dataesr/scientific-paragraphs-categorization huggingface dataset:
79(1) (see Supplementary section S8). A further interesting observation about Fig. 3  concerns the overlap between the histograms of self-consistency and intersubject distances. Its existence allows us to reconcile the strong subjectivity unveiled by experiments E1-2, and the universality reported in the literature. The couples of facial vectors which are involved in distances for which there is a high overlap correspond to commonly preferred faces, around the most probable vector in the dataset, f. Within a low experimental precision, or an accuracy larger than the standard deviation per coordinate a > |σ σ σ |/D, all the subjects appear to agree in their choices. Under this perspective, the reported universality of beauty could be the side-effect of an experimental procedure where subjects express their preferences among a limited set of predefined options, the real facial images, in a high-dimensional facespace (indeed, the effective number of relevant facial dimensions may be of the order of hundreds  42  ).
Differences induced by the subject gender An extensively debated question in the literature is to what extent the subject gender influences attractiveness, a question that the present experimental scheme is particularity suited to address. Partitioning the dataset accordingly, S 1 = S m ∪ S f , it is obtained that, again, some facial coordinates are barely distinguishable or completely indistinguishable in both sets (d 3,4,6,7 , see Supplementary Fig. S7 ). Conversely, some coordinates are noticeably distinguishable. Compared to female subjects, male subjects tend to prefer thinner faces and jaws (d 5,10 ), lower eyes (d 1 ), higher zygomatic bones (d 0 ), larger eye width (d 8 ). The difference becomes very distinguishable along d 2,9 (p < 3 • 10 -3 , Supplementary Fig. S7 ): males definitely prefer shorter and thinner noses.
These results are partially in agreement with previous findings in the literature, that highlight male subjects' preference for smaller lower face area and higher cheekbones  14, 44. Furthermore, they also provide accurate relative differences along each coordinate and reveal that, at least for the two reference portraits RP1-2, the facial feature leading to larger differences among men and women attractors is the nose. A deeper insight is obtained by the analysis of PC's. These are the projections of the physical coordinates on the C-matrix eigenvectors, y = Ey (where ECE † = diag(λ 1 ,. , λ D )). The different principal components y i are, in other words, uncorrelated linear combinations of the physical coordinates ( y i y j = λ i δ i j ). Principal components corresponding to large eigenvalues (as y 10 ) represent the linear combinations of physical coordinates accounting for as much of the database variability, while those corresponding to the lowest eigenvalues represent the most improbable, or "forbidden" linear combinations of fluctuations away from the average y = 0 (see the Supplementary Information).
Different principal axes (e  (k)  , the rows of matrix E) describe the different, independent sources of variability in the dataset, that could reflect the subjects' traits most distinguishing their aesthetic criteria (as the gender). It turns out that faces corresponding to different subject's gender are distinguishable on three PC's (see Supplementary Fig. S8 ). Quite interestingly, such principal axes are not the ones exhibiting the largest eigenvalue, suggesting that the largest differences among selected faces correspond to inter-subject criteria that are transversal with respect to the subject's gender. Fig. 5  shows some image deformations of the average face along two principal axes: e  (9)  , e  (7)  (the 2nd and the 3rd most variant eigenvectors of C). The PC defined by e  (9)  is male/female distinguishable (males preferring negative values of y 9 ).
Discussion In this article, we have introduced an experimental behavioural method that allows human subjects to efficiently select their preferred modification of a reference portrait in the multi-dimensional face-space (and, in principle, in general spaces of images that can be parametrised with 2D landmark coordinates). The method allows to flexibly and accurately determine the face-space regions which are representative of a given subject's criterion. It opens the path to a novel, data-driven approach to cognitive research in face perception, allowing scholars to: (1) quantitatively address the inter-subject differences in the resulting sculpted shapes, beyond the rating; (2) isolate the influence of a secondary set of variables (such as texture features) and a posteriori address their influence (something that cannot be directly done with databases of natural facial images); (3) analyse a resulting set of facial vectors without being limited or conditioned by the a priori correlations present in natural image databases.
