dataesr/scientific-paragraphs-categorization huggingface dataset:
Acknowledgments This work was supported in part by  Dominion Energy  through sponsored research projects at  Rensselaer Polytechnic Institute , United States; in part by the  New York State Energy Research and Development Authority (NYSERDA) ,  United States  through the  Electric Power Transmission and Distribution (EPTD) PON 3770 High Performing Grid Program  together with the New York Power Authority (NYPA); and in part by the  ERC Program of the National Science Foundation ,  United States  and  DOE  under  NSF  Award, United States Number  EEC-1041877  and by the  CURENT Industry Partnership Program ,  United States.
In this paper we demonstrated a method to reconstruct vector-valued lattice distortion fields within nanoscale crystals by optimization of a forward model of multi-reflection Bragg coherent diffraction imaging (MR-BCDI) data. The method flexibly accounts for geometric factors that arise when making BCDI measurements, is amenable to efficient inversion with modern optimization toolkits, and allows for globally constraining a single image reconstruction to multiple Bragg peak measurements. This is enabled by a forward model that emulates the multiple Bragg peaks of a MR-BCDI experiment from a single estimate of the 3D crystal sample. We present this forward model, we implement it within the stochastic gradient descent optimization framework, and we demonstrate it with simulated and experimental data of nanocrystals with inhomogeneous internal lattice displacement.
Thus phase retrieval approaches are needed to gain access to the reconstructed 3D image of the crystal and its internal lattice distortion field. The typical approach to solving this phase problem in BCDI is via iterative methods  [3] [4] [5]  that update an estimate of the 3D image based on the error between its diffraction (emulated via a 'forward model') and the experimentally observed diffraction of a Bragg peak from the sample. BCDI of this sort uses a family of relatively straightforward iterative phase retrieval algorithms to reconstruct the spatial distribution of a single scalar component of the lattice distortion field of a nanocrystal, with many examples in the literature from diverse materials systems  [6] [7] [8]. BCDI methods have also been developed to directly retrieve the full 3D lattice distortion field in a nanocrystal by solving the phase retrieval problems for multiple BCDI datasets from different independent Bragg reflections of the same crystal.
The multi-reflection approach (MR-BCDI) involves a more complex measurement as compared to standard BCDI, requiring multiple Bragg peaks from a single nanoparticle to be measured  9. This further complicates the image reconstruction process by imposing additional constraints, which then become difficult to reconcile simultaneously with the target image of interest. Various strategies of MR-BCDI image reconstruction have been developed that either utilize phase retrieval methods adapted from standard single-Bragg-peak approaches to reconstruct experimental data sets  [10] [11] [12]  , or that explore more sophisticated multi-Bragg peak reconstruction concepts within the realm of simplified simulated data  13, 14  that are more difficult to translate to as-measured MR-BCDI data sets. In this work, we introduce an MR-BCDI reconstruction approach that can reconstruct experimental data directly and that is compatible with modern optimization methods.
Thus, flexible multi-axis rotation and adaptable and accurate re-sampling of the sample object space to the different bases dictated by the measured data are needed. A final requirement, as discussed in the next section, is that in order for this forward model to be suitable for inversion using modern numerical optimization toolkits available as part of machine learning packages, it should be composable of differentiable elementary functions. This allows global optimization of a loss function based on rapid evaluation of gradients through the numerical process of automatic differentiation, which has recently gained traction in x-ray coherent diffraction imaging  15. As we describe here, our MR-BCDI forward model is designed to accommodate these requirements. The forward model for MR-BCDI is built upon a reference frame in which relevant conventions and operations can be defined.
The MR-BCDI inverse problem Having established a forward model for multi-reflection BCDI, establishing an inverse problem becomes a matter of expressing a loss function and implementing an automatic-differentiationbased optimization algorithm. The loss function we utilize for MR-BCDI, L multi , represents the mean error in signal amplitude per BCDI data set, aggregated over the number of data sets: L multi ½A; u ¼ X M i¼1 1 N vox X n F χ i AðT i mÞe ι2πG T i uðT i mÞ n o n À ffiffiffiffiffi I ðiÞ n q 2 (3) The quantities A, u, and the global scaling factors χ i are treated as parameters to be optimized. In this expression, χ represents the set of M scaling factors, and I ðiÞ n is the measured diffraction data corresponding to the i'th Bragg reflection. The scaling factors χ are needed to reconcile the different diffraction signal strengths encountered at different Bragg peaks with the constraint that A 2 ½0; 1.
