dataesr/scientific-paragraphs-categorization huggingface dataset:
ACKNOWLEDGEMENTS This research manuscript made use of Astropy (Astropy Collaboration 2013; Astropy Collaboration & Astropy Contributors 2018), ChainConsumer 1 (Hinton 2016) and Matplotlib (Hunter 2007), and has been prepared using  NASA's Astrophysics Data System Bibliographic Services. IH, RR, SB acknowledge support from the  European Research Council  in the form of a Consolidator Grant with number  681431. IH also acknowledges support from the  Beecroft Trust. JPC acknowledges support granted by  Agencia Nacional de Investigación y Desarrollo (ANID)   DOCTORADO BECAS CHILE/2016 -72170279. Funding for the DES Projects has been provided by the  U. S. Department of Energy , the  U. S. National Science Foundation , the  Ministry of Science and Education of Spain , the  Science and Technology Facilities Council of the United Kingdom , the Higher Education The Collaborating Institutions are  Argonne National Laboratory , the  University of California at Santa Cruz , the  University of Cambridge, Centro de Investigaciones Energéticas ,  Medioambientales y Tecnológicas-Madrid , the  University of Chicago ,  University College London , the  DES-Brazil Consortium , the  University of Edinburgh , the  Eidgenössische Technische Hochschule (ETH) Zürich ,  Fermi National Accelerator Laboratory , the  University of Illinois at Urbana-Champaign , the  Institut de Ciències de l'Espai (IEEC/CSIC) , the  Institut de Física d'Altes Energies ,  Lawrence Berkeley National Laboratory , the  Ludwig-Maximilians Universität München  and the associated  Excellence Cluster Universe , the  University of Michigan, NSF's NOIRLab , the  University of Nottingham , The  Ohio State University , the  University of Pennsylvania , the  University of Portsmouth ,  SLAC National Accelerator Laboratory ,  Stanford University , the  University of Sussex ,  Texas A&M University , and the  OzDES Membership Consortium.
DATA AVAILABILITY The DES Y3 data products used in this work, full ensemble of DES Y3 source galaxy redshift distributions, chains and data products of the tests conducted here will be made publicly available following publication, at the URL https://des. ncsa. illinois. edu/ releases. The code is available in the C SIS standard library repository https://bitbucket. org/joezuntz/ cosmosis-standard-library/src/des-y3/.
Results The starting point of our analysis is 28 datasets of single-unit spiking activity recorded from areas V1 and V2 of the visual cortex of anesthetized macaques during stimulation with visual patterns drawn from a high-dimensional space of visual textures  [42]. Each dataset is a recording at a separate recording site or in a different macaque, and at each site, the stimulus space is sampled along its 10 axes, corresponding to 10 independent and visually salient kinds of spatial correlation (Fig. 1 ). We sample each axis at four points: two levels of positive correlation and two levels of negative correlation (see Materials and Methods for details). 64 perceptually similar examples of each of these 40 texture types (10 axes, 4 sample points per axis) were presented in random order, with each stimulus lasting 320 ms.
This sequence was repeated four times at each recording site. We refer to the neuronal responses to the 64 perceptually similar stimuli obtained in this way in one repeat as a "collection"; thus, there were 160 collections (40 texture types, 4 repeats) in each dataset. For our analysis, we selected the 80 collections with the smallest number of empty responses from each dataset. Depending on the dataset, the responses consisted of the spike trains of one or more isolated neurons. If more than four neurons were simultaneously recorded, we considered only the four neurons with the highest firing rates. We then applied TDA to characterize the topology of the firing patterns in each of the collections, and summarize the resulting characterizations to identify their consistent features. The TDA method we used follows very closely the framework proposed by  [22] , but we started from a different way of endowing a set of neuronal responses with a notion of distance.