The method (based on our software FACEXPLORE, whose details are explained in the Supplementary Information) permits a highly accurate description of the single subject or subject category preferences in the face-space, thanks to the geometric/texture separation of facial degrees of freedom and to a genetic algorithm for efficient search in the face space. Using this technique, we have performed a set of experiments in which the single subjects preferred region in the face space have been determined with an unprecedented accuracy, below the millimeter per facial coordinate. Such experiments allow us to draw the following conclusions. First of all, attractiveness turns out to be associated with the existence of subject-dependent specific regions in the face space that we dubbed attractors, highlighting the essential subjectivity of attractiveness.
Despite the limited face-space dimension, and the homogeneity of the statistical universe (composed of subjects of the same cultural group), different subjects clearly tend to prefer different facial variations, suggesting that the subjectivity should be taken into account for a complete scientific picture of the phenomenon. Larger databases and more heterogeneous statistical universes would only make the essential subjectivity of attractiveness perception even more evident. In light of these facts, the validity of the natural selection hypothesis (universality, impact of averageness, symmetry and sexually dimorphic traits) may be arguably a matter of the precision of the length scale and of the facial image resolution of the facial description. Within a sufficiently accurate description of the subjects' criterion in face-space, the phenomenon emerges in its whole complexity, showing that the preferred faces of different subjects are systematically different among themselves and, consequently, different from the average face.
Our results suggest to consider attractiveness not as a scalar quantity, rather as the outcome of a complex process in which various semantic motives are evaluated. These are probably encoded in pairwise and higher-order correlations among facial features, more than in the value of single facial coordinates  35. A third result concerns the role of the subject's gender in the assessment of attractiveness. This is, indeed, an important source of diversity in our dataset. Nose length and width, eye height, face and jawbone width, zygomatic bone height, turn out to be the main facial traits distinguishing male and female observers. However, a principal component analysis suggests that the largest differences among selected facial variants correspond to principal axes that are independent of the subject's gender.
Methods). In summary, the novel experimental approach proposed in this article allowed us to unveil the essential subjectivity of attractiveness. The subjectivity emerges more evidently in the present scheme, since the reduction of the number of face space dimensions allows to avoid the undersampling occurring in experiments in which the subjects are asked to choose or rate natural faces. We believe that the generality and reliability of the present approach could have a strong impact on future studies about beauty and pleasantness in different domains. Possible completions of the present work are: an assessment of the robustness of principal components; an analysis of the intra-subject correlation matrix of facial coordinates; a variant of the analysis of correlations in an experiment with real facial images (whose landmarks could be automatically identified with deep learning techniques  46  ); an unsupervised inference analysis of the database (already being carried on in our group) within the framework of the Maximum Entropy method.
The reference portraits RP1-2 have been taken from the Chicago face database  50. Each experiment lasted roughly 25 minutes on average (see the histogram of time intervals among successive left-right choices in figure Supplementary Sec. S7). The subjects were asked to look away and relax for some second each N = 28 choices. All methods in experiments E1-3 were carried out in accordance with relevant guidelines and regulations. The experimental protocols used have been approved by the General Data Protection Regulation (EU) 2016/679. Informed consent was obtained from all subjects. , e  (9)  eigenvectors of the correlation matrix C, corresponding to the fourth and second larger eigenvalues, λ 7 , λ 9 ). The axes represent the principal components along these axes, (y 9 , y 7 ) in units of their standard deviations (λ 1/2 i ).
In other words, the image is generated from the facial vector y = E † (y 7 e  (7)  + y 9 e  (9)  ). Bottom figure: selected facial vectors. Each point is a projection of a selected facial vector in the principal axes corresponding to the Top figure, i. e. , each point has coordinates y (s,n) 7 , y (s,n) 9 , for all s, n in the E1 dataset. Blue points correspond to male subjects, and orange triangles to female subjects (male subjects tend to sculpt vectors with y 9 < 0, and vice-versa). The black points correspond to a population sculpted by a single, randomly selected, subject. 1 Detailed description of the face-space As explained in sections Results and Methods (main article), the face is parametrised as a vector d = (d i ) D i=0 of 11 inter-landmark distances, shown in figure  1 -A (main article).
