dataesr/scientific-paragraphs-categorization huggingface dataset:
Pointing performance To enhance the pointing accuracy of the GCT prototype in any direction, many technical pointing runs were taken to gather data. We have recorded the position of the telescope along with the environmental conditions, while recording images of stars in the telescope FoV. In order to take into account the pointing error due to the telescope geometry in the calculation of the alt-azimuthal coordinates, we have built a preliminary pointing model of the telescope using P. Wallace's TPOINT software  [11]. In this preliminary model, we have considered only 7 parameters, i. e. AN, AW, IA, NPAE, IE, CA and TF. The theoretical result is presented in Fig. 6 : with a simple model and 30 samples, we achieve a factor of 20 improvement in the pointing precision of the telescope. This first result confirms that the telescope has a very good behaviour over the sky and that the theoretical pointing precision before applying any predictive model for the deformations due to gravity and wind, and before improvement using real time monitoring devices, exceeds expectations considering the CTA requirements (210 " in ideal observing conditions and 600 " in standard conditions).
Nonetheless, limitations in spatial resolution of non-invasive stimulation methods  45  , the uncertainty with regards to the distribution of the electrical currents  21  , compromised signal-to-noise ratio under the influence of TMS/tACS generated electrical fields and localization power of scalp   ). The S-PLV index measures the stability of the phase difference (see Fig. 2C ) ranging from 0 (random behavior) to recording methods  46  calls for supplementary evidence that completes a convincing demonstration of oscillatory entrainment phenomena in well-circumscribed regions of the human brain and further studies on their underlying features and mechanisms. In the present study, we studied such phenomenon in datasets from clinically-guided causal mapping sessions performed in intracranially implanted epilepsy patients.
The study of these phenomena in datasets obtained during clinically-guided causal mapping sessions in intracranially implanted epilepsy patients poses some limitations. Very importantly, the variety of implantation schemes, the low number of stimulation parameters (frequency, duration), and the scarce number of samples per condition (combining a given site and stimulation intensity) that can be tested to keep mapping sessions within a reasonable duration, avoiding an overstimulation of the cerebral tissue, remain a limitation of this approach. Notwithstanding, we benefited from the high effectiveness and focality of these approaches applied to well anatomically characterized cerebral sites, combined with the unique localization power and the outstanding signal-to-noise ratio provided by human iEEG recordings  33.
Two additional limitations of this study deserve special discussion. The first one is the difficulty to disentangle whether the oscillatory activity observed during 50 Hz stimulation reflects a physiological response to the stimulation itself or is rather an effect of strong electrical artifacts recorded or generated during the analyses. A potential source of artifacts in our data could emerge from the artifact removal procedure used to eliminate undesirable noise tied to the electrical pulses. This method, which has been already used and validated in studies analyzing evoked activity induced by single intracranial electrical pulses  34, 47, 48  consists in the interpolation of the removed artifacted period using a third degree spline. We tested the ability of this approach to remove any contributions from oscillatory activity at the frequency of interest (50 Hz) originated from a non-physiological source, by conducting a series of statistical control analysis using real and artificially artifacted datasets.
An interesting approach to test this claim would be to compare in the same implanted region the likelihood and/or level of entrainment induced by different stimulation frequencies. Since the current study is based on existing iEEG datasets obtained following strict clinical criteria, hence using only 50 Hz bursts (the clinical state-of the-art frequency maximizing the likelihood of inducing seizures  63  ), we are unable at this time to test this hypothesis. Future studies will be directed to further characterize crucial features associated to oscillatory entrainment phenomena, in particular their local vs. network distributed effects, their dependence from local natural rhythms and cytoarchitecture and the detailed influence of ongoing rhythmic activity present in the targeted region prior to stimulation.
