dataesr/scientific-paragraphs-categorization huggingface dataset:
Acquaviva, 2008 Acquaviva, , 2016;; Lauwers and Lammert, 2016) , we include here data from a plurality rating task, in order to account for plurality-or, specifically the perceived plurality-of concepts as a scalar property 7. For this, we designed a questionnaire as described in section 2. 3. 2 below. Another possible explanation that we explore is the influence of frequency, since the principle of economy suggests that high-frequency concepts should have forms that are less costly to articulate, which in turn could influence the number of articulators used for specific signs (cf. Crasborn and Sáfár, 2016, p. 244). For this, we used the lemma frequency of the concept's English name in the British National Corpus  (Leech et al. , 2001).
Data Processing We estimate the number of articulators by calculating the total length of the path traced by each hand (in the normalized coordinate system) during a sign. If the path length of one hand exceeds the other's by a factor of more than 3, we classify the sign as one-handed. All other signs are classified as two-handed. In rare cases, the video processing stage fails to identify the hand(s). To deal with this we discard all signs with hands detected in <10 frames.
Plurality Rating Questionnaire Since little quantitative data exists on lexical plurality, we sent out an online questionnaire and collected plurality ratings from respondents (N = 23; 10 female, 13 male; mean age 29, SD 10), mainly those without a linguistics background. Respondents were asked to rate the lexical plurality of 100 concepts, 50 of which were taken from a previous study  (Börstell et al. , 2016) , collected from various sources  (Attarde, 2007; Haspelmath, 2007; Wisniewski, 2010)  identifying them as lexically plural concepts, and 50 which were random concepts frequency matched (pairwise) to the lexically plural concepts in another study  (Börstell et al. , 2016). Lexical plurality is defined in the questionnaire as "whether or not there is some inherent plural meaning of the concept (e.
g. , involving multiple parts/participants/events). " Concepts were presented in random order, and respondents were asked to provide ratings on a discrete scale from 1 ("not at all plural") to 7 ("definitely plural"). For our analysis, 19 concepts from the questionnaire were excluded for one of two reasons: 1. 5 concepts: Body parts for which  Börstell et al. (2016)  used a plural form (e. g. , "eyes") while Spread the Sign uses a singular form (e. g. , "eye"). 2. 14 concepts: Missing data from Spread the Sign. Thus, a total of 81 concepts with both plurality ratings and number of hands in Spread the Sign remained to be used in our analysis.
Distribution of One-vs. Two-Handed Signs Table  4  shows the distribution of one-and two-handed signs in each language, for both core vocabulary and extended vocabulary. We define the core vocabulary to include all signs available in the data that represent concepts in the Swadesh list from  Lepic et al. (2016) , in total 5,667 signs for 195 concepts. Going beyond the core vocabulary is problematic, since two-handedness becomes a less meaningful property when dealing with compound signs or whole phrases, and Spread the Sign does not contain enough information to distinguish these from simple signs. In order to obtain an extended vocabulary of mostly non-compound signs, we use all signs for concepts with single-word translations in an isolating language (English). This results in 122,935 signs, an amount that would be very time-consuming to classify manually, hence our automatic processing demonstrates its usefulness.
From these results, we see that the proportion of two-handed signs in the extended vocabulary (71. 0%) is much higher than the corresponding figure for the core vocabulary (56. 0%, cf. ). Note that all languages in our data are included here, i. e. , also those excluded from our analysis due to unreliable video processing (Czech SL, British SL, Russian SL, and Portuguese SL). Figure  4 ), although still lower than in the list of lexical plurals (81. 8%, cf. Figure  5 )  9. This may be explained by lexical frequency and articulatory economy. For instance,  Crasborn and Sáfár (2016)  show that the while the distribution of one-vs. twohanded signs in Sign Language of the Netherlands is more or less balanced in lexical databases, there is a bias toward onehanded signs in corpus tokens. The authors suggest that ease of articulation may cause lexically two-handed signs to be produced as one-handed signs  (Crasborn and Sáfár, 2016, p.
