dataesr/scientific-paragraphs-categorization huggingface dataset:
A change of variable yields the alternative expression V(x) = 1 σ √ 2π λ π +∞ -∞ exp (u-x) 2 2σ 2 u 2 + λ 2 du, (11) and it is not hard to see that  (11)  satisfies                σ 4 V ′′ (x) + 2σ 2 V ′ (x) + (x 2 + λ 2 + σ 2 )V(x) = λ π , V(0) = 1 σ √ 2π exp λ 2 2σ 2 erfc λ σ √ 2 , V ′ (0) = 0. (12) (To remain in our general setting, a homogeneous ODE can be derived by differentiating one more time. ) The Voigt profile with arbitrary parameters can be expressed in terms of the Faddeeva function, itself a renormalization of the complex error function. A general implementation of these functions, due to Johnson  [17] , is used for instance in the standard library of the Julia programming language. Here we are interested in implementing the function V(x) for fixed λ and σ, with an overall relative accuracy ε = 2 -45.
Rigorous bounds could likely be derived by the method of Olver  [26, Chap. 7]. NumGfun does not support evaluations near irregular singular points, but as L(ξ) stays away from zero on [0, 0. 1], we could directly pass it to the Frankenstein backend. The resulting code uses two polynomials of degree 11 with floating-point coefficients. We then manually combined the two automatically generated codes into implementation that works correctly on the whole of F. The Voigt function is even, so the final code starts by dropping the sign of the argument. Based on a simple comparison, it then calls either the code for V(x) around zero or computes ξ = 1/x (in double precision) and calls the code for V(1/x) around zero. Figure  4  shows a plot of the relative error of the implementation of V. The plot covers all subdomains, both around zero and around infinity.
Acknowledgements The authors are grateful to  S. Chevillard ,  F. Chyzak ,  B. Salvy  and  A. Vaugon  for interesting discussions on topics related to this work, to  V. Innocente  and  D. Piparo  for suggesting the Voigt profile as a case study, and to the referees for their comments. This work was partly supported by the  Agence nationale de la recherche  grant  ANR-13-INSE-0007-02  MetaLibm.
Fourier ptychography is a new computational microscopy technique that provides gigapixel-scale intensity and phase images with both wide field-of-view and high resolution. By capturing a stack of low-resolution images under different illumination angles, an inverse algorithm can be used to computationally reconstruct the highresolution complex field. Here, we compare and classify multiple proposed inverse algorithms in terms of experimental robustness. We find that the main sources of error are noise, aberrations and mis-calibration (i. e. model mis-match). Using simulations and experiments, we demonstrate that the choice of cost function plays a critical role, with amplitude-based cost functions performing better than intensitybased ones. The reason for this is that Fourier ptychography datasets consist of images from both brightfield and darkfield illumination, representing a large range of measured intensities.
Since intensity is amplitude squared, both drive the optimization in the correct direction; hence, one might expect that the choice between the two is of little consequence. Surprisingly, however, we find that the cost function is the key predictor of experimental performance for our experimental dataset. Intensity-based algorithms suffer from strong artifacts (see Fig. 1 ), which we show to be due to noise and model mismatch errors. Hence, amplitude-based algorithms perform better on imperfect data, so are more robust. Our goal is to explain why this happens. We will show that in order for a phase retrieval scheme to be robust to experimental imperfections, the choice of cost function is of crucial importance. One source of error in our experimental data is measurement noise, including Gaussian noise or Poisson shot noise.
Another main source of error is model mis-match, caused by experimental imperfections such as aberrations and LED misalignment. A particular problem of FPM datasets is that they contain both brightfield and darkfield images, which have drastically different intensity levels (see Fig. 2 ). Brightfield images can have several orders of magnitude higher intensity than darkfield images; thus, the amount of Poisson noise will also be significantly higher. If this difference in the noise levels is not properly accounted for, the brightfield noise may drown out the darkfield signal. We will further show that aberrations and LED mis-calibration -the two main model mis-match errors in our experiments -result also in intensity-dependent errors. Thus, by carefully designing the the cost function, we can develop algorithms that are significantly more robust to both noise and model mis-match.
