dataesr/scientific-paragraphs-categorization huggingface dataset:
Tracking and Analyzing Human Breast Cancer Cells As a proof of concept, we used CellMAPtracer to track and analyze human breast cancer cells migrating randomly in 2D space. We used the triple-negative breast cancer cell line of BT549, stably expressing nuclear green fluorescent protein (GFP). From the first frame of three multi-TIFF 8 bit image stacks  [37] , a total of 103 cells were randomly selected to be tracked. Other cells were also tracked but they were manually excluded due to fluorescence intensity issues (i. e. , the fluorescence intensity was too low) or early disappearance from the scanning field. These 103 ancestor cells (referred to as G0) and their descendants (referred to as G1, G2, and G3) were followed during 72 h of live imaging. All the calculated tracks are available at https: //github.
Evaluation of the Tracking Accuracy To evaluate the performance of our method, we assessed the tracking accuracy of CellMAPtracer using a well-known metric in multiobject tracking evaluation: the location error  [16, 46]. The location error was computed by examining the number of cells that can be detected in the first frame and followed across all the frames, where the x and y coordinates of the centroids of the cells are reported and evaluated as a comparison with the ground truth. For that purpose, we used a dataset of GFP-GOWT1 mouse stem cells  [47] , named "Flue-N2DH-GOWT1_02_GT", obtained from http://celltrackingchallenge. net (accessed on 20 February 2021), which provides a reference annotation according to consensual or majority opinion of several human experts  [48]. The reference annotation of the target dataset is available in the TRA folder in the 02_GT at http://data.
celltrackingchallenge. net/training-datasets/Fluo-N2DH-GOWT1. zip (accessed on 20 February 2021). The evaluation process consisted of three steps. Firstly, we tracked all the cells that appear in the first frame (Figure  8a ) and exported the trajectory coordinates. Secondly, we detected the identifiers (IDs) of the cells (Figure  8b ) and computed the true coordinates on the basis of the gold tracking truth using inhouse code available at https://github. com/ocbe-uio/CellMAPtracer/tree/master/Data/Evaluation (accessed on 20 February 2021). After extracting the true x and y coordinates, we calculated the location error by computing the coordinate difference between those generated by CellMAPtracer and the true x and y coordinates per cell per frame (Data S1, Supplementary Materials). The mean difference in the x coordinates was 1.
Discussion CellMAPtracer is an open-source and easy-to-use software for tracking and extracting trajectory data of fluorescently labeled cells through a user-friendly GUI. CellMAPtracer was designed with the aim of providing users with highly efficient tracking of migratory proliferating cells over multiple days through supervising, inspecting, and correcting the tracking data in an enjoyable manner. Moreover, CellMAPtracer can be used in a fully automated manner at the single-cell level. As a proof of concept, breast cancer cells were scanned for 3 days. Over 100 cells were randomly tracked. To better evaluate and understand the resulting tracks, CellMAPtracer offers options to visualize and extract the resulting trajectory data. Users can interactively visualize any tracked cell and its descendants and compare the values of their migration measures and trajectory data.
The correlation of focal adhesion disassembly with the terminal speed jump is an interesting area for future investigation. Currently, CellMAPtracer is applicable only for fluorescently labeled cells in 2D cell migration assays and enables users to select the cells only from the first frame, in addition to the needed user interaction to detect cell divisions. Importantly, the features of CellMAPtracer can be expanded in future work to have CellMAPtracer as an ImageJ plug-in to include the possibility of selecting target cells from any frame, in addition to inspecting the four-color FUCCI system  [58]  or enabling users to internally run all the trajectory analyses presented in this study without the need for using external tools to run the analysis. At the moment, we provide all the needed codes for the trajectory analysis as R scripts with tutorials so that users can track cells and analyze their trajectories.