244). In fact, it may even be possible that frequency effects on phonetic reduction pushes toward one-handed articulation with frequent signs, similarly to how frequent signs have been shown to be the most reduced in terms of sign duration  (Börstell et al. , 2016). However, seeing as other sign databases of similar size to Spread the Sign (per individual language) have been shown previously to exhibit a near 50/50 distribution of one-vs. two-handed signs  (Börstell et al. , 2016, p. 393) , it is also possible that the selection of concepts in the Spread the Sign project affects the distribution. As stated on their website, one objective of the project was to facilitate vocational training exchanges between countries, and possibly the inclusion of vocational school terminology results in a higher proportion of complex concepts that require compound, phrasal, and/or depicting constructions, which are more likely to be encoded (in part) by two-handed forms.
Overall, the activity areas are less distinct than for the individual concepts shown in Figure  8 , which is expected from the conflation of data from many signs across all languages into one image, but iconic mappings can still be observed. Besides the figures shown here, we have generated visualizations of sign locations across languages for all individual concepts and sign categories present in the Spread the Sign database at the time of download 10. This may prove useful for other researchers interested in further exploring the crosslinguistic patterns of iconicity with regard to sign locations and semantics.
Number of Articulators For our first study, we wanted to investigate the distribution of one-vs. two-handed signs across the sign languages in the dataset. Previous studies have suggested that sign language lexicons exhibit quite an even split between one-and twohanded signs  (Börstell et al. , 2016; Crasborn and Sáfár, 2016; Lepic et al. , 2016). Our statistical model (section 3. 1. 3), using 81 concepts for which we have lexical plurality ratings, indicates that none of the sign languages in our sample has a strong preference for either one-or two-handed signs. Sampling signs corresponding to the concepts in a Swadesh list, which may be used as an approximation of core vocabulary, we see that the distribution corresponds to the one predicted, with an even distribution across all signs and languages.
Although we do not have an answer to why this is the case, it is possible that less frequent signs are more likely to be two-handed, if one assumes that the the transition from two-handed to one-handed could be a frequency-induced economically motivated reduction (cf. Crasborn and Sáfár, 2016, p. 244). The frequency hypothesis was tested in our statistical model using 81 concepts, but could neither be supported nor conclusively rejected. It may also simply be the case that the sample, though consisting of simplex word forms in English, are encoded by complex, depicting, or multi-sign constructions to a larger extent than the smaller core vocabulary set, as larger lexical databases for individual sign languages-hence implying both frequent and infrequent lexical items included-have previously been found to adhere to the 50/50 pattern, too (see  Börstell et al.
Similarly, if the one-vs. two-handed division is a useful phonological distinction, it would be a severe limitation to not let that distinction be used arbitrarily. This does, however, not entail that it can never be used iconically, and we argue that two-handed forms are often iconically mapped onto plural meaning when possible, but plurality is not a strict requirement when forming two-handed signs. Concerning the association between lexical plurality and two-handed signs, as found by  Börstell et al. (2016) , we can say with certainty that this is a valid claim across the languages in our dataset. Our statistical model showed that concepts are significantly more likely to be encoded by a twohanded form if the concept carries plural semantics, even when taking language-and concept-specific variation as well as frequency into account.
The problem of finding parametric positive solution is essentially that of quantifier elimination over the first order theory of real closed fields. In 1930, Alfred Tarski  [26]  showed that real quantifier elimination can be carried out algorithmically. Since then, there have been intensive research, producing profound theories, dramatically improved algorithms, and highly refined implementations in widely available computer algebra software such as Mathematica, Maple, Qepcad B, or Reduce, e. g. ,  [26, 8, 2, 19, 13, 7, 14, 15, 9, 29, 25, 23, 6, 22, 16, 17]. However, existing general quantifier elimination algorithms are still too inefficient for tackling even small problems of finding parametric positive solutions. The main contribution of this paper is to provide simple and efficient algorithmic criteria for deciding whether or not a given signed parametric system has a parametric positive solution.
