dataesr/scientific-paragraphs-categorization huggingface dataset:
Analysis To characterize high-order statistics of natural images, we calculated the skewness and kurtosis (as "excess kurtosis") of the distribution of filter coefficients, i. e. , the distribution of values that result from convolving the images with TDH functions. To focus on the structure of the individual scenes (rather than the overall differences across scenes), skewness and kurtosis were calculated individually for each image, and values were then averaged across the image database. As shown in Figure  3 , this calculation was carried out across 7 spatial scales, spaced in approximately octave steps. The smallest scale used was σ = 7/12 (0. 58) pixels and the largest, σ = 511/12  (42. 6 ) pixels. At each scale, the image was convolved with polar TDH functions of ranks 0-7 (36 filters in all), and the convolution was sampled at points placed in a rectangular grid on the Symmetry 2016, 8,98 filtered image.
Currently, CNNs are being applied to object recognition tasks  [19, 20] , image description  [21] , and texture synthesis  [22] , and they have conquered other areas like speech recognition  [23]. CNNs learn a hierarchy of different filters that are applied to an input image, enabling them to extract useful information. The training algorithm works in a supervised manner, which means that, given an input image, the output is compared to the target output so that an error gradient can be computed. Using backpropagation, parameters of the model are changed so that the error is minimized and the network gets better at solving the task at hand. In our study, we use filter responses from CNNs that were trained on millions of images of objects  [24]  for measuring continuous symmetry in images. To validate our results, we collected a dataset of 300 different CD album covers and asked human observers to rate them according to their left/right symmetry.
Several fully-connected layers that are stacked on top of a network learn to map extracted features onto class labels. Interestingly, the filters on the first layer tend do develop oriented Gabor-like edge detectors, akin to those found in human vision, when trained on huge datasets containing millions of natural images  [25]  (see Figure  1 ). In our experiments, we drop the fully connected layers on top, which allows us to resize the input to have a dimension of 512 × 512 pixels. Using this modification of the CaffeNet model  [24] , we propose an algorithm that measures continuous left/right mirror symmetry of natural images, as follows. Symmetry 2016,  8, 144  First, every image is fed to the network, which yields 96 filter response maps after the first convolutional layer, 256 after the second, 384 after the third and fourth, and 256 after the last convolutional layer.
Image Dataset In order to evaluate the algorithm proposed in Section 2. 1, we used a dataset of 300 CD album covers that were collected from the internet in 2015 (kindly provided by Ms. Maria Grebenkina, University of Jena School of Medicine). Images were equally distributed between three different music genres (classic music, pop music and metal music). All cover images had a resolution of 500 × 500 pixels, or were down-sampled to this size by bicubic interpolation if the original image had a higher resolution. A complete list of the 300 CD covers used in this study is provided in Supplementary Table  S1. The dataset is made available on request for scientific purposes (please contact author C. R. ).
Conclusions We propose a novel computational method that was developed to predict human left/right symmetry ratings for complex, non-geometrical images, as exemplified by CD album covers. The aim of the model is to closely match subjective symmetry as judged by human observers. For this purpose, we used filters learned by CNNs because they are akin to receptive fields in the early human visual system and get more and more abstract at higher layers of the CNNs. In order to evaluate our method, Symmetry 2016, 8, 144 we compared the results from the computational model with subjective ratings by 20 participants who assessed left/right symmetry in a dataset of 300 different album covers. We evaluated different model configurations by calculating the correlation between the computationally obtained results and the ratings by humans.
Implementation of the Algorithm First, the input color image is rescaled to half the original resolution. Second, by using the de-correlation procedure described in Section 3. 3 on the resulting image, we get 9 de-correlated multi-resolution and chromatic channels. Third, a fixed block size (e. g. , 12) is selected, as discussed later in Section 4. 6; this choice is governed by the dataset. If the rows and columns of the de-correlated channels are not divisible by the block size, then they are padded with neighboring information along the right and bottom corners. Finally, the saliency map is generated by using the procedure outlined in Section 3. 2. The code is open source and is available at Matlab Central for the research community.