Similarly, k = 0 corresponds to ignoring the neuron of origin, while k = 1 corresponds to considering a change in the neuron of origin equivalent to the insertion of a spike. We carried out TDA for a grid of values of these two parameters: q = 1, 2, 5, 10, 20, 50, 100, 200 (sec -1 ) and k = 0, 1. The resulting grid covered the range found relevant to neural coding in previous studies  [43, 3]. For each choice of parameters of the Victor-Purpura distance we computed topological summaries via Betti curves  [22]  (Fig. 2 ) and characterized relevant features of the topological space by computing mean Betti curves averaged over the 80 collections drawn from of each dataset. The procedure for construction of the Betti curves is detailed in Materials and Methods and summarized here. We first create a sequence of graphs from each collection; in each graph, the nodes are the individual responses in the collection, and the edges are determined by the dissimilarities (Fig.
These are computed at each step of the filtration, and thus, the Betti numbers are functions of the edge density ρ, the fraction of potential edges that have been filled in: β 1 (ρ), β 2 (ρ) and β 3 (ρ). These quantities, which we computed over the range from ρ = 0 to 0. 6 and then averaged over the 80 collections in a dataset, are shown in Fig. 2B. Note that while the Betti curves are sensitive to the geometry and topology of the metric space of data points  [22, 37, 50]  they are invariant under monotonic transformations of the distance  [22]. This means that they are sensitive only to the relative ordering of all distances. Below, we will focus on the mean Betti curves from the 80 collections with the highest firing rates at each recording site, but first we investigated whether the Betti curves had a substantial dependence on the two critical experimental variables that distinguished the collections: whether the recordings were in V1 vs.
g. , by virtue of different firing rate profiles), but rather, to analyze the intrinsic geometry of each collection, via methods that focus on firing pattern. Our results up to this point suggest that this geometry is largely independent of the recording area, or the stimuli that drive the responses. Given the similarity of the results of TDA across recording areas and texture types, we pool these results in the further analysis below and now focus on the mean Betti curves over the 80 collections within each of the datasets. To assess which aspects of the spike train data might be responsible for the shape of these mean Betti curves (e. g. , Fig. 2B ), we synthesized surrogate spike train data of four different types by perturbing specific aspects of the original experimental data. The description of the surrogate data is detailed in Materials and Methods and summarized here.
1. Uniform resampling of spike times (U): the spike times of each response are resampled uniformly in the response interval (0 -320ms). 2. Exchange resampling of spike times between collections (EB): the spike times of each response are resampled uniformly, without replacement, in the set of spike times of the 80 collections of the dataset. 3. Exchange resampling of spike times within collections (EW): as in 2, but with the resampling restricted to the set of spike times of the collection to which the response belongs. 4. Poisson generated spike trains (P): each response is replaced with a sample of a Poisson process with the same firing rate. In all cases, the spike times are resampled independently for each neuron that participates in a response. For each experimental dataset, we generated 20 surrogate spike datasets for each of the above four types, and computed Betti curves for these surrogates just as the curves were computed for the experimental data.
An example of this analysis is shown in Fig. 5. As is typical across the datasets, the Betti curves associated with the experimental data were often quite distinct from those of the surrogate sets. These differences were most prominent in the mid-range values of q (5 to 50 sec -1 ), and also more prominent for the decreasing filtration than for the increasing filtration. In addition, the Poisson surrogates usually show a greater divergence from the real data than the other surrogates. One possible reason for this is that, unlike the other surrogates, the Poisson surrogates do not preserve the number of spikes in each response. To determine the consistency of these features across the 28 datasets, we used the integrated Betti values and the centers of mass of the Betti curves. Thus, for every fixed Betti number (β 1 , β 2 or β 3 ), we considered the difference between the integrated Betti value of each surrogate (mean value over the 20 computations) and the integrated Betti value of the experimental data, and averaged them over the 80 collections from each dataset (see Fig.
6  for β 1 and Figs. S4-S5 for β 2 -β 3 ). Consistent with Fig. 6 , Figs. S4-S5 , and with the single dataset of Fig. 5 , the behavior of the experimental data departs from the behavior of the surrogates, especially for the mid-range values of q (5 to 50 sec -1 ). This holds both when the neuron of origin is ignored (k = 0) and when it is considered relevant (k = 1), and it is seen for both increasing and decreasing filtrations. All surrogates behave in a way that is distinct from the experimental data. As in Fig. 6 , three of the surrogates (U, EB, EW) behave similarly to each other, while the Poisson surrogate (P) deviates from the data more extensively. We confirmed these observations using the centers of mass of the Betti curves in place of the integrated Betti values (see statistical tests below).