CellMAPtracer 2. 4. 1. Availability and Installation CellMAPtracer was built using MATLAB (v 9. 8) and can be freely obtained as (A) a standalone executable program for Microsoft Windows, macOS, or GNU/Linux, (B) a MATLAB App/Toolbox, and (C) the source MATLAB code. (A) Standalone executable program This can be accessed at https://github. com/ocbeuio/CellMAPtracer/releases/tag/v1. 1 (accessed on 20 February 2021). Three assets of CellMAPtracer for Windows, Linux, and macOS versions can be found and downloaded. After downloading the version compatible with their operating system, users should decompress the file and follow the instructions in the corresponding "readme. txt". (B) MATLAB App To be able to run CellMAPtracer App within the MATLAB environment, users should follow three simple steps: (1) download the "App" folder from the CellMAPtracer repository: https://github.
com/ocbe-uio/CellMAPtracer (accessed on 20 February 2021); (2) in MATLAB, go to the APPS tab and click "Install App", find the "CellMAPtracer. mlappinstall" file, and then install it; (3) open CellMAPtracer App from the Application list in MATLAB. (C) From the source MATLAB code To be able to run CellMAPtracer code, users should clone the CellMAPtracer repository from https://github. com/ocbe-uio/CellMAPtracer (accessed on 20 February 2021) and then run "CellMAPtracer_Main. m" after opening a project in MATLAB.
Acknowledgments: We would like to thank  Jeanette Gowen Cook ,  Katarzyna M. Kedziora ,  Frances Richards , and  Siang Boon Koh  for providing us with FUCCI multi-TIFF image stacks. S. G. is grateful to  Veronika Reiterer  for her great experimental technical support and valuable input. A. K. L was funded by the  UiO:Life Sciences initiative  through the convergence environment PerCaThe. A. K. L. also acknowledges the  Center for Digital Life Norway  for the support provided to the partner project PerCaThe.
Data Availability Statement: CellMAPtracer is an open-source multiplatform tracking system whose source code, data, and tutorials are deposited in a GitHub repository at https://github. com/ocbe-uio/CellMAPtracer. Moreover, the multi-TIFF image stacks are available at the following DOIs: 10. 5281/zenodo. 3878526 (BT549 sparse population), 10. 5281/zenodo. 4179028 (BT549 dense population), 10. 5281/zenodo. 4179316 (H322-FUCCI), 10. 5281/zenodo. 4179252 (REP-FUCCI), and 10. 5281/zenodo. 4485316 (Flue-N2DH-GOWT1_02_GT).
2. 4. 4 CellMAPtracer 2. 4. 1. Availability and Installation CellMAPtracer was built using MATLAB (v 9. 8) and can be freely obtained as (A) a standalone executable program for Microsoft Windows, macOS, or GNU/Linux, (B) a MATLAB App/Toolbox, and (C) the source MATLAB code. (A) Standalone executable program This can be accessed at https://github. com/ocbeuio/CellMAPtracer/releases/tag/v1. 1 (accessed on 20 February 2021). Three assets of CellMAPtracer for Windows, Linux, and macOS versions can be found and downloaded. After downloading the version compatible with their operating system, users should decompress the file and follow the instructions in the corresponding "readme. txt". (B) MATLAB App To be able to run CellMAPtracer App within the MATLAB environment, users should follow three simple steps: (1) download the "App" folder from the CellMAPtracer repository: https://github.
Chemical diversity is one of the key term when dealing with machine learning and molecular generation. This is particularly true for quantum chemical datasets. The composition of which should be done meticulously since the calculation is highly time demanding. Previously we have seen that the most known quantum chemical dataset QM9 lacks chemical diversity. As a consequence, ML models trained on QM9 showed generalizability shortcomings. In this paper we would like to present (i) a fast and generic method to evaluate chemical diversity, (ii) a new quantum chemical dataset of 435k molecules, OD9, that includes QM9 and new molecules generated with a diversity objective, (iii) an analysis of the diversity impact on unconstrained and goal-directed molecular generation on the example of QED optimization.
Our innovative approach makes it possible to individually estimate the impact of a solution to the diversity of a set, allowing for effective incremental evaluation. In the first application, we will see how the diversity constraint allows us to generate more than a million of molecules that would efficiently complete the reference datasets. The compounds were calculated with DFT thanks to a collaborative effort through the QuChemPedIA@home BOINC project. With regard to goal-directed molecular generation, getting a high QED score is not complicated, but adding a little diversity can cut the number of calls to the evaluation function by a factor of ten.
