PISA data clusters reveal student and school inequality that affects results.

The data from the PISA survey show that student performance correlates with socio-economic background, that private schools have higher results and more privileged students, and that this varies between countries. We explore this further and analyze the PISA data using methods from network theory and find clusters of countries whose students have similar performance and socio-economic background. Interestingly, we find a cluster of countries, including China, Spain and Portugal, characterized by less privileged students performing well. When considering private schools only, some countries, such as Portugal and Brazil, are in a cluster with mostly wealthy countries characterized by privileged students. Swedish grades are compared to PISA results, and we see that the higher grades in private schools are in line with the PISA results, suggesting that there is no grade inflation in this case, but differences in socio-economic background suggest that this is due to school segregation.

A multiscale view of the Phanerozoic fossil record reveals the three major biotic transitions.

The hypothesis of the Great Evolutionary Faunas is a foundational concept of macroevolutionary research postulating that three global mega-assemblages have dominated Phanerozoic oceans following abrupt biotic transitions. Empirical estimates of this large-scale pattern depend on several methodological decisions and are based on approaches unable to capture multiscale dynamics of the underlying Earth-Life System. Combining a multilayer network representation of fossil data with a multilevel clustering that eliminates the subjectivity inherent to distance-based approaches, we demonstrate that Phanerozoic oceans sequentially harbored four global benthic mega-assemblages. Shifts in dominance patterns among these global marine mega-assemblages were abrupt (end-Cambrian 494 Ma; end-Permian 252 Ma) or protracted (mid-Cretaceous 129 Ma), and represent the three major biotic transitions in Earth's history. Our findings suggest that gradual ecological changes associated with the Mesozoic Marine Revolution triggered a protracted biotic transition comparable in magnitude to the end-Permian transition initiated by the most severe biotic crisis of the past 500 million years. Overall, our study supports the notion that both long-term ecological changes and major geological events have played crucial roles in shaping the mega-assemblages that dominated Phanerozoic oceans.

Regularities in species' niches reveal the world's climate regions.

Climate regions form the basis of many ecological, evolutionary, and conservation studies. However, our understanding of climate regions is limited to how they shape vegetation: they do not account for the distribution of animals. Here, we develop a network-based framework to identify important climates worldwide based on regularities in realized niches of about 26,000 tetrapods. We show that high-energy climates, including deserts, tropical savannas, and steppes, are consistent across animal- and plant-derived classifications, indicating similar underlying climatic determinants. Conversely, temperate climates differ across all groups, suggesting that these climates allow for idiosyncratic adaptations. Finally, we show how the integration of niche classifications with geographical information enables the detection of climatic transition zones and the signal of geographic and historical processes. Our results identify the climates shaping the distribution of tetrapods and call for caution when using general climate classifications to study the ecology, evolution, or conservation of specific taxa.

There are many distinct climates on Earth, from tropical savannas and temperate forests to dry deserts. Historically, each region has been defined by how its annual weather patterns shape the type of vegetation present. For example, hot and humid environments support the growth of evergreen forests that would not survive in drier places. Identifying the boundaries between climate regions is key to understanding how life is organized on Earth and predicting how climate change will affect different species. Current climate classifications, however, do not account for where animals can be found or how local conditions, such as precipitation and average temperatures, shape the distribution of different animal species. To bridge this gap, Calatayud et al. analyzed the preferred climate of about 26,000 animal species, including amphibians, birds, mammals and reptiles. For each species, Calatayud et al. calculated the annual rainfall and temperature of its local environment, or 'niche', using previously collected data. They then used a computer algorithm to group together climates that had similar species. This identified 16 climate regions which govern the distribution of the animals studied. Calatayud et al. found that these newly defined climatic regions resembled some of the regions classified using plants. This was particularly true for high-energy climates that had lower levels of rainfall and hot temperatures, such as deserts and the tropical savanna. The animals and plant species living in high-energy regions were found to be fairly consistent across both classification systems. Whereas the species present in milder and colder climates, such as temperate forests or Mediterranean climates, were found to be much more varied. This suggests that temperate climates are harder to classify and may affect the distribution of plants and animals differently. It also implies that less extreme conditions support a larger range of species than harsher climates in which only species with certain adaptations are able to survive. These findings build the basis for a better understanding of how climates shape ecosystems. More specific climate classifications, based on such analyses, could be used to inform conservation strategies for animal species in the face of climate change.

Positive associations among rare species and their persistence in ecological assemblages.