The equivalence between (i) and (iii) in the corollary states the following: The procedure in  [12]  yields "sat" in contrast to "unknown" if and only if not only the input system is satisfiable, but that system with all real choices of coefficients with the same signs as in the input system. While there are no formal algorithms in  [12] , the work has been implemented within a combination of the veriT solver  [4]  with the library STROPSAT  [12, Sect. 6]. Our characterization applies in particular to the completeness of this software. We have added (ii) to the corollary, because we consider this form optimal for algorithmic purposes. Like the original input C ′′ used in  [12]  this is a conjunctive normal form, which is ideal for DPLL-based SMT solvers  [20]. Recall that u is the number of inequalities in the input, and d is the number of variables.
Acknowledgments This work has been supported by the  European Union 's  Horizon 2020 research and innovation programme  under grant agreement No  H2020-FETOPEN-2015-CSA 712689 SC-SQUARE  and by the  bilateral  project  ANR-17-CE40-0036  and  DFG-391322026  SYMBIONT. The second author would like to thank  Georg Regensburger  for his hospitality and an interesting week of inspiring discussions around the topic, and  Dima Grigoriev  for getting him started on the subject.
A final d is refined in Step 5. Step 3: Replace the phase sinogram with the modeled phase sinogram (from Step 2) within the window (defined in Step 1), as demonstrated in Fig. 1(c). Step 4: Reconstruct the corrected slice from the sinogram in Step 3. Step 5: Repeat Steps 2-4 and monitor the flatness of a uniform region of interest in the slice. The optimal model d value is the one which results in the flattest region of interest for a given replacement window, meaning that cupping has been completely removed. Figure  1  shows Steps 1 to 3 applied to sinograms from the paraffin-embedded cerebellum measurement. The correction has been implemented in MATLAB (The MathWorks, Inc. , Natick, Massachusetts, United States) and made available in the supplementary material as well as at github. com/grodg-ers1/phase_wrapping_correction along with sample data.
To confirm the quantitative accuracy of the correction, two specimens were measured with an double-grating XGI setup both with and without a water bath, allowing for a comparison between a not phase wrapped (NW) dataset, a phase wrapped (W) dataset, and the wrapped dataset corrected with our algorithm (WC). The first specimen consisted of a stack of cylindrical, plastic phantoms including two varieties of polyvinyl chloride (PVC1, PVC2), polyoxymethylene (POM), and polypropylene (PP) with 1 mm in height and 2. 5 mm in diameter. To demonstrate the correction in the context of a biological specimen, a cylindrical punch of a paraffin-embedded human cerebellum with a diameter of 6 mm was used. The brain was extracted postmortem and embedded in paraffin following standard histological preparation.
6 Â 6. 0 mm 2 field of view. The phantom and cerebellum datasets were taken with 501 and 1201 projections, respectively, with 5 phase steps per projection around 180. The exposure time was selected to maintain nearly equal counts within the specimen for projections of the same sample with and without water bath. Figure  2  shows the measured mean d values and associated standard deviations of the phantoms in the WC (blue) and W (green) datasets against the values from the NW dataset. All d values are relative to PVC2 because the surrounding medium was different (water for NW and air for W and WC). In Fig. 2 , the red line with a slope of one is a visual aid indicating perfect agreement with the NW dataset. The paraffin-embedded cerebellum is visualized in Figs. 3(a  artifacts in the W dataset (green), as well as the strong agreement between the NW and WC datasets (red and blue, respectively).
The histograms for 25 masked slices are shown in (e), with the W dataset smeared out due to cupping and a strong resemblance between the NW and WC datasets. These experimental results confirm the quantitative and qualitative accuracy of the proposed correction algorithm. The measured d values of the phantoms in the WC dataset match those of the NW dataset, while the W dataset produces inaccurate values with high variations due to cupping. This cupping is clearly visible in the paraffin-embedded cerebellum dataset, but has been removed by the correction algorithm, as demonstrated by slices and line profiles. The histograms of the three datasets demonstrate the improved density resolution after the application of our correction algorithm. In conclusion, we have presented an algorithm to remove phase wrapping artifacts from phase tomography.