Open Access Journal of Cheminformatics *Correspondence: thomas. cauchy@univ-angers. fr; benoit. damota@univangers. fr 2 Univ Angers, CNRS, MOLTECH-ANJOU, SFR MATRIX, 49000 Angers, France Full list of author information is available at the end of the article classical organic chemistry. However it would propose very bad estimations for under-represented chemical functions such as peroxide and derivatives, diaryl ethers and diaryl amines, etc. [12]. The QM9 dataset includes one third (134k) of the molecules with up to nine heavy atoms (C, N, O and F) of the GDB database, the chemical space enumeration attempts by Reymond et al. [13] [14] [15]. Furthermore, this chemical space enumeration is not exhaustive. The goal of the GDB is to serve as a catalog of supposedly stable and realistic molecules for virtual screening.
Constrained molecules, aminals, acyl fluorides and other reactive compounds have been discarded during the creation of the GDB since a full combinatorial approach would lead to several million molecules  [14]. This impressive sampling of the chemical space was indeed not designed to represent the exploration playgrounds of molecular materials chemistry that looks for peculiar compounds with uncommon (electronic) properties. To study the chemical diversity of QM9, we have proposed the PC9 dataset a subset of the PubChemQC that could be compared to QM9  [12, 16]. Very recent studies comparing QM9 and our PC9 dataset indicate indeed better performances when trained on a more diversified dataset  [17] [18] [19]. We have also recently published a generator, EvoMol, based on a genetic algorithm  [20].
On different problems, it has shown very good performances in optimization. But the study of the solutions shows that good candidates are very similar. This is the consequence of our algorithm, which intensifies around the best solutions. ML-based generators see also their solutions biased, by the datasets or by some specific issues. We can cite for example GANs which are prone to mode collapse. The generator rotates through few different solutions and mechanisms should be included to prevent this. A similar problem occurs with reinforcement learning (RL), where a learned policy without introduction of randomness always leads to one and only one molecule (policy collapse). Beyond the addition of randomness, several RL-based generators included other mechanisms to increase diversity  [21] [22] [23].
These solutions are quite specific to the proposed generator or to the generation method. We believe that the inclusion of a diversity criterion can improve the interest of the solutions proposed by any generator. During the course of this study,  Kwon et al. published  an article where they add a criterion based on the Tanimoto similarity on fingerprints into their evolutionary algorithm  [24]. This article confirms our opinion because MolFinder maintains great optimization performances in a reference benchmark despite this additional diversity criterion. Therefore the aim of our study here is to propose a new method to calculate the contribution of a compound to the chemical diversity of a set. In a first application, we will see how this method allows us to generate molecules that would efficiently complete the reference datasets.
Then we will study the impact of this diversity constraint on the set of solutions of a classical problem such as a QED optimization. The concept of chemical diversity is not clearly defined. On which criteria and with which metrics should diversity be measured? In the field of de novo molecular generation, the term diversity usually refers to external diversity, where the generated compounds are compared to a reference dataset. Some benchmarks propose to measure external diversity using dedicated distribution learning tasks  [25] [26] [27]. The metrics commonly used are mathematical tools to compare distributions (e. g. KL divergence  [28] ) or curves (e. g. Fréchet distances  [29] ). The descriptors used can be of different nature, such as physicochemical descriptors (molecular weight, number of aromatic rings, etc.
Another common metric used to measure diversity is the mean distance between the molecules using Tanimoto distance  [33]  on fingerprints. Benhenda et al. [27]  also proposed to use nearest neighbors, entropy and the Wasserstein distance. The aim of our work here is not to compare the different approaches to diversity but to select one that is effective in the context of molecular generation. In order for a population-based molecule generator to integrate it as an objective, it is necessary to choose a metric allowing to determine quickly the contribution of each molecule to the diversity of a set. We present in this paper a fast and chemically meaningful way to compute the internal diversity of a dataset. We propose two experiments to demonstrate the interest of this approach. Firstly, we optimize only this objective in order to generate a more diversified dataset of molecules up to nine heavy atoms among C, O, N and F.