Dataset For the analysis, we used the eye tracking database from the study by Judd et al. [16]. The database consists of 1003 images selected randomly from different categories and different geographical locations. In the eye tracking experiment  [16] , these images were shown to fifteen different users under free viewing conditions for a period of 3 s each. In the database, a majority of the images are 1024 pixels in width and 768 pixels in height. These landscape images were specifically used in the evaluation.
For this, we used MATLAB R2015 on a 64-bit windows PC with a 3. 16-GHz Intel processor and 4 GB RAM. From Figure  6 , we observe that the algorithms Hou, and Spec are the fastest. However, among the top six algorithms, the proposed fast GBA model is the fastest. Furthermore, it shows that Fast GBA is nearly 31-times faster than the original GBA algorithm. It is important to note that the original GBA algorithm is crude in implementation, i. e. , the eight group transformations are performed iteratively and kept in the memory. In the fast GBA model, reducing the computational complexity (by employing the steps mentioned in Section 3. 2) also reduces the memory and software complexity of the proposed model, which is reflected in the results. To observe if de-correlation of color image channels (mentioned in Section 3.
We note that from the rotations along opposite diagonals, faces and edges, we get 8, 9 and 6 elements, respectively. These elements along with the identity form the 24 elements of the S 4 group. Saliency for three-dimensional image data can be calculated by employing the same procedure as discussed in Section 3, but instead of computing in two-dimensional space using the D 4 group, we can calculate it in three-dimensional space using the S 4 × S 2 transformations. For example, after dividing the three-dimensional scene into uniform sized cubes, we can rotate and reflect a cube and record the values associated with the transformations. The recorded values can be collected in a matrix Symmetry 2016, 8,79 and rescaled along each of the three planes, i. e. , X-Y, Y-Z, Z-X, to get a three-dimensional feature map.
Conclusions In this article, first, we briefly describe the dihedral group D 4 that is used for calculating saliency in our proposed model. Second, our saliency model makes the two following changes in a latest state-of-the-art model known as group-based asymmetry: first, based on the properties of the dihedral group D 4 , we simplify the asymmetry calculations associated with the measurement of saliency. This results is an algorithm that reduces the number of calculations by at least half that makes it the fastest among the six best algorithms used in this research article. Two, in order to maximize the information across different chromatic and multi-resolution features, the color image space is de-correlated. We evaluate our algorithm against 10 state-of-the-art saliency models. Our results clearly show that by using optimal parameters for a given dataset our proposed model can outperform the best saliency algorithm in the literature.
One-dimensional fractal time series were generated from phase maps with amplitude series that varied in the specified β, β (input) (see Figure  6e-g ). Symmetry 2016, 8,66 Values of β (input) were paired with phase maps to create 2-dimensional fractal images as well (see Figure  7e-g ). Box counting was performed on the intersection of 1-dimensional fractals with a horizontal line at the trace's median height. For the 2-dimensional fractal images, a fractal dust set was formed by taking the intersection of the height values of each row of the image with a line intersecting the median height. This dust set was used to compute the box counting dimension through the use of custom Matlab scripts. Briefly, for each box size with side length L, from the length of the fractal to a single pixel in steps of L/2 for a total of n steps, the image is covered with a set of boxes, and the number of boxes that contain any non-zero quantity of points is counted.
The box counts of pairs of neighboring grid scales from L/(2 3 ) to L/(2 n ´3) were averaged to compute D, while the counts from the grid scales outside this range (the larger and smaller boxes, where n = {0, 1, 2, n ´2, n ´1, and n}), were not used. The embedding dimension of the series of points is 1, but the embedding dimension of the fractal mountain edge is 2, so we averaged these values of D, computed for pairs of grid sizes, and added 1 to report the fractal dimension of the 1-dimensional fractals, D (Mountain Edge) , which span the range 1<D (Mountain Edge) <2. To isolate the coastal edge of a fractal terrain, the median intensity value of the intensity image was selected as the level at which a binary threshold procedure was applied with the Matlab command im2bw. The median, in particular, was selected because it is the level at which all of the resultant binary images have roughly equivalent black and white regions across the range of D.
