dataesr/scientific-paragraphs-categorization huggingface dataset:
Risk assessment analysis The observed relationship between loyalty and infection potential can be used to define a strategy for the risk assessment analysis of an epidemic unfolding on an unknown networked system at present time, for which we have however information on its past configurations. This may become very useful in practice even in the case of complete datasets, as for example with emerging outbreaks of livestock infectious diseases. Data on livestock movements are routinely collected following European regulations  [55] , however they may not be readily available in a real-time fashion upon an emergency, and a certain delay may thus be expected. Following an alert for an emerging livestock disease epidemic, knowledge of past network configurations may instead be promptly used in order to characterize the loyalty of farmers, simulate the spread of the disease on past configurations and thus provide the expected risk of infection for the farms under the ongoing outbreak.
To make the above strategy operational, we still need to determine how we can exploit past data to predict the evolution of the loyalty of a node in future configurations (step 3) and use this information to compute nodes epidemic risk (point 5). As with all other variables characterizing the system, indeed, also θ may fluctuate from a pair of configurations (c -1, c) to another, as nodes may alter their loyal behavior over time, increasing or decreasing the memory of the system across time. Without any additional knowledge or prior assumption on the dynamics driving the system, we measure from available past data the probabilities of (dis)loyal nodes staying (dis)loyal across consecutive configurations, or conversely, of changing their loyalty status. This property can be quantified in terms of probabilities of transition across loyalty statuses.
Methods Datasets The cattle trade network is obtained from the database of the Italian national bovine registry recording all cattle displacements due to trade transactions. We consider animal movements during a 5 years time period, from 2006 to 2010, involving 215,264 premises and 2,973,710 directed links. Nodes may be active or inactive depending whether farms sell/buy cattle in a given timeframe. From the dataset we have removed slaughterhouses (∼ 1% of the nodes) as they are not relevant for transmission. The sexual contact network is extracted from an online Brazilian forum where male sex buyers rate and comment on their sexual encounters with female sex sellers  [16]. Time-stamped posts are used as proxies for sexual intercourse and multiple entries are considered separately, following previous works  [16, 31].
It led to new proofs of phase transition for those models, see  [3]  and  [8]. The CRCM is also studied in stochastic geometry and spatial statistics as an interacting random germ-grain model  [15]. For a suitable parameter q the CRCM fits as best as possible the clustering of the real dataset. The estimation of the parameter q and the law of radii Q is studied in  [16]. All these works, including those in statistical mechanics, involve only the finite volume CRCM. The infinite volume version has not really been studied and highlighted as in its analogous on deterministic graphs. However its interests are numerous in statistical physics and spatial statistics. Involving physical considerations, phase transition phenomenons are observable from infinite volume CRCM; it is believed that the uniqueness of the CRCM would be violated for special critical values of z, q.
Acknowledgement. M. Caspers is partially supported by the grant  SFB 878  "Groups, geometry and actions";  J. Parcet  and  M. Perrin  are partially supported by the  ERC StG-256997-CZOSQP (UE)  and  ICMAT Severo Ochoa   SEV-2011-0087  (Spain); and  É. Ricard  by  ANR-2011-BS01-008-11  (France).
Cluster mutations correspond to flips between triangulations, and the exchange relation is given by an analog of Ptolemy's relation between the length of the diagonals and of the edges of a quadrilateral pqrs inscribed on a CC was supported by the government of Canada through a Banting Postdoctoral Fellowship. He was also supported by a York University research grant. ‡ VP was partially supported by the Spanish MICINN grant MTM2011-22792 and the French ANR grant EGOS (12 JS02 002 01). These models provide useful tools to get intuition and to experiment on combinatorial properties of the corresponding cluster algebras. Moreover, many properties of the cluster algebra can be read directly from the geometric model. For example, for a cluster variable y and an initial cluster seed X in type A, the denominator of y with respect to X is the product of the variables in X whose diagonals cross the diagonal y, while the numerator of y can be computed in terms of perfect matching enumeration in a well-chosen weighted bipartite graph  [CP03, Pro05].