The 435k compounds of this dataset, called OD9, were calculated with DFT thanks to a collaborative effort through the QuChemPedIA@home BOINC project. We will present in detail the diversity of the newly generated compounds (250k) compared to the reference datasets (QM9 and PC9). Secondly, we integrate the internal diversity objective with the QED  [44] , to show the impact on the generated solutions and how the exploration of the chemical space is impacted.
Quantification of the diversity, descriptors and implementation As stated in the introduction, the objective of diversity must be calculated for each molecule and account for a contribution of the chemical diversity in the current dataset. For this purpose, we chose the Shannon entropy and we have selected several candidate descriptors : scaffolds, functional groups and shingles. The Jaynes' maximum entropy principle can be stated as follows: a distribution with the maximum entropy implies minimal assumptions about the true distribution of data  [45, 46]. One can easily see the interest of this principle to generate a diversified dataset when considering the chemical constraints, the distribution of the descriptors is neither equiprobable nor known. In addition, knowing that some optimization problems are solved more efficiently if the portfolio of solutions is diversified  [47] , we also believe that this approach could be useful for all population-based molecular generators.
Shannon entropy The entropy of a dataset X, described by n binary descriptors for which the proportion of the ith descriptor in X is denoted P i (X) , is defined by Eq. 1. Each term in the summation is 0 for P i (X) = 0 or P i (X) = 1 , and reaches its maximum value for P i (X) = e -1. Adding a rare descriptor contributes more to the entropy of a dataset than a common descriptor. Very common descriptors contribute very little to the entropy. Thus, to maximize H(X), the distribution of all descriptors must be as balanced as possible. Equation  1 only takes into account the on-bits. To have the complete entropy considering this equation, it would be necessary to integrate for each vector of descriptor the complementary vector (where the 0's are 1's and vice versa). For all the remainder of this section, we consider only the onbits part for two main reasons.
First, we will try to quickly evaluate the diversity and this simplification divides by 2 the amount of computation. Secondly, the descriptor vectors are in general very sparse and this simplification has no impact. One could even find that favoring a larger amount of off-bits is an advantage. When the proportion (1) H (X) = n i=1 -P i (X) log P i (X) of on-bits exceeds e -1 , the investigator will have to chose between this imbalance or a classical equilibrium (a proportion at 0. 5). In that case, it will be necessary to integrate the complementary vectors to use our estimator in its complete version of the entropy. In a naive way, it is possible to calculate the entropy of the dataset without a molecule m in order to evaluate the contribution � r (m, X) of m in X with Eq. 2. The contribution for adding a molecule can be calculated in the same way.
Thus, it is possible to transform a global problem where the aim is to maximize diversity into a problem of optimizing individuals. It is possible to remove a molecule that decreases or contributes only a little to the diversity or to choose a molecule that, on the contrary, increases it. Above all, it is possible to rank them. Computational efficiency Calculating the contribution of a molecule with Eqs. 2 and 3 is very expensive. With a dataset of several thousands molecules and a rich chemical diversity (several different descriptors), this equation would be a limiting point in terms of computing time. However, we have chosen descriptors which for each molecule are in limited number, i. e. one scaffold and less than ten IFGs. It is thus possible to no longer consider molecules, but the space of descriptors (denoted * ).
The key point to speed up the computation is to consider that the size of the dataset is constant during the entire optimization process. Even when starting with a single molecule, it will always be the final size of the dataset that will be used at any time. This approximation (denoted ′ ), allows to reuse a very large amount of calculation. The entropy of a descriptor D i , with C i (X) the number of occurrences of the descriptor in the dataset, and |X| the size of the dataset is defined as in Eq. 4. We can define the entropy variation for a descriptor D i by removing a molecule m containing or not this descriptor. As we will see later, we will add as many molecules at each step of the optimization as we remove. In the space of descriptors, this is equivalent to removing m and adding an empty molecule ∅ , i.
e. without descriptor, to obtain a dataset of the same size. In this case, if the molecule does not contain the descriptor D i , the variation of entropy is 0 (see Eq. 5). ( ) � r (m, X) = H(X \ {m}) -H(X) (3) � a (m, X) = H(X ∪ {m}) -H(X) (4) H * (D i , X) = - C i (X) |X| log C i (X) |X| 2 Thus, the contribution of a molecule m is calculated by only considering the few descriptors involved in m (see  Eq. 6). This equation allows to sort the molecules by contribution to the total entropy of the dataset. In an algorithm, when a molecule must be removed, this equation should be used. In a very comparable way, it is possible to evaluate the variation in entropy caused by the addition of a molecule, denoted � ′ a (m, X) , since it is the opposite operation (see Eqs. 7  and 8 ). This equation is used to rank the compounds proposed by a molecular generator.