Methods Patients. The iEEG datasets of three medication-resistant epilepsy patients (2 females and 1 male, respectively 29, 32 and 25 years old) obtained during direct intracranial stimulation performed in the context of clinically guided causal mapping sessions, aiming to causally identify epileptic foci, prior to considering the feasibility of surgical removal  31, 32  , were included in our analyses. Two patients were implanted with 9 multi-electrodes each, whereas a third one received 7 multi-electrodes. Patients provided an informed consent, and recordings were performed under ethical committee agreement. Implantation sites were planed and selected exclusively on purely clinical criteria, with no reference to the present analysis. The study was sponsored by the INSERM and approved by the ethical committee (CPPRB, Comité Consultatif de Protection des Personnes participant à une Recherche Biomédicale) Ile de France I (reference number C11-16, 5-04), which regulates the publication of anonymized versions of participant's data.
Stimulation was delivered between pairs of adjacent contacts from the same multi-electrode while iEEG raw data were recorded from the remaining contacts. Data acquisition was performed using a 16 bits Micromed Amplifier system (Micromed, Mogliano Veneto, Italy). The sampling rate was set to 1024 Hz and during the acquisition, the signal was band-pass filtered at 0. 15-350 Hz. An external electrode located on the scalp FCz position (10/20 EEG system) was used as a reference for the iEEG recordings. These recordings were obtained from each available contact on each of the implanted multi-electrodes. Nonetheless, only iEEG data from sites classified and logged post-hoc as non-epileptogenic by an expert neurologist according to iEEG and clinical criteria were considered for further analyses. During intracranial stimulation sessions (direct brain stimulation), patients were fully awake and comfortably seated in a chair placed in a well-lighted room.
5 mA, 29 at 1 mA, 29 at 2 mA, 10 at 3 mA and 4 at 4 mA). iEEG data pre-processing. Intracranial EEG responses to electrical stimulations were recorded from the remaining sensors within the same multi-electrode prior, during and shortly after low intensity stimulation of non-epileptogenic cerebral sites (Figs  1A  and 2A ). To avoid the confounding of long stimulation artifacts, only trials carried out at stimulation intensities of 0. 5 mA, 1 mA and 2 mA were considered for further analyses. For each stimulation trial, we analyzed 28 seconds of iEEG data (8 s prior and 20 s following the onset of the burst, hence including burst duration) recorded by contacts of the same multi-electrode not involved in the delivery of the stimulation. A pre-processing pipeline was designed using in-house software coded in Matlab (Mathworks, MA, USA).
Only recordings from contacts showing average power increases in the [45-55 Hz] band during the stimulation period 20 times higher than the pre-stimulation onset baseline were considered in these analyses  69. We computed for each time sample, the instantaneous phase difference between the gamma [45-55 Hz] iEEG components (post-artifact removal) recorded by each contact and a modeled signal emulating the 50 Hz pattern delivered by the electrical stimulator (Fig. 2C ). In order to create a signal emulating the stimulation bursts, we implemented computational approaches with an in-house-programmed script in Matlab (Mathworks, MA, USA) to design and generate an artificial signal at the same sampling rate (1024 Hz) as the original data, with the value "+ 1" (followed by a "-1" to account for its biphasic waveform) repeated every 20 ms and a value of "0" everywhere else in the time series.
For each stimulation burst delivered through a pair of active contacts, we considered the iEEG traces recorded from contacts within the same multi-electrode, not assigned to deliver the electrical current. Each single-trial value of power and S-PLV from each of the 3 patients was included in our analyses as an independent observation. Those values were consolidated as part of the same dataset and integrated in the same analysis to assess general effects of entrainment phenomena. These same values were also analyzed for each patient in order to assess consistency across individual participants. Analyses of power and S-PLV, were based on three different temporal windows introduced as dependent variables in the Friedman's test (Time-period factor): [-4000 to -2000 ms] before 50 Hz electrical bursts onset (Power pre and S-PLV pre); [2000 to 4000 ms] after the 50 Hz burst onset (Power during and S-PLV during) and [8000 to 10000 ms] after the 50 Hz burst onset (Power post and S-PVL post: 3000 to 5000 ms after the 50 Hz burst offset).
Acknowledgements The activities of the laboratory of  Dr. Valero-Cabré  included in this project are supported by research grants from eraNET  NEURON Beyondvis  by  ANR Génerique Oscilloscopus  and  FP6  and  IHU-A-ICM-Translationnel  from the  IHU-ICM. JLA was supported by a  FYSSEN postdoctoral Fellowship  and MV was supported by the  FRM (Fondation pour la Recherche Médicale ) and a post-doctoral contract with the  IHU-A-ICM. The  Naturalia & Biologia Foundation  provided travel funds to attends meeting and discuss this work with international experts in the field.