For each random or geometric model, we computed the Betti curves of 300 sets of samples. We then compared these distributions with the Betti curves selected from our data via integrated Betti values and centers of mass. We restricted the analysis to collections with at most one empty response, in order to have 64 data points (and to exactly match the geometric models), and we randomly chose one such collection for every dataset that had collections meeting this criterion. This yielded Betti curves from 18 different datasets. To determine compatibility with the geometric models, we first tallied how many of the experimental integrated Betti values were within 3 standard deviations of the mean of the 300 values of the model for all Betti numbers β 1 -β 3 and for both increasing and decreasing filtrations.
Considerations regarding the experimental procedure The data analyzed here were collected from monkeys under propofol anesthesia/sufentanil analgesia and neuromuscular blockade. As a consequence, fixational eye movements could not have contributed to the fluctuations in spiking activity we observed in V1 and V2, but conversely, the natural dynamics of the visual input due to such eye movements is only partially approximated by the transient mode of stimulus presentation that we used. Another caveat is that the anesthesia and opiate analgesia may have produced noise correlations in the neural activity that contributed to the topological structure we extracted through TDA. While it is impossible to rule out any impact of anesthesia and analgesia on our results, there are two reasons that it is probably minor.
In 20 of the 28 analyzed datasets, the 64 analyzed responses to visual stimuli of the same type are part of a larger sequence of 128 responses to 128 unique stimuli; in these cases, we selected for our analysis the responses to the first 64 unique stimuli shown during the experiment. The patterns were presented in extended pseudorandom sequences at 100% contrast, surrounded by a mid-level gray background. Each pattern appeared for 0. 32 seconds and was immediately followed by the next pattern in the sequence. A different pseudorandom sequence was used for each of the four times a sequence was run during a recording block. There was a pause of about 1 minute between these repeats, during which time the gray background was displayed.
Analyzed data For each of the 28 datasets, the responses to all non-random stimulus types (each determined by a choice of an axis and a strength level for the correlations) for all repeats were then assembled to yield a total of 40×4 =160 collections. To study the topology of the space that neural activity occupies, we selected the 80 collections in each dataset with the smallest number of empty responses (i. e. , responses with 0 spikes). The vast majority of these collections had at least 60 non-empty responses; see Fig. S1 (D ). This choice for selecting collections is motivated by the fact that our analysis maps spike trains with at least one spike to distinct points in the topological space, while all empty spike trains are mapped to the same point. Thus, this selection criterion maximized the sampling of the space occupied by a collection.
The parameters q and k ranged over a grid of values: q = 1, 2, 5, 10, 20, 50, 100, 200 (sec -1 ), and k = 0, 1. The Victor-Purpura distance between spike trains is computed using the "labdist faster qkpara opt" Matlab function implemented by Thomas Kreuz, available at: http://www-users. med. cornell. edu/ ~jdvicto/labdist faster qkpara opt. html TDA methods We applied and extended the clique topology method introduced in  [22] , which corresponds to computing the Betti curves associated with our increasing filtration. Given a symmetric matrix M with zeros on its main diagonal, the first step of the method consists in considering the above-diagonal part of the matrix, transforming it by rank ordering its entries (thus replacing the original entry values by natural numbers 0, 1,. ), and completing the below-diagonal part of the rank-ordered matrix by symmetry.
The Betti numbers are viewed as functions of the edge density ρ, the number of filled-in edges divided by the number N = n(n -1) 2 of potential edges. These functions (β 1 (ρ), β 2 (ρ) and β 3 (ρ)) are the Betti curves, which we computed over the range from ρ = 0 to 0. 6 in our analysis. TDA software To compute clique topology and persistent homology, we use a faster and equivalent alternative to the original CliqueTop scripts (https://github. com/nebneuron/clique-top; see  [22] ), namely Ripser  [6]  (https://github. com/Ripser/ripser) on a rank-ordered distance matrix. Starting from a distance matrix D = (D ij ), we added small (symmetric) Gaussian noise and transformed the resulting symmetric matrix by rank-ordering its entries in increasing (resp. , decreasing) order for the increasing (resp.