This algorithm uses the absorption sinogram to determine the specimen geometry, then models and replaces the phase sinogram in the wrapped regions. The selection of d for the modeled sinogram can be determined automatically by minimizing cupping in the resulting reconstruction. Finally, we present experimental results from phase tomography datasets with phase wrapping, with phase wrapping and corrected with the proposed algorithm, and without phase wrapping. These results confirm that datasets corrected with our proposed algorithm are quantitatively and qualitatively consistent with datasets that had no phase wrapping. Our correction algorithm allows for measurements without submerging the sample in a water bath, improving the experimental setup and avoiding motion artifacts from gas bubbles.
While we used this algorithm with phase-stepping data from a double-grating setup, its application is not restricted to these modalities; the method could also be used, e. g. , for single-grating setups or for data acquired in moir e mode. See supplementary material for the Matlab source code of the proposed correction algorithm. It is also available along with sample data and examples at github. com/grodg-ers1/phase_wrapping_correction.
The authors thank  Professor S. Theocharis  ( National and Kapodistrian University of Athens ) for providing the cerebellum specimen. The authors thank  Dr. C. Rau  for providing the beam time. The project was supported by  Diamond Manchester Imaging Branchline  ( I13-2   Diamond Light Source, UK) , Project No. MT 19829-1. One of the authors (T. W. ) acknowledges support from the  French National Research Agency (ANR)  through the  EQUIPEX investment program , project  NanoimagesX ,  Grant  No. ANR-11-EQPX-0031.
For instance, in the Figure, the 8 tokens are associated to distinct versions of the variable U (the U i 's) after consuming the input a b c: one for each subset of the alphabet. However, timed constraints most often improve the situation by removing expired tokens. Thus, in practice there are ways to avoid the worst-case scenarios. This is similar to the practical "regex" tools, which in general go well beyond regular expressions, also leading to exponential blowups in the worst case  [6, 7]. νU. U U νN. N. νN U 0 a b c U 1 a b U 2 a c U 3 b c U 4 a U 5 b U 6 c U 7 ε This makes experimental evaluation of our method particularly appealing to estimate its practical performances and applicability. In order to do so, we consider two link streams built from two different real-world datasets: (1) a recording of traffic routed by a large internet trans-Pacific router  [11] , and (2) a one month capture of tweets on Twitter France.
To obtain this scale-invariance property, we rely heavily on the bootstrapping procedure. We refine the recent FHE construction by Chillotti et al. (ASIACRYPT 2016)  in order to increase the message space and apply the sign function (that we use to activate the neurons in the network) during the bootstrapping. We derive some empirical results, using TFHE library as a starting point, and classify encrypted images from the MNIST dataset with more than 96% accuracy in less than 1. 7 seconds. Finally, as a side contribution, we analyze and introduce some variations to the bootstrapping technique of Chillotti et al. that offer an improvement in efficiency at the cost of increasing the storage requirements.
However, this setting raises new issues concerning the privacy of the uploaded input data. Users want to send their encrypted data to a cloud service that offers privacy-preserving predictions, and fulfills this task using its powerful yet undisclosed, state-of-the-art predictive models. In this paper, we put forward a new and versatile FHE framework that makes it efficient for the cloud to operate a neural network dedicated to some specific machine learning task. The network, previously trained on plaintext dataset, does not have access to the input data in the clear, but is only given user-provided encrypted inputs and returns encrypted predictions. Obviously, encrypting the user's data ensures its confidentiality, since the private key under which the data is encrypted is assumed never to leave the owner's controlled domain.