A simple example is the "lazy" (or coinductive) list LCons 0 (LCons 1 (LCons 2. )) that enumerates the natural numbers. It can be specified via the corecursive equation enum n = LCons n (enum (n + 1)). In 2011, we started an effort to enrich the Isabelle/HOL proof assistant with definitional mechanisms for codatatypes and corecursion. Until then, Isabelle/HOL and the other main systems based on higher-order logic (HOL4, HOL Light, and ProofPower-HOL) provided at most (inductive) datatypes, recursive functions, and (co)inductive predicates. Our aim was to support formalizations such as Lochbihler's verified compiler for a Java-like language  [32]  and his mathematization of the Java memory model  [33] , both of which rely on codatatypes to represent infinite traces. Creating a monolithic codatatype package to supplement Isabelle/HOL's existing datatype package  [4]  was not an attractive prospect, because many applications need to mix datatypes and codatatypes, as in the following nested (co)recursive specification: datatype α list = Nil | Cons α (α list) codatatype α ltree = LNode α ((α ltree) list) The first command introduces a polymorphic type of finite lists over an element type α, freely generated by the constructors Nil : α list and Cons : α → α list → α list.
10). Crucially, all our specification mechanisms follow the definitional approach, as is typical in Isabelle/HOL and the HOL family of systems. This means that the desired types and terms are explicitly constructed and introduced using more primitive mechanisms and their characteristic properties are derived as theorems. This guarantees that they introduce no inconsistencies, reducing the amount of code that must be trusted. The main drawback of this approach is that it puts a heavy burden on the mechanisms' designers and implementers. For example, the (co)datatype commands explicitly construct solutions to fixpoint equations and nonemptiness witnesses, and the constructions must be performed efficiently. Other approaches-such as the intrinsic approach, where the specification mechanism is built directly into the logic, and the axiomatic approach, where types and terms are added to the signature and characterized by axioms-require less work but do not guard against inconsistencies [4, Sect.
1]. The work described in this paper was first presented in conference and journal publications between 2012 and 2017  [7, 9, 10, 12, 13, [15] [16] [17] [18] 46, 50, 51]. The current text is partly based on these papers. The source code consists of about 29 000 lines of Standard ML distributed as part of Isabelle and the Archive of Formal Proofs  [47]. It is complemented by Isabelle lemma libraries necessary for the constructions, notably a theory of cardinals  [15]. We refer to our earlier papers  [10, 13, 18, 51]  for discussions of related work.
Tool Integration Lifting and Transfer. Isabelle/HOL's Lifting and Transfer tools  [26]  provide automation for working with type abstractions introduced via the typedef command. Lifting defines constants on the newly introduced abstract type from constants on the original raw type. Transfer reduces proof goals about the abstract type to goals about the raw type. Both tools are centered around parametricity and relators. The BNF infrastructure serves as an abundant supply of relator constants, their properties, and parametricity theorems about the constructors, 'case' combinators, recursors, and the BNF map, set, and relator constants. The interaction between Lifting, Transfer, and the BNF and (co)datatype databases is implemented using Isabelle's plugin mechanism. Plugins are callbacks that are executed upon every update to the BNF or (co)datatype database, as well as for all existing database entries at the moment of the registration of the plugin.
The Lifting and Transfer plugins derive and register properties in the format accepted by those tools from the corresponding properties in the BNF and (co)datatype databases. To enable nested recursion through types introduced by typedef, we must register the types as BNFs. The BNF structure can often be lifted from the raw type to the abstract type in a canonical way. The command lift_bnf automates this lifting based on a few properties of the carved-out subset: Essentially, the subset must be closed under map f for any f , where map is the map function of the raw type's BNF. If the carved out subset is the entire type, the copy_bnf command performs the trivial lifting of the BNF structure. This command is particularly useful to register types defined via Isabelle/HOL's record command, which are type copies of some product type, as BNFs.