Integrated Betti values and centers of mass In the analysis we use integrated Betti values  [22]  (see Figs. The center of mass of the Betti curve is defined as 1 I(β) ρmax 0 ρβ(ρ) dρ when I(β) > 0, and it is defined to be zero when I(β) = 0. Boxplots and KS statistical test Boxplots are generated with the Matlab function "boxplot". The two-sample Kolmogorov-Smirnov (KS) test was performed using the Matlab function "kstest2". In Fig. 7  and Figs. S6-S10 the significance level of the KS test has been corrected for multiple comparisons via the false discovery rate correction  [7].
Surrogate spike train data In our analysis, we compared the Betti curves computed from the experimental data to the Betti curves of four types of surrogate spike train data (Figs. 5-7 and S4-S10). For each experimental dataset, we generated 20 surrogate spike datasets for each of the four types. The four types of surrogate spike train data were generated by perturbing specific aspects of the spiking patterns in the original experimental data. 1. Uniform resampling of spike times (U). Each sequence of spikes from each neuron from each response is replaced by a sequence of the same number of spikes randomly distributed over the length of the response interval (0 -320ms). The sequence of labels indicating which neuron fired the spikes is preserved, as is the number of spikes of each neuron in the response.
2. Exchange resampling of spike times between collections (EB). Spikes are randomly swapped between the 80 selected collections of a dataset, preserving their time of occurrence in the 320ms response and their neuron of origin. Thus, each response in the surrogate dataset has the same number of spikes as the original, and the overall distribution of spike times across the dataset are maintained. 3. Exchange resampling of spike times within collections (EW). As in 2, but with the swapping restricted to responses within each collection. Thus, spike counts are unchanged within each response, as is the distribution of spike times within each collection.
4. Poisson generated spike trains (P). For each neuron contributing to a dataset, we determined its overall firing rate across the dataset. We then replaced each neuron's spike train in all non-empty responses in the dataset with a sample of a Poisson process with that rate. We set the bin width in the Poisson generator to 0. 0001ms. Note that this surrogate dataset does not preserve the number of spikes of each neuron in each response, only the average.
Each entry D ij is set equal to the Euclidean distance between the randomly-chosen ith and jth points. 3. Hyperbolic geometry model. Similarly to  [50] , we generated a random hyperbolic distance matrix D = (D ij ) by uniformly sampling 64 points in the d-dimensional hyperbolic space (for a fixed dimension d between 1 and 15), using the hyperbolic ball model  [29]  with curvature ζ = 1. We sampled a standard d-variate Gaussian (using the Matlab function "randn") and rescaled the radii of the sampled points by selecting radii r within [0, R max ] following the distribution ρ(r) ∼ sinh((d -1)r). We examined R max values in the range from 1 to 10, and results for R max = 1, 2, 5 are shown in Fig. 8  and Fig. S11. The distance D ij between two points of radii r i and r j with an angle ∆θ between them is determined from the hyperbolic law of cosines cosh ζD ij = cosh(ζr i ) cosh(ζr j ) -sinh(ζr i ) sinh(ζr j ) cos(∆θ) with curvature ζ = 1 in our setting.
Right: Betti curves are computed from each filtration. Betti curves are a topological descriptor that captures how the number of topological voids of different dimensions (holes, "bubbles", etc. ) depends on the proportion of added edges in the filtration process. B. Average Betti curves of one dataset. The average Betti curves for β 1 -β 3 over the 80 collections of one dataset (L7301TT6), containing recordings of spiking activity of 4 neurons in layer 5 of area V2, are displayed for increasing and decreasing filtrations, and for each value of the parameters q (timescale, sec -1 ) and k (sensitivity to neuron of origin) of the Victor-Purpura distance. The two top (respectively, bottom) rows correspond to the increasing (resp. , decreasing) filtration method. The odd (resp. , even) rows correspond to k = 0 (resp.