All of the participants responded to the four series of stimuli, with short pauses of four minutes between one series and the next. The overall duration of the experiment was 36 min. A stand alone software (programming language: Actionscript 3 for Adobe AIR runtime environments) was used for the presentation of the visual and acoustic stimuli. A Dell P2210 56 cm  (22  In. ) screen (Dell, Round Rock, TX, USA) with a resolution of 1680 × 1050 pixels (475 × 300 mm, equivalent to approximately 43. 2 × 28. 1 degrees of visual angle at the recommended viewing distance 650 mm) and a refresh rate of 60 Hz was used for the experiment. The visual stimuli were made up of 1680 × 1050 pixels and thus filled the entire screen. The visual stimuli consisted of five small square red dots presented in succession, with each dot lasting 600 ms in the isochronous condition, and 400 ms or 800 ms in the non-isochronous condition, and disappearing when the next dot appeared on the screen (i.
e. , the inter-dot interval was null). Each stimulus started from left to right and was centered with respect to the screen. The acoustic stimuli were created using MakeMusic Finale 2011 (MakeMusic Corporate, Boulder, CO, USA) at a sampling rate of 44,100 Hz-32 bit (and presented with Creative Sound Blaster Audigy FX PCIe 5. 1 (Creative Technology, Singapore, Asia) using high quality loudspeakers Audioengine A2+ (Audioengine, Austin, TX, USA). Auditory stimuli were equalized for overall sound pressure using Audition CC 2015 (Adobe Systems Software, San Jose, CA, USA). The stimuli consisted of five tones (Timbre: Guitar; attack: 10 ms; decay: 31 ms). Each tone had an overall duration of 600 ms in the isochronous condition, and 400 ms or 800 ms in the non-isochronous condition. The inter-tone spacing was null.
In order to use the same type of analysis for B" (whose values ranged between -1 and 1, with positive numbers representing a conservative bias, i. e. , a tendency to answer "no", while negative numbers representing a liberal bias, i. e. , a tendency to answer "yes", and with 0 representing no bias), a linear transformation was preliminarily applied to the original B" values in order to rescale them within the interval 0-1 ((B" + 1)/2). All analyses were carried our using the statistical software program R 3. 3. 1, with the "lme4"  [66] , "car"  [67] , "lsmeans"  [68] , and "effects"  [69]  packages. We performed Mixed Model ANOVA Tables (Type 3 tests) via likelihood ratio tests  [70] [71] [72]  implemented in the "afex" package  [73]. Bonferroni corrections were applied to post-hoc comparisons.
Ease of Recognition The scatter plots of A ′ values in Figure  2  provide a first overview of the participants' average sensitivity. The degree of sensitivity was assessed according to the ease with which the participant recognized the target mirror forms in the acoustic (diagrams on the left) and visual (diagrams on the right) tasks. The A ′ values typically range from 0 to 1, with 0. 5 indicating that the signal cannot be distinguished from noise, and 1 which corresponds to perfect performance. Values less than 0. 5 may arise from sampling error or indicate that the participant was somewhat confused when responding. We know from previous literature on the recognition of acoustic mirror forms that the task is difficult for non-expert subjects, whereas no former data are available concerning how easy/difficult it is to recognize corresponding dynamic visual configurations.
Supplementary Materials: The following are available online at www. mdpi. com/2073-8994/9/3/39/s1, Table  S1 : database_sym. Symmetry 2017, 9,39 signaled at the first note (as by convention) but they hold until the end of the bar, which in our case means until the end of the stimulus. The corresponding visual stimuli are shown in the section headed V: in the isochronous condition, each dot remained on the screen for 600 ms before disappearing; in the non-isochronous condition, some dots (i. e. , those corresponding to the chromes in the acoustic stimuli) lasted 400 ms and the others lasted 800 ms. The grids in the background of the visual stimuli are shown here so that the correspondence between the spatial distance and the difference in pitch in the acoustic stimuli is clear, but these were not displayed in the actual stimuli shown to the participants.
Materials and Methods The experiments were conducted in accordance with the Declaration of Helsinki (1964) and with the full approval of the corresponding author's institutional (CNRS) ethics committee. Informed written consent was obtained from each of the participants. Experimental sessions were organized following conditions of randomized, trial-by-trial free image viewing using Python for Windows 7 and a computer with a keyboard and a high resolution monitor. 15 mirror tree images were generated using a comprehensive vector graphics environment (Adobe Illustrator CC) and computer shape library.