, D: v (j) i = f (j) i (t) + µ (f (j1) i (t) -f (j2) i (t)) with prob. ρ f (j) i (t) with prob. 1 -ρ The selection and generation update steps can be written as: f (j) (t + 1) = v (j) if L[f (j) (t)] < L[v (j) ] f (j) (t) otherwise Note that the algorithm acts on every i-th single coordinate independently. ρ is called the crossover probability and µ the mutation factor, quantifying the amount of stochastic mutation in the genetic evolution. In our experiment, the evaluation of the inequality (3) corresponds to the choice between the corresponding facial images, I[v  (j)  ] and I[f (j) (t)], by the subject. He/she chooses among the images corresponding to the first parent's vector and its child; the selected vector survives and becomes part of the successive generation. The FACEXPLORE software operates, in this way, in a regime defined by four parameters, ρ, µ, N and T (and by other algorithm details, such as the way in which the initial population of vectors is initialised, the reference portrait, the constraints imposed to the facial vectors at each generation, or the size of the sub-grid to be warped in the image deformation algorithm, see sec.
Methods (main article)). Especially for large values of ρ, and for small values of µ, N and T , the results of single realisations of the experiment depend on the sequence of random numbers and on the random initial condition used in the particular realisation. This is a general characteristic of the genetic algorithm, arising also in the optimisation of deterministic functions, not a specific characteristic of the FACEXPLORE software. For lower values of N , the algorithm does not perform an exhaustive local search in the parameter space at each generation. The offspring generation is biased by its finiteness, a fact that conditions the experimental course and, consequently, the outcome. Depending on the parameters P, the algorithm stochasticity could become large enough to hinder the differences among different subjects' choices.
Distances among different partitions of the dataset In figure  3  (main article) we report the self-consistency (among couples of populations sculpted by the same subject, for all the subjects in E2) and inter-subject (among couples of populations sculpted by different subjects in E1) distance histograms. The distances have been computed using the angle-metrics with n pc = 7 principal components. In figure  3  we present a comparison of the difference among histograms, t 12 = (µ 1 -µ 2 )/(σ 2 1 +σ 2 2 ) 1/2 , using different values of n pc in the face-space metrics definition. Such difference among histograms provides an estimation of the overlap among both distributions: the cumulative normal distribution of t 12 , p 12 , is actually the overlap probability of both histograms, if they are supposed to be normal distributions.
Statistical distinguishability of partitions of the dataset We have performed single component (in physical, y i or principal, y i coordinates) statistical tests between different sets of populations of facial vectors. Given two sets of populations, S 1 = {f (s,n) } S1,N s=1,n=1 , S 2 = {g (s,n) } S2,N s=1,n=1 , we consider the t-value, and the consequent p-value, of the differences among the averages of the y i (or of the y i ) coordinate in both sets of populations, f (s1,•) i -g (s2,•) i s1,s2. The average • • • s1,s2 is performed again by bootstrapping, summing over all the couples (s 1 , s 2 ) and over many (B = 500) realisations in which different population indices (n 1 (s 1 ), n 2 (s 2 ) are chosen for each tuple s 1 , s 2. In this way, the error of this quantity is of order ∼ (S 1 S 2 ) -1/2 : f i -g i b = 1 S 1 S 2 S1,S2 s1,s2=1 f (s1,n1,b(s1)) i -g (s2,n2,b(s2)) i (18) f (s1,•) i -g (s2,•) i s1,s2 = average ( f i -g i 1 , • • • , f i -g i B ) (19) σ( f (s1,•) i -g (s2,•) i s1,s2 ) = std ( f i -g i 1 , • • • , f i -g i B ) (20) where, again, n According to the reference portrait.
f. figure  11 ). The e  (1)  eigenvector, for instance, is a linear combination such that the type i, j belonging to a random partition of the dataset of female (circles) and male subjects (crosses). Symbols, errorbars and inset are as in Fig. 6. The i = 0, 3, 4, 6, 7 coordinates result barely distinguishable or completely undistinguishable. belonging, respectively, to the set of populations of vectors sculpted by female and subjects in E1, respectively, as a function of the coordinate index i (squares). Symbols, error-bars and inset are as in figure  6. The i = 3, 5, 7, 8, 10 principal components result barely distinguishable or completely undistinguishable. face width increases while the jaw width decreases, or vice-versa, an uncommon, "forbidden" deformation according to the correlation matrix (see table  3 ), which indicates that these distances tend to increase or decrease together.