According to the competitive exclusion principle, species with low competitive abilities should be excluded by more efficient competitors; yet, they generally remain as rare species. Here, we describe the positive and negative spatial association networks of 326 disparate assemblages, showing a general organization pattern that simultaneously supports the primacy of competition and the persistence of rare species. Abundant species monopolize negative associations in about 90% of the assemblages. On the other hand, rare species are mostly involved in positive associations, forming small network modules. Simulations suggest that positive interactions among rare species and microhabitat preferences are the most probable mechanisms underpinning this pattern and rare species persistence. The consistent results across taxa and geography suggest a general explanation for the maintenance of biodiversity in competitive environments.

Exploring the solution landscape enables more reliable network community detection.

To understand how a complex system is organized and functions, researchers often identify communities in the system's network of interactions. Because it is practically impossible to explore all solutions to guarantee the best one, many community-detection algorithms rely on multiple stochastic searches. But for a given combination of network and stochastic algorithms, how many searches are sufficient to find a solution that is good enough? The standard approach is to pick a reasonably large number of searches and select the network partition with the highest quality or derive a consensus solution based on all network partitions. However, if different partitions have similar qualities such that the solution landscape is degenerate, the single best partition may miss relevant information, and a consensus solution may blur complementary communities. Here we address this degeneracy problem with coarse-grained descriptions of the solution landscape. We cluster network partitions based on their similarity and suggest an approach to determine the minimum number of searches required to describe the solution landscape adequately. To make good use of all partitions, we also propose different ways to explore the solution landscape, including a significance clustering procedure. We test these approaches on synthetic networks and a real-world network using two contrasting community-detection algorithms: The algorithm that can identify more general structures requires more searches, and networks with clearer community structures require fewer searches. We also find that exploring the coarse-grained solution landscape can reveal complementary solutions and enable more reliable community detection.

Angular dependence of fluorescence from turbid media.

We perform Monte Carlo light scattering simulations to study the angular distribution of the fluorescence emission from turbid media and compare the results to measured angular distributions from fluorescing white paper samples. The angular distribution of fluorescence emission is significantly depending on the concentration of fluorophores. The simulations show also a dependence on the angle of incidence that is however not as evident in the measurements. A detailed analysis of the factors affecting this angular distribution indicates that it is strongly correlated to the mean depth of the fluorescence process. The findings can find applications in fluorescence spectroscopy and are of particular interest when optimizing the impact of fluorescence on e.g. the appearance of paper as the measured values are angle dependent.

Solving the radiative transfer equation with a mathematical particle method.

We solve the radiative transfer equation (RTE) using a recently proposed mathematical particle method, originally developed for solving general functional equations. We show that, in the case of the RTE, it gives several advantages, such as handling arbitrary boundary conditions and phase functions and avoiding numerical instability in strongly forward-scattering media. We also solve the RTE, including fluorescence, and an example is shown with a fluorescence cascade where light is absorbed and emitted in several steps. We show that the evaluated particle method is straightforward to implement, which is in contrast with many traditional RTE solvers, but a potential drawback is the tuning of the method parameters.

Influence of finite-sized detection solid angle on bidirectional reflectance distribution function measurements.

This paper deals with limitations and often overlooked sources of error introduced in compact double-beam goniophotometers. It is shown that relative errors in measured radiance factor, comparable to the total measurement uncertainty, can be introduced if recommended corrections are not carried out. Two different error sources are investigated, both related to the size of the detection solid angle. The first is a geometrical error that occurs when the size of the illuminated area and detector aperture are comparable to the distance between them. The second is a convolution error due to variations in radiant flux over the detector aperture, which is quantified by simulating the full 3D bidirectional reflectance distribution function (BRDF) of a set of samples with different degrees of anisotropic reflectance. The evaluation is performed for a compact double-beam goniophotometer using different detection solid angles, and it is shown that both error sources introduce relative errors of 1%-3%, depending on viewing angle and optical properties of the sample. Commercially available compact goniophotometers, capable of absolute measurements, are becoming more and more common, and the findings in this paper are therefore important for anyone using or planning to use this type of instrument.

Separation of surface and bulk reflectance by absorption of bulk scattered light.

A method is proposed for separating light reflected from turbid media with a rough surface into a bulk and a surface component. Dye is added to the sample, thereby increasing absorption and canceling bulk scattering. The remaining reflected light is surface reflectance, which can be subtracted from the total reflectance of an undyed sample to obtain the bulk component. The method is applied to paper where the addition of dye is accomplished by inkjet printing. The results show that the bulk scattered light is efficiently canceled, and that both the spectrally neutral surface reflectance and the surface topography of the undyed paper is maintained. The proposed method is particularly suitable for characterization of dielectric, highly randomized materials with significant bulk reflectance and rough surfaces, which are difficult to analyze with existing methods. A reliable separation method opens up for new ways of analyzing, e.g., biological tissues and optical coatings, and is also a valuable tool in the development of more comprehensive reflectance models.

Lateral light scattering in fibrous media.