Coinductive Languages. Rutten  [44]  views formal languages as infinite tries-i. e. , prefix trees branching over the alphabet with Boolean labels at the nodes indicating whether the path from the root denotes a word in the language. Traytel  [50]  formalized these tries in Isabelle as codatatype α lang = Lang bool (α → α lang) a type that nests corecursion through the right-hand side of the function space arrow (→). He also defined regular operations on them as corecursive functions and proved by coinduction that the defined operations form a Kleene algebra. Completeness of First-Order Logic. Gödel's completeness theorem  [21]  is a central result about first-order logic. Blanchette, Popescu, and Traytel  [9, 14, 16]  formalized a Beth-Hintikka-style proof  [27]  in Isabelle/HOL. It depends on a Gentzen or tableau system and performs a search that builds either a finite deduction tree yielding a proof (or refutation, depending on the system) or an infinite tree from which a countermodel (or model) can be extracted.
Acknowledgments. We first want to acknowledge the support and encouragement of past and current bosses:  David Basin ,  Wan Fokkink ,  Stephan Merz ,  Aart Middeldorp ,  Tobias Nipkow , and  Christoph Weidenbach. We are grateful to the  FroCoS 2017 program  chairs,  Clare Dixon  and  Marcelo Finger , and to the program committee for giving us this opportunity to present our research. We are also indebted to  Andreas Abel ,  Stefan Berghofer ,  Sascha Böhme ,  Lukas Bulwahn ,  Elsa Gunter ,  Florian Haftmann ,  Martin Hofmann ,  Brian Huffman ,  Lars Hupel ,  Alexander Krauss ,  Peter Lammich ,  Rustan Leino ,  Stefan Milius ,  Lutz Schröder ,  Mark Summerfield ,  Christian Urban ,  Daniel Wand , and  Makarius Wenzel , and to dozens of anonymous reviewers (including those who rejected our manuscript "Witnessing (co)datatypes" [18] six times).
For NGS data, paired tumoral and non-tumoral whole exome/genome sequencing bam data are converted into seqz format and processed by Sequenza for CNV detection. aCNViewer converts CNV data into a CNV matrix with the window size defined by the user and which is subsequently used to compute dendrograms and heatmaps. Quantitative stacked histograms can be generated using the same matrix or a matrix of segments at base resolution (default behaviour). Text files are also available through GISTIC  [33]  providing a robust statistical way to select recurrent CNVs. https://doi. org/10. 1371/journal. pone. 0189334. g003 (chr 1q gain, chr 8p loss, and chr 8q gain). Differences between the two tumors would not have been revealed in the pseudo-tetraploid HCC sample if the ploidy baseline of both samples were set by default to 2.
See Supplementary section "Comparison of the quantitative stacked histograms between SNP array and WES data" in S1 File for more details). By using CGHregions  [18]  on the Affymetrix data set  [1] , we confirmed that the global trend of gains and losses are consistent with ASCAT results (S2 Fig) (some differences are notable though and this is discussed in the supplementary section "Comparison of the quantitative stacked histograms using SNP array data from  [1]  processed with ASCAT and CGHregions" in S1 File). Finally, we merged HCC CNV data from Affymetrix 500K Human Mapping Array and WES sequencing experiments processed with ASCAT and Sequenza respectively to obtain a whole-genome visualization of recurrent CNV and cn-LOH events on a larger group of samples. Thus, we demonstrate the possibility by aCNViewer to generate a single graph based on data from multiple experimental designs in order to gain more statistical power (Fig  2C ).
Finally, using either the matrix of relative copy number values or a matrix of segments at base resolution (see section "Construction of M s , a matrix of segments at base resolution" below), a quantitative stacked histogram is generated with absolute whole genome copy number and copy neutral variation profiles showing the frequency of recurrent events across all selected samples (Fig 1A ). A similar histogram is generated with a whole genome view of homozygous/heterozygous CNVs (Fig  1B ). aCNViewer is implemented in python for the pipelining steps and in R for the generation of dendrograms, heatmaps, and stacked histograms and thus runs on all linux/unix platforms. Let us define C = {C A (i)} as the list of copy number segments extracted from ASCAT / Sequenza or any other CNV caller chosen by the user for all samples A and genomic positions i.