Acknowledgements The program described here was the content of the  PRAGMATIC 2013 Research School in Algebraic Geometry and Commutative Algebra "Topics in Higher Dimensional Algebraic Geometry " held in Catania, Italy, in September 2013. This paper was largely completed at the  EMS School "New Perspectives on the classification of Fano Manifolds" held in Udine, Italy , in September 2014. We are very grateful to  Alfio Ragusa ,  Francesco Russo , and  Giuseppe Zappalà , the organizers of the PRAGMATIC school, and to  Pietro De Poi  and  Francesco Zucconi , the organisers of the EMS school, for creating a wonderful atmosphere for us to work in. We thank  Sándor Kovács  for advice on vanishing theorems.
In Section 5, we provide a list of open questions, directly related to the results of the paper. Acknowledgements. WH is pleased to thank the organizers of the Journées MAS 2014 where the project of this note was initiated. During this work, AH was supported by the grant KAW 2010. 0063 from the Knut and Alice Wallenberg Foundation. The work of WH and JN was partially supported by the program "modèles numériques" of the French Agence Nationale de la Recherche under the grant ANR-12-MONU-0003 (project DIONISOS).
ACKNOWLEDGMENTS The work of AHC is supported in part by the  National Science Foundation Phys-1202671. WDvS would like to thank  Gert Heckman  for pointing to reference [17], and  Florian Lyonnet  for his help with PyR@TE. Also, WDvS thanks IH ÉS for hospitality and support during a visit in June 2015 and  NWO  under  VIDI-grant   016. 133. 326.
Acknowledgement: We thank  N. Crampé ,  R. A. Pimenta ,  R. I. Nepomechie  for discussions and  P. Baseilhac  that suggest the adjective Modified in MABA to avoid confusion with usual and generalized ABA. We thank  J. Bajnok  and the " MTA Lendlet Holographic QFT Group, Wigner Research Centre for Physics" of Budapest  for their invitation and hospitality during the workshop " Finite-size Technology in Low Dimensional Quantum Systems (VII )" where a part of this work was done. We also thank the L2C of Montpellier where a part of this work was done. This work has been partially supported by  Sao Paulo Research Foundation (FAPESP) , grant  2014/09832-1.
Cases and Epidemiological Investigations Patients that met the World Health Organization (WHO) case definitions for suspected or probable EVD were investigated by District Health Medical Teams (DHMT) and investigation teams led by the Sierra Leone Ministry of Health and Sanitation (MOHS) and supported by international partners. Demographic, geographic, epidemiological, and clinical data were recorded on standard case investigation forms delivered by the WHO. Source of infection of each case was sought by tracing contacts retrospectively.
Acknowledgements The work of S. P. was supported in part by  RFBR  grant  14-01-00474 -a. E. R. was supported by  ANR  Project  DIADEMS  ( Programme Blanc   ANR SIMI1 2010-BLAN-0120-02 ). N. A. S. was supported by the  Program of RAS "Nonlinear Dynamics in Mathematics and Physics" ,  RFBR-14-01-00860-a ,  RFBR-13-01-12405-ofi-m2.
Patients and observations We analyzed data from 120 LGG patients treated between 1999 and 2007. 12 Data included information on tumor size in all patients and on up to three molecular (genetic) characteristics in 77 patients: 1p/19q chromosomal codeletion, p53 overexpression (a surrogate marker for TP53 missense mutations  17  ), and IDH mutation status. The model was built using the data from these 77 patients. Among these patients, information on all molecular characteristics was available for 42 patients (54. 5%), and information on at least one item of molecular characteristic in 35 patients (45. 5%). The data from the 43 patients without molecular information were used as an external dataset to evaluate model quality. Tumor sizes were measured manually from printed MRI images and expressed as mean tumor diameter (MTD) in millimeters, according to the formula MTD 5 (2V)  1/3  , where V ¼ D13D23D3 2 is the approximated tumor volume with D 1 , D 2 , and D 3 referring to the three largest perpendicular diameters.