We develop a maximum likelihood theory which provides a flexible framework for formulating the FPM optimization problem with various noise models. In particular, we will focus on Gaussian and Poisson noise models. We find that amplitude-based algorithms effectively use a Poisson noise model, while intensity-based algorithms use a Gaussian noise model. To illustrate, we simulate four FPM datasets, three of which are contaminated with measurement errors (see Fig. 3 ): Poisson noise, aberrations, and LED misalignment. We compare the performance of various algorithms on these datasets to demonstrate that the imperfections in our experimental data are more consistent with a Poisson noise model. This explains our observations that amplitudebased algorithms are more experimentally robust than intensity-based algorithms.
Possible noise and simulated dataset Ideally, all algorithms based on the forward model above should give good reconstructions. However, noise and model mis-match errors cause deviations from our forward model. Thus, a noise model that accurately describes the error will be important for noise tolerance. Heuristically, we have identified three experimental non-idealities that cause error: Poisson noise, aberrations and LED mis-alignment. We aim to separate and analyze the artifacts caused by each through controlled simulations that incur only one type of error. The simulated data (Fig. 3 ) uses the same parameters as our experimental setup, where a 32 × 32 green LED array (central wavelength λ = 514 nm) is placed 77 mm above the sample. LEDs are nominally 4 mm apart from each other and only the central 293 LEDs are used, giving a maximum N A illu = 0.
45. Samples are imaged with a 4× objective lens having N A obj = 0. 1. Using our forward model, we simulate four datasets: 1. Ideal data: no noise is added. The object and pupil follow exactly the FPM forward model that is assumed in the algorithm. 2. Poisson noise data: the ideal data is corrupted by Poisson-distributed noise at each pixel. To emphasize the effect and to emulate experiments with lowerperformance sensors, we simulate 20× more noise than is present in our experiments (details in Section 2. 3). 3. Aberrated data: simulated images are corrupted by imaging system aberrations, which are described by the aberrated complex pupil function shown in Fig. 3. The pupil function used in these simulations was obtained from experimental measurements. 4. LED mis-aligned data: the illumination angle of each LED is perturbed slightly (following a normal distribution with standard deviation σ θ = 0.
However, it is easier to solve this problem by turning the likelihood function into a negative log-likelihood function which can be minimized. The negative log-likelihood function associated with this probability distribution can be calculated as L Gaussian (O(u)) = -log r p[I (r)|O(u)] = r 1 2 log(2πσ 2 w ) + (I (r) -Î (r)) 2 2σ 2 w. (4) The next step is to minimize this negative log-likelihood function by estimating O(u) so that the overall probability is maximized. For white Gaussian noise, it is assumed that σ 2 w are the same across all pixels for all images (i. e. all measurements have the same amount of noise), though this will not be the case for FPM datasets. By making a Gaussian noise assumption, the first term in (4) is a constant and can be ignored. The optimization problem then reduces to min O(u) f I (O(u)) = min O(u) r |I (r) -|F -1 {P (u)O(u -u )}| 2 | 2.
Reconstruction of the simulated and experimental data Error = O recover -O true 2 2 O true 2 2 , (29) where O recover and O true are the reconstructed and true images, respectively, in vector form. In order to ensure that all algorithms converge to their stable solutions, we use 200 iterations for each algorithm, except for Wirtinger flow, which requires 500 iterations. The tuning parameters for each algorithm are summarized in Table  1. We have attempted to optimize each parameter as fairly as possible; for example, we use a large σ in the PhaseLift algorithm to achieve a better reconstruction. Small σ trades resolution for flatter background artifacts. In analyzing results from the simulated datasets, we find that algorithms with the same cost function give similar reconstruction artifacts.