Generation of a matrix of relative copy number values. Copy number values are calculated by ASCAT or Sequenza if aCNViewer is used on SNP array or raw sequencing data. Alternatively, they can be calculated from other tools as long as they are provided in the ASCAT segment format (https://github. com/FJD-CEPH/aCNViewer#othercnvformats). By default, these copy number values are used by aCNViewer to produce dendrograms and heatmaps. Relative copy number values can also be used (set option useRelativeCopyNbForClustering to 1) to produce the same types of graphical representations. In this case, for each sample A, the relative copy number values C' A are calculated using the following formula for all genomic positions i: C' A (i) = C A (i)-p A where C A (i) is the copy number value for genomic position i and sample A and p A is the estimated ploidy of sample A.
Heatmaps Using M or M' as an input, R's heatmap. 2 function in the gplots package is used in aCNViewer with the default hierarchical clustering function set to hclust and the default agglomeration method set to "ward. D" (both parameters are customizable by the user). Similarly to dendrograms, it is possible to generate one heatmap for each feature listed in a file with clinical information (see option "sampleFile" in Table  1 ). The other options for bi-dimensional heatmap include the possibility to cluster the chromosomal windows (S3A   1 ).
Stacked histograms Stacked histograms allow the representation and identification of recurrent CNV and cn-LOH events along the genome in groups of samples while retaining the quantitative information present in CNV data. This has never been performed before. Default stacked histograms will be generated using the matrix of segments at base resolution M s obtained from raw copy number data or alternatively M'. Construction of M s , a matrix of segments at base resolution. Let us define M s = {K A (i)} as the matrix of segments at base resolution for all samples A and genomic positions i. M s will be constructed from C simply by segmenting the genomic positions i so that they are all nonoverlapping. This is equivalent to having the windowing approach, described in section "Generation of M, a matrix of copy number values", with the advantage of not having to fill in "the blanks" for a given window.
Category Option (default value) Description General -plotAll (1) specify whether all available plots should be generated (values are 0 or 1) -refBuild REF_BUILD the genome build used to generate the CNV segments (hg18 and hg19 are currently supported. For custom build, please check the github websitew WINDOW_SIZE (2000000) / -p PERCENT WINDOW_SIZE defines the window length in bp used to cut the genome in order to generate a matrix of CNV events. Alternatively, PERCENT can be used instead of WINDOW_SIZE in order to set the window size in percentage of chromosome length where PERCENT is a floating number between 0 and 100. -t TARGET_DIR set the path of the output folder -b BIN_DIR set the path of the folder containing all required binaries. For a detailed description of the structure, please refer to https://github.
-rColorFile FILE_NAME file* allowing to customize graph colors -outputFormat FORMAT allow to customize output formats for the different types of available plots (histograms, heatmaps and dendrograms). The default value is hist:png (width = 4000,height = 1800,res = 300);hetHom:png(width = 4000, height = 1800,res = 300);dend:png(width = 4000,height = 2200,res = 300);heat: pdf(width = 10,height = 12). For more information, please refer to https://github. com/FJD-CEPH/aCNViewer#outputFormat.
Heatmap/ dendrogram -sampleFile SAMPLE_FILE a tab-delimited file that should contain a column named Sample with the name of each sample and at least another column with the phenotypic/clinical feature. This file can contain a sample alias, which will be used as the official sample id if provided. This parameter can be used for dendrograms as well. -G FEATURE_NAME refers to the name of the column of the phenotypic/clinical feature of interest in SAMPLE_FILE if specified. If you omit this parameter, one plot per feature defined in SAMPLE_FILE will be generated. This file can contain a sample alias, which will be used as the official sample id if provided. This parameter can be used for dendrograms as well. * an example can be found at https://github. Histogram creation. M s (default value) or M' is used as an input and for each segment S (or window for M') and for each copy number value C (ranging from -4 to +6), the percentage of overall samples in S having the copy number value C can now be calculated.