Furthermore, the empirical correlations are, in principle, an indirect manifestation of the effective interactions which cause them. The Maximum Entropy method allows to infer such effective interactions, from which we can more significantly assess the relative importance of various inter-landmark segments [1]. As can be seen in table  4  and figure  4  (main article), the sign of C ij coincides with that of ∆ y /∆ x for all the oblique C ij elements, except y 9 x 10. This matrix element has a reason to be peculiar: the 9-th and 10-th landmarks are subject to a constraint. In the construction of the facial image, y 9y 10 is constant for all the vectors in the dataset (and equal to the value of this quantity in the reference portrait). For a similar reason, we have not included the segment 7-12 in figure  4  (main article), despite there being a strong oblique correlation involving both quantities, since this correlation reflects another a priori constraint in the dataset: the 12-th landmark height coincides with the mouth's height by con-struction.
Application of the Maximum Entropy method The above arguments motivate a Maximum Entropy-based approach to the problem [6, 7]. The goal is to infer a probability distribution L(y) from the experimental dataset S (see 2). L reproduces by construction some data sufficient statistics (at least two-coordinate correlations). L(y) is a probabilistic generative model of the dataset S, and can be interpreted as the probability of the facial image with facial coordinates y (and fixed reference portrait) of being sculpted by any subject (or by a given subject having selected or sculpted the dataset S). Inferring L, one also infers a matrix (or a tensor) of effective interactions between couples (or p > 2-plets) of facial coordinates, that reflect the relative influence of the facial feature ins each other.
Higher order and spurious correlations A natural and relevant question is to what extent higher-order correlations of the data are statistically significant. In other words, whether three-coordinate empirical correlations y i y j y k in our dataset exhibit a large t-value. The answer is that, although we do observe non-negligible three-coordinate correlations, we cannot attribute a cognitive origin to them-they are rather generated by an artifact of the genetic algorithm. In experiments E1-3, the vectors of the initial population, f (s,n) (0) (see sec. 3) exhibit small 2-and 3-distance correlations that self-propagate and grow through the generations. Indeed, different populations sculpted (after T = 10 generations) by the genetic null model (with random left-right choices) exhibit significant 2-and 3-distance correlations, C (2,3)   null.
The null correlations are to be "subtracted" from those of the experiments with human subjects, C ). This is an interesting inference problem per se, of wide generality. It would arise also in experiments with natural facial images that are selected by subjects. The C null correlations in this case would correspond to the background correlations corresponding to the database of natural images, prior to the selection by the subjects. Subtraction of 3-order null correlations. On the one hand, 3-order correlation tensors C (3) obs and C (3) null coincide within their statistical errors. We interpret this fact concluding that our experimental scheme does not allow to elicit relevant 3-coordinate correlations of cognitive origin. Nevertheless, we believe that such high-order correlations may exist and play a role in the cognitive process of facial discrimination, and would probably emerge in larger experimental datasets, with higher values of S.
