice. The result is a topology that reads like a family tree of cell states rather than a tangled web of shortest connections.

A key practical strength of the new method is its modularity. Rather than building a complete trajectory pipeline from scratch, the authors implemented their degree-restricted tree construction as a plug-in module that can be inserted into existing graph-based and tree-based trajectory inference frameworks. To demonstrate this flexibility, they integrated the module into Slingshot, one of the most widely used pseudotime inference tools in the single-cell genomics community. Slingshot traditionally constructs a minimum spanning tree over cluster centroids and then fits principal curves along its branches to order cells in pseudotime. By swapping the unconstrained tree for the degree-restricted one, the researchers showed that the downstream pseudotime machinery can operate on a topology that is simultaneously cost-efficient and biologically constrained.

Validation of the constrained topologies required an independent reference against which the reconstructed trees could be compared. The team turned to CoSpar, a method that infers cell fate hierarchies using lineage information, often derived from experimental lineage tracing. By evaluating the consistency of their degree-restricted trees against a CoSpar-derived reference hierarchy, the authors could assess whether the binary constraint, imposed purely on the basis of expression data and optimization, recovered relationships that an orthogonal lineage-aware approach also supports. This cross-method consistency check is important because trajectory inference is notoriously sensitive to the assumptions baked into any single algorithm, and agreement between structurally different approaches lends credibility to the inferred hierarchy.

The researchers applied their framework to three biologically rich datasets: bone marrow mononuclear cells, human fetal immune cells, and a mouse hematopoiesis dataset. Hematopoiesis, the process by which blood cells are generated, is a canonical testing ground for trajectory methods because its branching structure, from stem cells through progenitors to mature lineages, has been mapped in detail over decades of experimental work. Across these datasets, the degree-restricted trees produced trajectories whose branching patterns were more interpretable than those generated by unconstrained minimum spanning tree baselines. The comparison with the unconstrained baselines was descriptive rather than a claim of universal superiority, but it illustrated concretely how the binary constraint reshapes the inferred lineage structure into forms that match developmental expectations.

Behind the biological narrative lies a substantial computational challenge. Minimum spanning trees can be computed in near-linear time for the number of edges considered, but degree-constrained spanning tree problems belong to a family of combinatorial optimization problems that are computationally hard in general. Integer programming solvers handle such problems by exploring the space of feasible integer solutions with techniques such as branch and bound, cutting planes, and linear programming relaxations. The feasibility of the approach at the scale of single-cell datasets, where cluster-level graphs may contain dozens to hundreds of nodes after preprocessing and clustering, depends on careful formulation that keeps the integer program tractable. The authors’ decision to operate at the level of cluster representatives rather than individual cells is central to this tractability, since it dramatically reduces the number of nodes over which the constrained tree must be built.

The conceptual appeal of the method extends beyond hematopoiesis. Waddington’s epigenetic landscape, sketched in the 1950s as a metaphor for how cells navigate a landscape of developmental potential, has become a guiding intuition for the entire field of pseudotime analysis. Yet most computational implementations of trajectory inference treat topology as an emergent property of the data rather than an explicit modeling choice. By encoding the binary branching structure directly into the optimization objective and constraints, the new approach makes the Waddingtonian assumption a formal part of the inference procedure. This explicitness is a virtue: it allows users to see exactly what biological prior is being imposed, and it opens the door to future variants in which different degree restrictions or additional structural constraints could encode other hypotheses about how cell states relate.

The work, led by Jiaying Zhao and Takuma Iwaki, who contributed equally, together with Tomoya Mori, Wai-Ki Ching, and Tatsuya Akutsu, was supported by the Hong Kong Research Grants Council and released as open access, with source code publicly available on GitHub for researchers who wish to integrate the degree-restricted module into their own pipelines. As single-cell RNA sequencing continues to generate atlases of ever greater scale and complexity, the demand for trajectory inference methods that are both computationally principled and biologically legible will only grow. This study demonstrates that ideas from discrete optimization, a field seemingly distant from developmental biology, can supply exactly the kind of structural discipline that turns a tangle of gene expression similarities into a readable map of cellular destiny.

Subject of Research: Degree-restricted minimum spanning tree algorithms for binary cell trajectory inference in single-cell RNA-seq data

Article Title: Degree-restricted minimum spanning trees for binary cell trajectory inference in single-cell RNA-seq data

Article References: Zhao, J., Iwaki, T., Mori, T., Ching, W.-K., & Akutsu, T. (2026). Degree-restricted minimum spanning trees for binary cell trajectory inference in single-cell RNA-seq data. BMC Bioinformatics. https://doi.org/10.1186/s12859-026-06674-y

Image Credits: AI Generated

DOI: 10.1186/s12859-026-06674-y

Keywords: single-cell RNA-seq, trajectory inference, pseudotime, minimum spanning tree, integer programming, Waddington's epigenetic landscape, hematopoiesis, Slingshot, CoSpar, cell fate decisions, computational biology, discrete optimization