N vox ,the number of voxels in a single BCDI data set, is 128 3 in all of the examples in this paper. We note that by using ffi ffi I p , the MR-BCDI loss function mirrors what is typically used in coherent diffraction phase retrieval approaches  21, 22. It is important to consider the degree to which the above optimization problem is overdetermined. This can be established by taking V to have an edge size of n voxels within a buffered array of size N (with n < N/2). Combining χ, A, and the three scalar components of u yields M + 4n 3 unknowns. The number of measurements (total pixels in the data constraint space) is given by MN 3 , for M BCDI scans. The MR-BCDI problem is therefore overdetermined by a factor of MN 3 /(M + 4n 3 ). In the case of our first numerical test presented below, M = 5, N = 128 and n = 46.
This strategy is valuable in cases where the starting guesses of the quantities of interest are likely far from the eventual solutions, and coarse updates based on gradients with respect to subsets of the full constraint space prove effective in reducing error in early iterations. In our work, α ⋆ , u ⋆ , χ ⋆ are updated first by constraining to two of the available Bragg peaks data sets. Then a gradually stricter global constraint to the data is imposed as the reconstruction progresses by constraining to an increasing number of Bragg peaks until the complete data set is used as the basis of the update. Owing to the complexity of our MR-BCDI model, we implement SCG using automatic differentiation (AD) using the PyTorch toolkit, which simplifies evaluation of the loss function and its gradient.
AD-based optimization evaluates the gradient automatically and exactly via the chain rule applied repeatedly to the constituent elementary functions. This feature allows increasingly complicated forward models of coherent diffraction to be developed corresponding to more sophisticated measurements, enabling image inversion without the need to derive loss function gradients analytically. Given the complexity of the forward model presented here, MR-BCDI leverages this ability. The use of AD optimization does require that the mathematical operations composing the forward model be differentiable, as we have taken care to enforce here. In this work, we implement the "Adam" optimization algorithm, which is an extension of SCG that is commonly used in machine learning, in a Python-based MR-BCDI reconstruction software  26  for CPU and GPU hardware using PyTorch  27.
Method demonstration In this section we present three reconstruction results with the MR-BCDI technique described above. Two of these use numerically synthesized coherent Bragg diffraction intensity data sets from digital nanocrystals. In the numerical studies, one crystal has a slowly varying continuous inhomogeneous distortion field and the other has a discontinuous, winding displacement field, which emulates two orthogonal screw dislocations within the crystal. The third reconstruction is from experimental diffraction data consisting of six Bragg reflections of a silicon carbide (SiC) nanocrystal measured using BCDI at Beamline 34-ID-C of the Advanced Photon Source. In each case, we present the MR-BCDI reconstruction of the scattering amplitude AðxÞ and the lattice deformation u(x). All reconstructions were performed using a single Nvidia Tesla P100 GPU with 16 GB of RAM, and typical reconstruction times were 2-4 hours.
We have adopted the matrix coordinate convention for all the cross-section plots in this paper. As an example, a cross-section image labeled as X -Y implies that the X-axis is directed from top to bottom along the image, and the Y-axis from left to right. The third axis (in this example, the Z-axis) emerges out of the plane of the figure in order to maintain right-handedness. The X, Y, and Z axes correspond to the laboratory frame of reference (i. e. , the ŝ1 , ŝ2 and ŝ3 directions in Fig. 1 , respectively). With this convention, we ensure that the reference frame of the reconstructed crystal is consistent with the programmed order of the array axes in the multi-dimensional FFT routines in Python and PyTorch. Simulated crystal without dislocations. A synthetic crystal with arbitrary facets was generated on a Cartesian grid of size 128 × 128 × 128 voxels, with a voxel size of s 0 = 12 nm along each axis in the laboratory frame (½ŝ 1 ŝ2 ŝ3 in Fig.