In this setting, only the legitimate owner of the secret key can decrypt the result returned by the delegated computation that has been homomorphically performed in the cloud. The cloud service only learns superficial information, but can still charge the user for using the service. Neural networks (NNs) are often built from medical, financial or otherwise sensitive data. They are usually trained to solve a classification problem: all possible observations are categorized into classes and, given a training dataset of observation/class pairs, the network should be able to assign the correct class to new observations. Such framework can be easily applied to problems like establishing a diagnosis from medical observations. In this work we do not consider the problem of privacy-preserving datamining, intended as training a neural network over encrypted data, which can be addressed, e.
g. , with the approach of [AS00]. Instead, we assume that the neural network is trained with data in the clear and we focus on the evaluation part. Another potential concern for the service provider is that users might be sending malicious requests in order to either learn what is considered a company secret (the neural network itself), or specific sensitive information encoded in the weights (which could be a breach into the privacy of the training dataset). In this latter case, a statistical database can be used in the training phase, as is discussed in the differential privacy literature [Dwo06]. Prior works. Cryptonets [DGBL + 16] was the first initiative to address the challenge of achieving blind, non-interactive classification. The main idea consists in applying a leveled SHE scheme such as BGV [BGV12] to the network inputs and propagating the signals across the network homomorphically, thereby consuming levels of homomorphic evaluation whenever non-linearities are met.
So the evaluation of DiNNs boils down to repeatedly computing the sign of a weighted sum of ±1 inputs. In order to perform this classification on encrypted data, we adapt the recent construction by  Chillotti et al. , known as TFHE [CGGI16b]  to support sign and weighted sum as the two basic operations of the scheme, the sign being computed during a bootstrapping procedure in order to refresh the ciphertext. As a side contribution, we also present a few techniques to optimize the usage of TFHE in applications: how to reduce the required bandwidth, how to reduce the overall noises in the ciphertexts, and a slightly faster alternative to the bootstrapping procedure that also produces ciphertexts with less noise, at the expense of a bigger bootstrapping key. Finally, we conducted experiments on the MNIST dataset  [LBBH98].
However, it should be noted that (a) the networks that we use for our experiments are considerably smaller than that used in Cryptonets, so we also compare the time-per-neuron and, in this case, our solution is faster by roughly a factor 36; moreover (b) once again Cryptonets support image batching, so 8192 images can be classified in 570 seconds, resulting in only 0. 07 s per image. Cryptonets' ability to batch images together can be useful in some applications where the same user wants to classify a large number of samples together. In the simplest case where the user only wants a single image to be classified, this feature does not help. Regarding classification accuracy, the NN used by Cryptonets achieves 98. 95 % of correctly classified samples, when evaluated on the MNIST dataset. In our case, a loss of accuracy occurs due to the preliminary simplification of the MNIST images, and especially because of the discretization of the network.
The MNIST dataset The MNIST database (Modified National Institute of Standards and Technology database) is a dataset of images representing digits handwritten by more than 500 different writers, and is commonly used as a benchmark for machine learning systems  [LBBH98]. The MNIST database contains 60 000 training images and 10 000 testing images. The format of the images is 28 × 28 and the value of each pixel represents a level of gray. Moreover, each image is labeled with the digit it depicts. A typical neural network for the MNIST dataset has 28•28 = 784 input nodes (one per pixel), an arbitrary number of hidden layers with an arbitrary number of neurons per layer, and finally 10 output nodes (one per possible digit). The output values can be interpreted as "scores" given by the NN: the classification is then given by the digit that achieves the highest score.
Over the years, the MNIST dataset has been a typical benchmark for classifiers, and many approaches have been applied: linear classifiers, principal component analysis, support vector machines, neural networks, convolutional neural networks, etc. For a more complete review on these approaches, we refer the reader to, e. g. ,  [LBBH98]. Neural networks are known to perform well on this dataset. For example,  [LBBH98]  proposes different architectures for neural networks and obtains more than 97% of correct classifications. More recent works even surpassed 99% of accuracy  [CMS12]. For a nice overview on the results obtained on this dataset and on the techniques that were used, we refer the reader to [LCB98].