If the set of solutions is of limited size, this value alone is not sufficient since the decision to add a molecule must take into account the contribution of the molecule it will replace and these two molecules may share common descriptors. Let m r be the molecule to be removed and m a the molecule to be added, then m a \ m r denote the molecule m a without the descriptors of m r. It is then possible to define the entropy variation of a substitution � ′ s (m r , m a , X) (see Eq. 9). if the value of ′ s is greater than or equal to 0, the substitution is considered as an improving one. With this approach it is possible to update only the scores of molecules that share one or more descriptors with m r ou m a. Moreover, depending on the size of the dataset to be considered, the update can take place only after a certain number of substitutions.
To summarize, our entropy calculation is an approximation, performed in the dual space of the descriptors. The approximation comes from two main reasons. First, the size of the population is considered as constant to optimize the caching of results, which saves a lot of calculation. Secondly, in our implementation we operate by batch and we do not consider the interactions between the molecules that are added and removed. The entropy gain is considered only with the dataset before (5) δ * r (D i , m, X) =H * (D i , (X \ {m}) ∪ {∅}) -H * (D i , X) (6) � ′ r (m, X) = D i ∈m δ * r (D i , m, X) (7) δ * a (D i , m, X) =H * (D i , (X \ {∅}) ∪ {m}) -H * (D i , X) (8) � ′ a (m, X) = D i ∈m δ * a (D i , m, X) (9) � ′ s (m r , m a , X) =� ′ r (m r \ m a , X) +� ′ a (m a \ m r , X) the beginning of the batch treatment as reference.
Therefore, we will also use an alternative approach to generate what we will call here generic scaffolds. All heteroatoms are transformed as carbons and all bonds are considered as single bonds. The benzene and the cyclohexane have the same generic scaffolds but the toluene and the benzene will not anymore. We have integrated either the scaffolds or the generic scaffolds into our objective function to improve the topological diversity of the dataset. Functional groups: CheckMol and IFGs In our previous study concerning the diversity, we have also seen that functional groups underrepresented in a training dataset could lead to huge errors in machine learning based predictions. The role of functional groups in the properties of an organic compound even shapes the way of teaching organic chemistry.
There is two main solutions for the automatic classification inside an established chemical ontology, the CheckMol and ClassyFire programs  [49, 50]. However, our unconstrained nature of generating molecules will leads to uncharted or neglected new sets of connected atoms i. e. new functional groups. Therefore, we have chosen to use the automatic approach of identifying functional groups proposed by Peter Ertl  [51]. It is centered on heteroatoms and their surroundings (atoms and bonds). It will merge connected surroundings to form new identified functional groups (IFGs). We have used the IFG detection program as implemented by Guillaume Godin and Richard Hall for the RDKit package  [52]. Shingles Finally, we have used an automatic and unbiased approach of defining chemical moieties called shingles.
They are subgraphs centered around each atoms. Depending on the cut-off radius, noted r, they can capture the chemical environment up to 3 bonds away (r= 3). We have used the shingles detection program as proposed by the group of Jean-Louis Reymond for the calculation of the CLscore  [53, 54]  which also relies on the RDKit package  [52]. Combining several categories of descriptors The contribution of each category of descriptors are computed separately, scaffolds and IFGs for instance, in order to be able to weight each one in an objective function (see Eq. 10). It would be easy to add other descriptors and weight them in this way. Between the topological diversity measured by the scaffolds and the functional groups diversity measured by the IFGs, we think that an objective function that combines both can deal with classical chemistry and also unstable molecules.