(B) UMAP of cells sampled from all stages of the life cycle, with cells colored according to their stage from (A). (C) The first three principal components from all stages in the life cycle. Our survey of the P. berghei life cycle enables a global view of gene expression and prediction of function based on co-expression patterns. We constructed a k-nearest neighbour graph, where each node represents one of 5156 genes detected in the data set (file S1). Graph spectral clustering  ( 8 )  was used to assign each gene to one of twenty modules based on the graph distance matrix (Fig. 2A , file S1). We observed gene clusters (1 and 2) consisting mainly of housekeeping genes and rRNA components that were highly expressed across the full life cycle. At the other extreme, some clusters (clusters  [18] [19] [20]  showed low overall expression and were primarily composed of genes from rapidly evolving multigene families ( pirs and fams ), which have no 1:1 orthologs with Plasmodium falciparum (fig.
berghei cells and 4237 P. knowlesi cells. We mapped P. berghei life stages between the 10X and Smart-seq2 technologies using Canonical Correlation Analysis (CCA) and scmap (Fig. 3A , fig. S12 )  ( 17 , 18 ). CCA clustering shows good representation of all stages in both Smart-seq2 and 10X data sets within the IDC (fig. S12 ). Using scmap-cell, 94% of cells in the 10X data were assigned to a Smart-seq2 cell with high confidence, allowing us to align data sets (Fig. 3A ). The additional P. berghei 10X data increases the coverage of cells in our atlas and confirms our ability to evaluate single cells characterised by different methodologies. To account for the continuous cyclical nature of the data, we ordered the 10X cells in pseudotime by fitting an ellipse to the first two principal components and calculating the angle around the centre of this ellipse for each cell relative to a start cell (Fig.
3B , Methods). Additionally, to confirm the orientation of the cycle with real time, we correlated each single-cell transcriptome with published bulk reference data sets and observed a high correspondence between bulk time point and pseudotime order (Fig. 3B , fig. S13 ). We next used RNA velocity  ( 19 )  , which provides a snapshot of the dynamic state of each cell, to examine transcriptional rates across this deeply sampled set of P. berghei parasites. We find that transcription rates vary dramatically over the IDC, with peak transcription occurring in late rings, consistent with bulk studies of nascent RNA transcription (Fig. 3C , fig. S14 )  ( 20 ). Additionally, we generated a 10X data set comprising 6737 cells from the IDC stages of the human parasite, P. falciparum. We used scmap-cell to assign each P.
falciparum and P. knowlesi cell to the P. berghei 10X reference index built with 1:1 orthologs, thus enabling us to align the developmental trajectories of these three species (Fig. 3C , fig. S14 ). We find the pace of transcription as measured by RNA velocity is similar across species, revealing conserved transcriptional rate in the intra-erythrocytic life of different malaria species in spite of vastly different hosts, and different life cycle lengths (24 hours for P. berghei, 27 hours for P. knowlesi, and 48 hours for P. falciparum ; Fig. 3C , fig. S15 ). Transcriptomic studies of both in vivo and in vitro malaria parasites are often confounded by multiple life stages within a single sample. The Malaria Cell Atlas can be used to deconvolve bulk transcriptomic data and identify the specific life stages that were present in a bulk RNA-seq sample.
One of the volunteers was also infected with P. malariae leading to the first transcriptomic data for this species. Notably, we observed late developmental stages, which is expected as unlike P. falciparum , P. malariae late stages do not sequester in the deep tissue (Fig. 4 ). As a proof of concept, we have shown that parasite species that have previously been inaccessible for expression analysis can now be characterised by combining scRNA-seq with the atlas. The Malaria Cell Atlas reference data set catalogs transcriptomes of every life stage along the parasite's life cycle at single-cell resolution, and spans different technologies and different parasite species. The data are freely accessible as a processed data set and user-friendly web interface ( 25 ). As such, this will be a key resource for the malaria community in the study of transcriptional regulation and control of developmental progression at the highest resolution.
10X data alignment, cell barcode assignment, and UMI counting The Cell Ranger Single-Cell Software (version 2. 1. 0) was used to process sequencing reads, assigning each read to a cell barcode and UMI using standard parameters  ( 16 ). After barcode assignment, the cDNA insert read was aligned using cell ranger (v 2. 1. 0) to a combined reference genome of P. knowlesi (March 2014) and P. berghei (July 2015), and the P. falciparum run was aligned to the 3D7 genome v3 (January 2016). These reference genomes were all obtained from https://www. sanger. ac. uk/resources/downloads/protozoa/.