For example, the intensitybased algorithms suffer from high-frequency artifacts and phase wrapping when the data is not perfect. Almost all algorithms give a satisfactory reconstruction when using the error-free ideal dataset, except for intensity-based Wirtinger flow, which suffers some phase-amplitude leakage and phase blurring (see Figs. 4 5 ). When the dataset contains noise or model mis-match, we observe a distinct trend that amplitudebased and Poisson-likelihood-based algorithms give a better result, compared with intensity-based algorithms. The exception to this trend is the Gerchberg-Saxton algorithm, which is somewhat unstable and gets stuck in local minima, so is not robust to any type of error. The goal of our simulations was to determine the main error sources that cause artifacts in the experimental reconstructions of Fig.
The consequence is that algorithms which use a more accurate noise model (amplitude and Poisson likelihood-based) will not only be more robust to noise, but also to model mis-match errors. To examine the convergence of each algorithm, Figure  6  plots the error for each iteration when using the aberrated dataset and LED misaligned dataset with different algorithms. The intensity-based algorithms (red curves) clearly do not converge to the correct solution and can incur large errors when the data is not perfect. Compared to PhaseLift and the intensity-based Newton's method, the Wirtinger-flow algorithm seems to have lower error; however, this is only due to its slow divergence. If run for many iterations, it will eventually settle on a similarly error-corrupted result as the other two intensity-based algorithms (not shown).
The convergence speed of each algorithm can be determined from Figure  6  using two metrics: number of iterations required and total runtime. We choose the convergence curves from the cases of ideal data and LED misaligned data and compare their iteration numbers and runtimes in Table  2. All the algorithms were implemented in MATLAB on an Intel i7 2. 8 GHz CPU computer with 16G DDR3 RAM under OS X operating system. We define convergence as the point when the relative phase error reaches its stable point. The comparison does not consider the divergent cases. In the ideal data case, we can see that the sequential methods outperform all the other algorithms in terms of runtime. The Gerchberg-Saxton algorithm is the fastest in terms of both iteration number and runtime for this perfect dataset.
The main conclusions to be drawn from this section are that the FPM optimization algorithms which are formulated from amplitude-based and Poisson-likelihood-based cost functions are more tolerant to imperfect datasets with both Poisson noise and physical deviations like model mis-match, which were represented by aberrations and LED misalignment here. In the next section, we will explain more about the causes for this trend. The reason why amplitude-based and Poisson-likelihood-based algorithms have superior tolerance to experimental errors is due to their Poisson noise model. Each of these algorithms makes an implicit or explicit assumption that the magnitude of the errors in the data scale with the measured intensity. This is obviously a good model for Poisson noise errors, which are defined as noise which scales with intensity.
It is not as obvious that the model mis-match errors (aberrations and LED misalignment) scale with intensity as well. To demonstrate this, Fig. 7  shows the histogram of the difference between the deviated dataset and the ideal dataset, for the cases of both brightfield and darkfield images. The histograms show a similar trend -all of the brightfield errors are much larger than the darkfield errors, with a similar statistical variation. Thus, the errors from Poisson noise, aberrations and LED misalignment all scale with the measured intensity. In our experimental data, there are always aberrations in the objective lens, LED misalignment, and Poisson shot noise. Since the noise model for the amplitude-based and Poisson-likelihood-based algorithms match the actual noise properties, these algorithms perform better than the intensity-based algorithms.
), a system (geometry, materials, parameters, etc. ) and its environment (boundary conditions). Then, the problem is discretised with respect to its dimensions (spatial, time and other parameters). Finally, solving algorithm parameters are set. It can imply different methods, depending on the problem, objectives and results expected: iterative methods, DoE, optimisation methods, etc. This step is carried out with CAE softwares, supported by CAD softwares for the geometry definition. The second step is the solving: equations are formulated from the previously discretised model and solved by the solver program according to chosen algorithms. This step can be improved by optimising the used methods  [9]. Finite Element models may be solved in 1 h, 1 day, 1 week or even more. Thus, loops on this step (iterations or DoE) may demand an extremely high computational cost, without certainty about results correctness.