The approximate angular height of a fractal tree was 2. 25 • (vertical mid-axis), the angular width 1. 64 • (horizontal mid-axis). A trial-loop algorithm written in Python for Windows 7 selected the images or image pairs in random order, and recorded the individual key board responses from the experimental trials. Fifteen images of fractal mirror trees were designed using some of the principles of transformation shown in Figures  2  and 3. The first five trees (top) possess perfect "symmetry of things in a thing" across the vertical axis. In the next set of five (middle), the smallest of fractal details is missing on the right. The remaining five trees (bottom) are asymmetrical. It is noted that in these tree structures here, only the symmetrical ones (top) appear perceptually complete.
Results The raw data were analyzed using Systat/Sigmaplot 11 (Systat Software Inc. , 2010, San Jose, CA, USA). One-way analysis of variance (ANOVA) for repeated measures was performed to assess the statistical significance of differences in means across subjects and figure types: 'symmetrical', 'detail missing' and 'asymmetrical'. In the data from the preference judgment experiment with figure pairs, a first check of the means showed no effect of secondary variables such as the spatial position (left vs. right) of figures of a type in a pair (M left = 4. 92 vs. M right = 5. 07), or the order (first vs. second) in which a judgment was formed in response to a figure pair (M first = 5. 02 vs. M second = 4. 95).
Acknowledgments : We thank  Scott B. Stevenson  ( University of Houston College of Optometry ) for useful discussions about the generation of noise images for stimulus presentation. Acknowledgments: This research was carried out when the author was on the Faculty of  The State College of Optometry, SUNY, New York, NY, USA. It was supported by a grant from the  U. S. National Institute of Mental Health  ( R01-MH30840 ). The author wishes to thank  Tarryn Balsdon  for help with the figures. Acknowledgments: This research was supported by the  National Eye Institute of the National Institutes of Health  under award number  1R01EY024666-01. The content of this paper is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.
Acknowledgments: This work was supported by funds of the  Department of Human Sciences at the University of Verona  under Grant (ex60%MIUR). We thank two anonymous reviewers whose observations have helped us to improve the quality of the paper. Acknowledgments: The author expresses his sincere thanks to the anonymous reviewers for their valuable comments, by which the author could improve the manuscript. This work is partly supported by the  Grant-in-Aid for Basic Research 24360039  and  Challenging Exploratory Research 15K12067 of Ministry of Education, Culture, Sports, Science and Technology of Japan  (MEXT). Acknowledgments: This work is supported by the  National Eye Institute  ( 1F32EY025520-01A1 ) to  Gennady Erlikhman  and the  National Science Foundation  ( NSF 1632738  and  NSF   1632849 ) to  Gideon Paul Caplovitz.
Acknowledgments: We thank  Paola Boccacci  for help in data collection (study 1). Author Contributions:  Ivana Bianchi ,  Marco Bertamini  and  Ugo Savardi  conceived and designed the experiments;  Ivana Bianchi  and  Ugo Savardi  performed the experiments;  Ivana Bianchi  and  Roberto Burro  analyzed the data;  Ivana Bianchi ,  Marco Bertamini ,  Roberto Burro  and  Ugo Savardi  wrote the paper.
Introduction The CERN Large Hadron Collider has been running at an energy of 13 TeV in the centreof-mass frame, thus reaching energies far above the electroweak scale. Consequently, Z/W ± , Higgs, top quarks and any new particle with a mass around the electroweak scale can be produced with a large boost, causing their hadronic decays to become collimated so that they may be reconstructed as a single jet  [1, 2]. As a results, jet substructure is playing a central role during Run-II of the LHC and its importance is only going to increase for future runs, as well as at future higher-energy colliders  [3] [4] [5] [6]. For example, even though not confirmed in Run-II (see e. g. [7] ), an interesting excess in the invariant mass distribution of two W bosons was observed with Run-I data  [8, 9] , relying on jet-substructure techniques to isolate the signal from the QCD background.