Integration of genetic information The data from the 42 patients with complete molecular status (codeletion 1p/19q, p53, and IDH mutations) was used as a training dataset to obtain statistics on this genetic information. We computed the percentage of patients with a given genetic profile and derived the probability to exhibit it. So for patients with one or two missing covariates, we could compute the probability to exhibit the lacking mutation status(es), knowing the other(s) one(s). We therefore attributed genetic characteristics for patients with missing covariates. In our training dataset, in line with previous literature,  12  1p/ 19q codeletion and the p53 mutation were mutually exclusive. We incorporated the molecular information into the model and identified the effect of each status on the tumor size kinetic parameters.
21 pirical Bayes estimates to predict LGG response to temozolomide Following a Bayesian approach in which population parameter estimates constituted prior information, we analyzed each patient's data individually, considering only the MTD observations prior to treatment and the first MTD observations obtained after treatment onset, i. e. , the observations obtained in the first 3 months of treatment. If, for a given patient, no observations were available prior to treatment, we used only the MTD observations obtained within the first 3 months after treatment onset. Patients for whom no information was available for the first 3 months of treatment were excluded from the analysis. Overall, data from 45 patients were analyzed. Among these, 31 patients had a single MTD observation during the first 3 months of treatment, and 14 patients had two MTD observations.
External analysis In the analysis described above, the model's predictive capacity was assessed on patients whose full time-course data were used to estimate the population parameters; these population parameters constituted prior information for the calculation of EBEs. To explore whether this caused a bias, we subsequently performed predictive analysis on the 43 "external" patients whose data had been excluded from the initial model-building process, owing to a lack of genetic information. In this case, we used early MTD observations as in the original predictive analysis, but without covariates. We then used population parameters to simulate 200 new virtual patients, and we made predictions for these patients using the model without covariates in a first step, and we incorporated genetic statuses into the predictions in a second step.
This paper deals with measuring the influence of observations on the results obtained with classification trees. To define the influence of individuals on the analysis, we propose criterions to measure the sensitivity of the Classification And Regression Trees (CART) analysis. The proposals are based on predictions and use jackknife trees. The analysis is extended to the pruned subtrees sequences of CART to produce specific notions of influence. Using the framework of influence functions, distributional results are derived. A real dataset relating the administrative classification of cities surrounding Paris, France, to the characteristics of their tax revenues distribution, is analyzed using the new influencebased tools.
,X p i ) =Yi + α|T | ( 2 ) where 1l is the indicator function, n the total number of observations, α a positive penalty constant, |T | denotes the number of leaves of the tree T and Y i is the ith random realization of Y. The R package rpart provides both the sequence of subtrees pruned from a deep maximal tree and a final tree selected from this sequence by using the 1-SE rule (see  [4] ). The penalized criterion used in the pruning of rpart is Rpen defined by  (2). The cost complexity parameter denoted by cp corresponds to the temperature α used in the original penalized criterion (2) divided by the misclassification rate of the root of the tree. The pruning step leads to a sequence {T 1 ;. ; T K } of nested subtrees (where T K is reduced to the root of the tree) associated with a nondecreasing sequence of temperatures {cp 1 ;.
Influence based on subtrees sequences Another way to look at the data is to consider the complexity cost constant, penalizing bigger trees in the pruning step of the CART tree design, as a tuning parameter. It allows to scan the data and sort them with respect to their influence on the CART tree. Let us consider on the one hand the sequence of subtrees based on the complete dataset, denoted by T cpj , and on the other hand the n jackknife sequences of subtrees based on the jackknife subsamples L -i , denoted by T (-i) cpj. Suppose that the sequence T cpj contains K T elements, and that each sequence T (-i) cpj contains K T (-i) elements (i = 1,. , n). This leads to a total of N cp K T + 1 i n K T (-i) distinct values {cp 1 ;. ; cp Ncp } of the cost complexity parameter in increasing order from cp 1 to cp Ncp = max 1 j Ncp cp j.