The last step consists in checking results and model validity (post-processing), and storing relevant data. There are five sources of error identified by  [8, 10]  which must be checked: (1) physical problem interpretation, (2) physical modeling, (3) numerical modeling, (4) solving and (5) results interpretation. Then, the model can be checked and results can be compared to customer's specifications for product validation. These steps are, most of the time, embedded in CAE systems. Actually, softwares are progressively integrating different tools, for modelling, simulation and validation to cover the whole process and simplify it. Multiple data types are generated from multiple systems at different steps. In addition to that, a simulation may be very expensive (highly nonlinear problem, iterative process, DoE, etc.
Definition and challenges SDM, covered by Product Data Management, is defined  [11]  as a technology which uses database solutions to enable users to manage structures of simulation data across the product lifecycle. It can also be defined, as Engineering Data Management defined by  [4] , as a process which aims to organise, structure, store and track information produced by simulation, in order to "create a coherent knowledge", from process data and product data. Workflow management and administration support may also be added  [11] [12] [13]. SDM can also be considered as a part of Simulation Lifecycle Management (SLM)  [14]. SLM, belonging to PLM, manages the process while SDM manages data. SLM covers collaborative product development, data traceability, decision-support and simulation systems integration for process automation.
Applications of SDM strategy in companies were classified in three maturity levels, defined by  [13] : -Level 1: "Isolated Islands". Local manual processes with low data volume stored in scattered and small databases. -Level 2: "Archipelago". Many linked databases with general rules and governances. -Level 3: "centralised/cloud". Automated processes, managing a very huge amount of high-value data stored in centralised database, led by a dedicated Information Technologies department in a collaborative environment. Benefits of this third level are numerous: fast access to data from anywhere, and for each stakeholder, enhanced decision support, data re-using, automated reporting, improved productivity, centralised and secured database, support for internal policies, etc. [15]  assess trends for input data management, used for modeling, by a survey (over 86 companies).
g. accuracy, timeliness, etc. ). Thus, SDM requires methods to deal with heterogeneous data from multiple sources and to ensure good properties. Data models support data collection, filtration, structuring and control. These functions may enhance data sharing. Data models may also integrate multiple data sources as systems or different designers  [21]. To deal with a large variety of data from multiple sources, a solution is the use of a neutral format  [4, 13]. Hence, standard models have been specified. One of the most well-known standard data-model is ISO 10303-209. It belongs to the Standard for Exchange of Product data-model family (STEP). The Application Protocol 209 (AP209), created in 2001, improves design analysis and manufacturing productivity of composites and metallic structures.
SDM strategy should also support DoE, optimisation and stochastic computations  [13, 31]. Thus, a SDM system prevents designers and analysts from creating data which already exist. SDM solutions can be provided by PLM softwares and CAE softwares. PLM softwares offer general solutions to manage projects and related data, as workflows, CAD models, versions, results, etc. CAE softwares may embed DoE and very specific SDM solutions, as automatic report generation, link between numerical models and material databases. Both of them may be used to reuse best practices but it must be enriched to manage the whole DoE process with accuracy. In addition to data models, ontologies can be used to enrich them. An ontology is a system of fundamental concepts set up to model, represent and describe a specific domain in terms of axiomatic definitions and taxonomic structures  [16].
According to  [36] , one static database for everything and everyone is unrealistic. Then, they propose an adaptive database, to ensure a heterogeneous data management from different sources in a collaborative environment. A method for decision-support related to the modelling step was developed by  [8]. It involves re-using previous studies by comparing their similarity to the current study. DoE and a metamodel (detailed further) are used to classify and compare performance of previous studies according to their different assumptions. Then, optimal modelling assumptions are proposed to the designer, regarding to quality, cost and time objectives.
DoE may involve a very high computational cost if a large number of experiments on a Finite Element model are demanded. Many different DoE exist and it implies some difficulties to select the best DoE. To reduce the computational cost, many methods were developed, as Adaptive DoE and surrogate modelling. But, these methods may increase the modelling step time. It may be very difficult to select and tune each technic used to obtain an adaptive DoE. A SDM strategy should be set to capitalise best practices related to DoE. It may avoid useless operations by using a centralised database. Such a strategy may enhance decision support for designers.