Insets zoom in on some boxplots at a smaller scale. When present, a dashed line bounds an area at the extreme of a plot beyond which data are shown on a compressed ordinate. The four panels are for increasing (A,B) and decreasing (C,D) filtrations, and for k = 0 (A,C) and k = 1 (B,D). For example, in A, the means of the integrated Betti values for the Poisson surrogates for all timescales, q are greater than the means of the integrated Betti values for the experimental spiking responses from the 28 datasets. Note that the deviation of the behavior of the surrogates is maximal for the range q = 5 sec -1 to q = 50 sec -1. < l a t e x i t s h a 1 _ b a s e 6 4 = " e q g b P D z m i 9 r P 5 Q Z y u e D v 8 Q J B 3 t     In the range q = 5 to 20 sec -1 , the greatest compatibility occurs for dimensions 3-5, and for the Euclidean or hyperbolic models with moderate curvature (R max = 1).
Acknowledgments JDV and KPP acknowledge  Qin Hu ,  Ferenc Mechler ,  Eyal Nitzany ,  Anita Schmid ,  Dan Thengone  and  Yunguo Yu  for assisting with data collection. They also acknowledge  NIH  grants number  EY09314  and  EY07977  from the  National Eye Institute  of the  NIH. KPP acknowledges  NIH  grants  EY034150  from the  National Eye Institute  and  NS111019  from the  National Institute of Neurological Disorders and Stroke. SR was supported by  Ikerbasque (The Basque Foundation for Science) ; AG and SR were supported by the  Basque Government  through the  BERC 2018-2021 program  and by the  Ministry of Science, Innovation and Universities :  BCAM Severo Ochoa  accreditation  SEV-2017-0718  and through project  RTI2018-093860B-C21  funded by ( AEI/FEDER, UE)  with acronym " MathNEURO ".
Betti curves are a topological descriptor that captures how the number of topological voids of different dimensions (holes, "bubbles", etc. ) depends on the proportion of added edges in the filtration process. B. Average Betti curves of one dataset. The average Betti curves for β 1 -β 3 over the 80 collections of one dataset (L7301TT6), containing recordings of spiking activity of 4 neurons in layer 5 of area V2, are displayed for increasing and decreasing filtrations, and for each value of the parameters q (timescale, sec -1 ) and k (sensitivity to neuron of origin) of the Victor-Purpura distance. The two top (respectively, bottom) rows correspond to the increasing (resp. , decreasing) filtration method. The odd (resp. , even) rows correspond to k = 0 (resp. , k = 1). In the increasing filtration plots, the Betti curves for β 3 are close to zero.
To generate the distribution of integrated Betti values, individual (non-averaged over the dataset) Betti curves of each collection of responses are considered. The four panels are for increasing (A,B) and decreasing (C,D) filtrations, and for k = 0 (A,C) and k = 1 (B,D). Each panel shows the distribution of integrated Betti values for all values of the timescale parameter q of the Victor-Purpura distance.
1 <Figure S2 :DFigure S7 : 1S2S7 Figure S2: Comparison of centers of mass of the Betti curves for data recorded in V1 vs. V2. The figure is similar to Fig. 3 of the main text, but Betti curves are summarized via their centers of mass (see Materials and Methods of the main text) instead of their integrated Betti values. The values of the centers of mass of the Betti curves for β 1 -β 3 of the experimental data are shown divided into two groups, according to whether the data were recorded in area V1 (blue) or V2 (red) of the visual cortex. To generate the distributions of centers of mass displayed in the figure, individual (non-averaged over the dataset) Betti curves of each collection of responses are considered. The four panels are for increasing (A,B) and decreasing (C,D) filtrations, and for k = 0 (A,C) and k = 1 (B,D).
1 (Figure S8 : 1S8 Figure S8: Two-sample Kolmogorov-Smirnov test for the centers of mass of the Betti curves for β 1. Two-sample Kolmogorov-Smirnov test statistic D * (ordinate) for comparison of the samples of centers of mass of the Betti curves for β 1 of the experimental data with each type of surrogate data. The sample for the experimental data consists of the (28 × 80) center of mass values from all 80 collections from all 28 datasets. The samples for each surrogate consist of the (20 × 28 × 80) center of mass values of the 20 computations. Values above the dashed line, corresponding to p = 0. 05, indicate rejection of the null hypothesis that the two samples come from the same distribution. The dotted line corresponds to the value p = 0. 05 corrected for multiple comparisons, using the false discovery rate method.