Dataset and reference tree We apply the tools presented in the previous section on tax revenues of households in 2007 from the 143 cities surrounding Paris. Cities are grouped into four counties (corresponding to the french administrative "département"). The PATARE data (PAris TAx REvenues) are freely available on http://www. data-publica. com/data. For confidentiality reason we do not have access to the tax revenues of the individual households but we have characteristics of the distribution of the tax revenues per city. For each city, we have the first and the 9th deciles (named respectively D1 and D9 ), the quartiles (named respectively Q1, Q2 and Q3 ), the mean, and the percentage of the tax revenues coming from the salaries and treatments (named PtSal ). Basically we tried to predict the county of the city with the characteristics of the tax revenues distribution.
Acknowledgements The work of P. C. was founded by  PIA-CONICYT  grant  PFBasal-01 ,  DIUBB GI 153209/C  and  DIUBB GI 152920/EF. The work of A. C. was founded by  DIUBB 121909 GI/C. C. C. thanks partial support from Ecos-Conicyt  C13E05. He is also partially supported by PFBasal-01 and PFBasal-03 projects and by  Fondecyt 1140773. The work of C. E. was founded by Fondecyt  1140586 , Fondequip  EQM140104 ,  DIUBB GI153109/EF ,  GI 152920/EF. We would like to acknowledge  Dr. Gareth Owen  from  Pontificia Universidad Católica de Chile  for donating us ovarian cancer cells. Finally, we would like to thank you to  Dr. Andrés Rodríguez  for your invaluable comments on this work, as well as, your English corrections.
The results will reflect uncertainty in the final model and will report the range of possible candidate models and their respective estimated probabilities from a single run. Label switching is resolved with a computationally light-weight method, Zswitch, developed for overfitted mixtures by exploiting the intuitiveness of allocation-based relabelling algorithms and the precision of label-invariant loss functions. Four simulation studies are included to illustrate Zmix and Zswitch, as well as three case studies from the literature. All methods are available as part of the R package Zmix, which can currently be applied to univariate Gaussian mixture models.
Replicate simulations a. Number of non-empty components For n = 100 and n = 200, produce 20 replicates of each simulation. Run Zmix for 20,000 iterations with K = 10 and 25 chains, saving the target chain (j = J) for each run after 5000 iterations. b. Compute K ðtÞ 0 for each iteration, storing the vector K 0. Compute the proportion of each configuration represented, and the mode of the empirical distribution of K J 0. Case Studies. Three case studies are described to illustrate the results of Zmix and Zswitch in practice. The first case study is the Acidity dataset, which consists of the log acidity index for 155 lakes in the North-Eastern United States  [18]. These have been previously analysed as a mixture of Gaussian distributions on the log scale by  [18]  who found evidence for two or three groups.
[14]  found evidence for three to five components with the same model with a Reversible Jump MCMC algorithm, while  [21]  overfit this dataset resulting in a posterior with two true components. The second case study involves the Enzyme dataset found in  [33] , which consists of measurements of enzymatic activity in blood for an enzyme involved in the metabolism of carcinogenic substances (velocity and substrate concentration), for a group of 245 unrelated individuals. [33]  first analysed this data and found a mixture of 2 skewed components using MLE. [14]  found evidence for 3 to 5 components using RJMCMC. [34]  also modelled this data with 2 skewed Gaussian components. Finally, Galaxy data  [35]  is considered since it has been investigated by many researchers with a wide range of results  [36] [37] [38].
It is a small dataset of 82 measurements of galaxy speeds from 6 segments of the sky. It is of particular interest as different order estimation methods have suggested that the data contains anywhere from 3 to 9 components  [11, 19, 21, 37, [39] [40] [41]. [40]  observed that extra components appears to be modelling underlying skewness present in the sample. Evaluation strategy for Case Studies. For each case study, run Zmix for 50,000 iterations. Extract the last 20,000 iterations of the target posterior. Subset by value of K ðtÞ 0 , and apply Zswitch and post-processing to each subset. Compute and save posterior mean of all estimated parameters, including 95% credible intervals, and posterior allocation probabilities for each configuration considered.
