Phylogenetic invariants are equations that vanish on algebraic varieties associated with Markov processes that model molecular substitutions on phylogenetic trees. For practical applications, it is essential to understand these equations across a wide range of substitution models. Recent work has shown that, for equivariant models, phylogenetic invariants can be derived from those of the general Markov model by restricting to the linear space defined by the model (namely, the space of mixtures of distributions on the model). Following this philosophy, we describe the space of mixtures and phylogenetic invariants for time-reversible models that are not equivariant. Specifically, we study two submodels of the Tamura-Nei nucleotide substitution model (Felsenstein 81 and 84) using an orthogonal change of basis recently introduced for algebraic time-reversible models. For tripods, we prove that the algebraic variety of each submodel coincides with the variety of Tamura-Nei intersected with the linear space of the submodel. In the case of quartets, we show that it is an irreducible component of this intersection. Moreover, we demonstrate that it suffices to consider only the binomial equations defining the linear space, which correspond to the natural symmetries of the model in the new coordinates. For each submodel, we explicitly provide equations defining a local complete intersection that characterizes the phylogenetic variety on a dense open subset containing the biologically relevant points.
Monitoring biodiversity in agricultural landscapes is essential for addressing global biodiversity decline. Emerging remote sensing and artificial intelligence technologies enable large-scale, low-impact and cost-effective assessments. This chapter provides a concise review of remote sensing applications for farmland biodiversity monitoring, structured around the Essential Biodiversity Variable framework. We examine plants, animals, fungi and microorganisms, and their habitats in productive and semi-natural areas. Spaceborne and airborne sensors effectively assess agroecosystem structure and functioning, and detect plants and large mammals with distinct spectral or phenological traits. UAV imagery and camera traps offer higher resolution for monitoring smaller or cryptic species. Remote sensing also supports indirect methods, such as species distribution modeling, to infer the occurrence of species that are difficult to detect. Key challenges include technological, methodological and operational limitations. Integrating multi-platform data, establishing shared benchmarks, and broadening taxonomic coverage, supported by policy incentives and farmer-friendly technologies, are essential for scaling biodiversity monitoring and promoting sustainable strategies that reconcile conservation with agricultural production.
Background Contradictory results have emerged from empirical research into the relationship between boredom and creativity. Theories suggest that states of low arousal and positive valence promote creative processes. Studies have differentiated students' experiences of boredom based on valence and arousal as latent profiles. Aims We will examine whether latent profiles of boredom described in previous research can be found in a younger age group sample in a school context, and whether different latent boredom profiles vary in terms of their creativity value. Sample A total of 111 ninth-grade secondary school students participated. Each student received 18–19 signals (a sum of 2057 momentary assessments, 345 missing, total number of completed momentary assessments k = 1712). Methods We conducted an experience sampling study and analysed the assessed data (boredom, valence, arousal, creativity) using latent profile analyses. Results In line with previous research, we identified five profiles of boredom. According to our hypothesis, the identified boredom profiles differed in their mean creativity scores. In particular, the boredom profile characterized by slightly positive valence and low arousal showed the highest mean creativity score. In contrast, profiles characterized by strongly negative valence showed lower creativity scores. Moments that were not perceived as boring had a higher creativity value on average compared to moments perceived as boring. Conclusions Our findings help to clarify the controversy surrounding the relationship between boredom and creativity. We demonstrate that creativity varies considerably depending on the specific profile of boredom, and outline implications for research and practice.
We investigate the quantum structure of spacetime at fundamental scales via a novel, Lorentz-invariant noncommutative coordinate framework. Building on insights from noncommutative geometry, spectral theory, and algebraic quantum field theory, we systematically construct a quantum spacetime algebra whose geometric and causal properties are derived from first principles. Using the Weyl algebra formalism and the Gelfand--Naimark--Segal (GNS) construction, we rigorously define operator-valued coordinates that respect Lorentz symmetry and encode quantum gravitational effects through nontrivial commutation relations. We show how the emergent quantum spacetime exhibits minimal length effects, which deliver both classical Minkowski distances and quantum corrections proportional to the Planck length squared. Furthermore, we establish that noncommutativity respects a fuzzy form of causality, where the quantum causal structure gives back the light cone in the classical limit, vanishing for spacelike separations and encoding a time orientation for timelike intervals.
This study explores the differences and similarities between migrant and non-migrant entrepreneurs in Norway to enhance the design of migrant-specific entrepreneurship support programmes (MSPs) using qualitative comparative analysis (QCA), our findings reveal greater-than-expected in-group heterogeneity and between-group homogeneity, challenging existing literature. In other words, the differences between transnational and non-transnational entrepreneurs are more prominent than the ones between migrants and non-migrants. Within the group of migrant entrepreneurs, we see that those generally exhibit more transnational activity and less access to host-country networks and finance, while non-migrants have more diverse ventures. Notably, some migrants could benefit from joining open support programmes (OSPs) alongside non-migrants, and many do not need deep host-country embeddedness due to their transnational business focus. These insights can refine MSP designs, better aligning them with migrant entrepreneurs' needs. Future research should build on these findings through larger-scale quantitative studies and assess ES programmes across various political and cultural contexts.