Fixed-order calculations and matching prescription The resummed jet mass spectrum discussed in the previous section is reliable in the ρ 1 region, where the distribution is dominated by collinear splittings. In order to accurately describe the ρ ∼ 1 region we have to resort to fixed-order computations. Ultimately, we will match the two calculations yielding theoretical predictions which are accurate at both small and large ρ, as discussed in the following. All our fixed-order predictions are obtained using the public code NLOJet++ [58, 59] together with the parton distribution set CT14  [60]  at NLO. Jets are then clustered with the anti-k t algorithm as implemented in FastJet  [61, 62]  and we use the implementation of mMDT in fjcontrib  [63]. Jet mass distributions are obtained by considering 2 → 3 partonic processes at LO and NLO.
One way to explicitly show the IRC unsafety of the p t,mMDT distribution is to study fixed-order distributions in e + e -collisions using the program EVENT2  [58, 65] , for which we can easily control the infrared cut-off scale. In practice, we simulate events at Born level and at O(α s ), including both real emissions and virtual corrections. We cluster the full event with the e + e -version of the anti-k t algorithm with radius R = 0. 4 and select jets with an energy larger than 0. 95 √ s/2, with √ s = 1 TeV. We note that, at this order in perturbation theory, jets have either one or two constituents. We then run the following e + e -version of mMDT: jets with one constituent are kept untouched, and for jets with two constituents we. Dependence of the jet cross-section before and after applying mMDT, as a function of the infrared cut-off used in EVENT2.
Acknowledgments We thank  Mrinal Dasgupta ,  Andrew Larkoski ,  Sal Rappoccio ,  Gavin Salam  and  Jesse Thaler  for many useful discussions. SM would like to thank  IPhT Saclay  for hospitality during the course of this project. The work of SM is supported by the  U. S. National Science Foundation , under grant  PHY-1619867 ,  All-Order Precision  for LHC Phenomenology. GS's work is supported in part by the  French Agence Nationale de la Recherche , under grant  ANR-15-CE31-0016  and by the  ERC Advanced Grant Higgs@LHC  (No. 321133 ).
We have resummed this contribution to LL accuracy. In doing so we have lifted the small-z cut approximation which has been used in other studies aimed at a higher logarithmic accuracy  [32, 33]. In order to also describe the high-mass tail of the distribution we match to fixed-order matrix elements at NLO using the program NLOJet++. We have considered two different choices for the transverse momentum selection. The first option consists in selecting and binning the jets according to their transverse momentum before grooming, namely p t,jet , while in the second one the transverse momentum after grooming p t,mMDT is used. We note that a calculation performed in the small-z cut limit cannot resolve this difference, as the two are equal at z cut = 0. We have found that the p t,jet selection is better suited for theoretical calculations and the resulting resummation has a relatively simple form that can be, in principle, extended to higher-logarithmic accuracy.
In silico analysis of AOX citrus genes and proteins The identification and structural analysis of the AOX genes (introns/exons) were performed using the Citrus Genome Database (https://www. citrusgenomedb. org/). Open reading frame (ORF) analysis was performed using the ORFinder software (http://www. ncbi. nlm. nih. gov/ orffinder/). The prediction of the theoretical isoelectric point (pI) and the molecular weight (MW) was obtained using the pI/Mw tool (www. expasy. org). Conserved domain and family protein were analyzed using the Pfam (http://pfam. sanger. ac. uk/search/sequence) and Inter-ProScan software  [16]. The predictions of the subcellular location of the protein and of the location of the cleavage site were performed by the MitoProt II software (https://ihg. gsf. de/ ihg/mitoprot.
html). Transmembrane helices were predicted using the TMPred software  [17] , whereas hydropathicity levels were identified using the ProtScale program (http://web. expasy. org/protscale/). The NetPhos 3. 1 Server  [18]  and the NetNGlyc 1. 0 Server (http://www. cbs. dtu. dk/services/NetNGlyc/) were used to identify putative phosphorylation sites (Ser/Thr/Tyr) and putative N-glycosylation sites (Asn-X-Ser/Thr type), respectively. The protein motif analysis was conducted using the program MEME/MAST  [19]. The maximum number of motifs was set to 20, the maximum motif length was set to 80 amino acids, the optimum motif width was constrained to between 6 and 300 residues, and the other parameters were used as default.