Measurements EsCCO was displayed continuously on a laptop computer, using a Nihon Kohden BSM9101 bedside monitor (Nihon Kohden, Tokyo, Japan), in which the esCCO system program software (esCCOMon, version 01-04) was installed. The pulse wave transit time is the measure of the interval between the ECG R wave and the pulse plethysmograph upstroke  [16]. Details of CO calculation have previously been published elsewhere  [11]. All transthoracic echocardiography (TTE) measurement was performed using a CX 50 device (Philips Medical Systems, Andover, MA, USA). Measurements were performed by an investigator (MF, JB) who was blinded to the measurements determined by esCCO. The Doppler echocardiography estimated CO (CO TTE ) was derived from the Doppler estimated Stroke Volume (SV) using the velocity-time integral (VTI) of flow through the left ventricular outflow tract (LVOT), the diameter of the LVOT, and heart rate recorded during the imaging study  [14].
Statistical analysis All data are presented as mean ± SD for quantitative variables and number (percentage) for qualitative variables. Inter-observer variability was calculated from 3 measures by each observer in each of 10 randomly selected patients, and was expressed as the mean percent error (i. e. the difference between the 2 observed values divided by the mean of the 2 observed values). Intra-observer variability was calculated from 3 CO TTE measures by the same observer from the same 10 randomly selected patients, Agreement between CO esCCO and CO TTE was assessed in three steps: Firstly, the relationship between the two methods was estimated using simple linear regression. Robust variance estimator and bootstrapped variance estimator were also used. Secondly, Pearson's correlation coefficient between CO esCCO and CO TTE was calculated.
Materials and Methods Search Strategy for Identification of the Three Seed Structures and Their Connections in Rat and Primates, Including Humans Relevant publications were obtained using the PubMed database and references from the consulted articles. The PubMed database was manually searched for articles describing connections of the three nuclei, globus pallidus internus, subthalamic nucleus, and nucleus accumbens. MeSH headings used were "globus pallidus, " "entopeduncular nucleus" (corresponding to the medial segment of the globus pallidus in rats), "subthalamic nucleus, " and "nucleus accumbens. " We further searched for the following terms: "globus pallidus internus, " "pallidum internum, " "internal globus pallidus, " "globus pallidus pars interna, " and "medial globus pallidus. " We combined them with the following MeSH headings for the studied species: "rats, " "primates, " and "human" and with the following key words: "connections, " "projections, " "afferents, " and "efferents.
Automatic Information Extraction from the Neuroscientific Literature To accelerate manual literature search, we used TM methods that distill very large amount of scientific articles in order to extract brain regions that are potentially connected. The TM process consist of three phases: first, identifying mentions of brain regions in text; second, determining which of these brain regions are connected, and third, aggregating and reporting on potential connections in a database easily searchable by neuroscientists. For the identification of brain regions, two complementary named entity recognizers (NER) were developed. The first NER uses a lexicon of all 1197 brain regions from the Allen Mouse Brain Atlas (ABA) (http://www. brainmap. org) that is automatically augmented with corresponding synonyms found in several lexica  (Richardet et al.
To this end, three different models were combined: (1) FILTER considers all possible brain region co-occurrences, and subsequently applies filters to remove unlikely ones; (2) KERNEL relies on a supervised machinelearning classifier; (3) RULES consist of 9 manually crafted rules of the kind "projection from the region A to the region C and the region D. " The resulting database shows, by selecting a region of interest, all other connected regions extracted from the literature and the possibility to drill down to the individual sentences for detailed analysis. The complete methodology can be found in  Richardet et al. (2015). The database is publicly accessible through a simple and intuitive web application. This application provides a matrix of brain regions co-occurences displaying the top N regions for which the most connection mentions was found (see Supplementary Figure  1 ).