When K k 0 = K 0 , the proportion of the observations whose predicted allocations corresponds to their true groupings is computed. The mean absolute error (MAE) and mean squared error (MSE) are calculated using the unswitched parameter estimates. The remaining statistics are based on posterior predictive testing, which are found by resampling the posterior samples of the parameters in the target chain in order to predict 10,000 datasets of the same size as the original data. Mean absolute errors (MAPE) and mean squared prediction errors (MSPE) are reported as an average over the replicates. Bayesian Pvalues estimating p(min(Y rep ) < min(Y)) and p(max(Y rep ) < max(Y)) are included, which we call P min and P max. Both are included as they can be useful in identifying a skewed fit. Predictive concordance is then computed, which can be interpreted as the average proportion of y i 's that are not outliers given the model (based on the suggestion that any y i that is in either 2.
5% tail area of y rep i should be considered an outlier)  [42]. An ideal fit should have a predictive concordance of around 95%  [42]. A small set of plots is also created for each candidate configuration. Density plots of the posterior paramaters illustrate their distribution and the success of Zswitch at relabelling the output of Zmix. Also included is a plot of estimated allocation probabilities, and a plot of the density of 10,000 predicted datasets overlaid by a that of Y to allow for the overall fit to be explored and identification of areas of bad fit. R Code. Please refer to S1 File to obtain the R code to perform all analyses described in the methods.
Case Studies In the analysis of the three case studies, Zmix results in posterior configurations with the same number of components as the smallest number found by previous literature. Acidity. Zmix finds that 2 components are best suited to model the Acidity data, with p (K k 0 = 2) = 1. The target posterior does not contain any estimates from another configuration, indicating there is no ambiguity in this decision. Referring to Fig  5 , the two components are well separated and there is little uncertainty in the posterior allocations, which are slightly less sharply defined in a small region of overlap between the two groups. Posterior predictive plots indicate the model represents the data well, with no need for any more components. The resulting mixture has tightly estimated posterior parameter estimates, included here with 95% credible intervals in brackets.
Concordance is observed to decrease with the addition of a third component. The posterior predictive density plots in Fig 6 reveals little difference between the fit of the two models, but the plot of the allocation probabilities reveals the difference in the candidate configurations. It is clear that the 2 component posterior provides a much more certain fit with no uncertainty in the clustering of the data, whereas the 3 component model exhibits much less clarity in the posterior allocation probabilities. This case study illustrates the importance of making a final choice based on the original goal of the analysis. Recall that the Enzyme dataset comprises measurements of enzymatic activity in blood for an enzyme involved in the metabolism of a carcinogenic substance. While the posterior may strongly favour 2 components, the fact that multiple configurations are included in K J 0 indicates there is some non-negligible probability that this is the true number of components.
The added cluster describes a smaller component with a larger mean, suggesting that a small group of patients with a different distribution of enzymatic activity characterised by a larger mean may be present. If a higher level of activity is believed to relate to a higher risk of cancer, for example, then further analyses on a subset of individuals with potentially higher risk may be of interest and the less likely model may be reported. Galaxy. Surprisingly given the small sample size, analysis of this dataset results in a stable target consistently representing only 2 components with similar means, m1 ¼ 21:33ð20:76; 21:9Þ and m2 ¼ 19:47ð15:8; 22:69Þ (see  Fig 7). One has a large weight of p1 ¼ 0:72ð0:54; 0:86Þ and small variance ŝ2 1 ¼ 3:69ð2:31; 5:66Þ, modelling the peak at the center of the range of Y, and the other is described by a smaller weight p2 ¼ 0:28ð0:14; 0:46Þ, but a very large variance of ŝ2 2 ¼ 57:23ð30:41; 106:97Þ.
This second group models the outlying  values of the dataset at both tails. The posterior predictive density plot reveals that this is a reasonable model for these data, resulting in similar predicted replicates. Since the fitted mixture model places no restrictions on the variance of the underlying mixture, this configuration is possible, and it appears reasonable to conclude that these data could have originated from such a model. Given the physical origins of the data however, it may be warranted to impose some restrictions on other priors or on the variances. [43]  use astronomically motivated priors to model this dataset, and find evidence for 7 components. In the sensitivity study conducted in  [19] , it is shown that while there appears to be evidence for anywhere from two to eight components, there is a very large probability assigned to two components when the variances is allowed to be large.