Lateral light scattering in fibrous media is investigated by computing the modulation transfer function (MTF) of 22 paper samples using a Monte Carlo model. The simulation tool uses phase functions from infinitely long homogenous cylinders and the directional inhomogeneity of paper is achieved by aligning the cylinders in the plane. The inverse frequency at half maximum of the MTF is compared to both measurements and previous simulations with isotropic and strongly forward single scattering phase functions. It is found that the conical scattering by cylinders enhances the lateral scattering and therefore predicts a larger extent of lateral light scattering than models using rotationally invariant single scattering phase functions. However, it does not fully reach the levels of lateral scattering observed in measurements. It is argued that the hollow lumen of a wood fiber or dependent scattering effects must be considered for a complete description of lateral light scattering in paper.

Extension of the Stokes equation for layered constructions to fluorescent turbid media.

Expressions relating the bispectral reflectance of a stack of n fluorescing layers to each individual layer's reflectance and transmittance are derived. This theoretical framework is used together with recently proposed extensions of the Kubelka-Munk model to study the fluorescence from layered turbid media. For one layer over a reflecting background, the model is shown to give the same results as a previous model. The extension to n layers with different optical properties allows simulating the bispectral reflectance from a pad of layered turbid media. The applicability of the model is exemplified with an optimization of fluorophore distribution in layered turbid media.

Angle resolved color of bulk scattering media.

The angle resolved reflectance factor of matte samples is measured with a goniophotometer and simulated using radiative transfer theory. Both measurements and simulations display the same characteristic dependence of the reflectance factor on the observation angle. The angle resolved reflectance spectra are translated to CIELAB color coordinates and the angular color differences are found to be surprisingly large. A chromatic adaptation that is dependent on the observation angle is suggested, in which a nonabsorbing opaque medium is used as the reference white, and the angular color differences are then reduced. Furthermore, the use of an undyed paper as the reference white is evaluated. The angular lightness differences are then reduced further, but the angular differences in chroma are still large. It is suggested that smaller variations in perceived color could be explained by angle dependent chromatic adaptation and a limited sensitivity of the human visual system to changes in chroma.

Point spreading in turbid media with anisotropic single scattering.

Point spreading is investigated using general radiative transfer theory. We find that the single scattering anisotropy plays a significant role for point spreading together with the medium mean free path, single scattering albedo and thickness. When forward scattering dominates, the light will on average undergo more scattering events to give a specific optical response in reflectance measurements. This will significantly increase point spreading if the medium is low absorbing with large mean free path. Any fundamental and generic model of point spreading must capture the dependence on all of these medium characteristics.

Lateral light scattering in paper - MTF simulation and measurement.

The modulation transfer function (MTF) of 22 paper samples is computed using Monte Carlo simulations with isotropic or strongly forward single scattering. The inverse frequency at half maximum of the MTF (kp) is found inappropriate as a single metric for the MTF since it is insensitive to the shape of the modeled and simulated MTF. The single scattering phase function has a significant impact on the shape of the MTF, leading to more lateral scattering. However, anisotropic single scattering cannot explain the larger lateral scattering observed in paper. It is argued that the directional inhomogeneity of paper requires a light scattering model with both the phase function and scattering distances being dependent on the absolute direction.

Anisotropic reflectance from turbid media. I. Theory.

It is shown that the intensity of light reflected from plane-parallel turbid media is anisotropic in all situations encountered in practice. The anisotropy, in the form of higher intensity at large polar angles, increases when the amount of near-surface bulk scattering is increased, which dominates in optically thin and highly absorbing media. The only situation with isotropic intensity is when a non-absorbing infinitely thick medium is illuminated diffusely. This is the only case where the Kubelka-Munk model gives exact results and there exists an exact translation between Kubelka-Munk and general radiative transfer. This also means that a bulk scattering perfect diffusor does not exist. Angle-resolved models are thus crucial for a correct understanding of light scattering in turbid media. The results are derived using simulations and analytical calculations. It is also shown that there exists an optimal angle for directional detection that minimizes the error introduced when using the Kubelka-Munk model to interpret reflectance measurements with diffuse illumination.

Anisotropic reflectance from turbid media. II. Measurements.

The anisotropic reflectance from turbid media predicted using the radiative transfer based DORT2002 model is experimentally verified through goniophotometric measurements. A set of paper samples with varying amounts of dye and thickness is prepared, and their angle resolved reflectance is measured. An alleged perfect diffusor is also included. The corresponding simulations are performed. A complete agreement between the measurements and model predictions is seen regarding the characteristics of the anisotropy. They show that relatively more light is reflected at large polar angles when the absorption or illumination angle is increased or when the medium thickness is decreased. This is due to the relative amount of near-surface bulk scattering increasing in these cases. This affects the application of the Kubelka-Munk model as well as standards for reflectance measurements and calibration routines.