1 ). To emulate realistic BCDI scans at a diverse set of sample and detector orientations, a face-centered cubic (FCC) gold lattice with a lattice constant of a 0 = 4. 078 Å was assumed for the simulated particle. The orientation of the FCC unit cell with respect to the lab frame was assigned arbitrarily. A slowly-varying internal field u(x) was created by first generating uniform random samples for the three components of u(x) (-0. 1a 0 ≤ u i (x) ≤ 0. 1a 0 ) and then retaining the long-period variations by convolving each u i (x) with a low-pass filter. The crystal spanned (39, 39, 40) voxels along the laboratory frame axes, and a cubic bounding box V of size 46 × 46 × 46 voxels was chosen for the reconstruction. Numerical MR-BCDI diffraction data were generated in a manner consistent with the measurement of a real FCCstructured crystal at the BCDI diffractometer at the APS Sector 34-ID-C beamline.
The u(x) fields for each dislocation were calculated with the continuum model of lattice distortion for screw dislocations, as in other BCDI work  30, 31  , and the net displacement field was modeled as the vector sum of the displacement fields of the pair of screw dislocations. The simulation procedure of calculating the BCDI data sets, including the selection criterion for Bragg reflections, selection of rocking directions, and introduction of Poisson noise, followed the same procedure as for the dislocation-free crystal. Four Bragg peaks with high reciprocal-space mutual orthogonality were chosen for modeling BCDI intensity patterns: [200], [002], [202] and ½220. The simulation box V was chosen to be 40 × 40 × 40 voxels in size. The Adam optimizer was initialized with a learning rate of 0.
02, the object initialization was done as in the previous example, and a similar optimization schedule was used (see Table  2  in Methods). The final optimization stretch for the interior voxels of the object was carried out for 5000 iterations constrained by all four Bragg peak data sets. A median filter of size 7 × 7 × 7 voxels was applied to the components of u(x) after each optimization epoch. Figure  5  compares the simulated and reconstructed electron densities AðxÞ and u(x), and Fig. 6  compares Bragg peak intensity distributions. (Reconstruction metrics are shown in Supplementary Fig. 4 ). As in the dislocation-free case, there is good agreement between the simulation and reconstructed images as well as in the diffraction intensity patterns. One noteworthy feature of this reconstruction is the presence of regions of low electron density where the discontinuous lattice distortion in the u(x) field intersects the plane of the figure (regions indicated with blue arrows) and the surface of the crystal (regions circled in red).
This effect is attributed to the fact that the highest spatial resolution components of the signal (the "high-q" regions of the detector) are suppressed with the introduction of Poisson counting statistics into the simulated BCDI data sets, effectively imposing a low-pass spatial filter on the reconstructed image. As before, a comparison was also made to BCDI images reconstructed from the individual Bragg peak data sets from the dislocated crystal lattice using convention phase retrieval approaches. The recipe used was the same for the dislocationfree crystal. A representative amplitude cross-section of a singlepeak BCDI image from the [202] Bragg peak is show in Fig. 7. From this image, it is clear by comparing to Fig. 5  that the conventional phase retrieval approach from a single peak struggles to converge to the uniform amplitude distribution expected in the ground truth.
In terms of signal strength, the maximum pixel intensities in each of the 6 measured Bragg peaks were respectively: 40,980, 16,072, 32,661, 14,577, 34,123 and 7805 peak photons. Note: The BCDI scans within each minibatch were randomly selected. Several steps were taken to process this data for MR-BCDI reconstruction. The data sets were clipped to a size of 128 × 128 pixels in the detector plane, and the angular rocking curve dimensions of the data sets were zero-padded to a size of 128, resulting in a cubic data array space of 128 × 128 × 128 voxels for each Bragg peak. This uniform array size ensured that the T i transformation operations acts as intended. The lab frame crystal orientation of the SiC particle was determined by a least squares optimization of the crystal orientation (expressed as a 3-parameter rotation vector) over the δ, γ and θ motor orientations of all 6 BCDI scans with the Nelder-Mead optimizer  38.
DISCUSSION In this paper we demonstrated a method by which to reconstruct vector-valued lattice distortion fields within nanocrystals by optimization of a comprehensive forward model of multi-Bragg-peak BCDI data. This forward model flexibly accounts for important geometric factors that arise when making BCDI measurements, is amenable to efficient inversion with modern optimization toolkits, and allows for globally constraining a single image reconstruction to multiple Bragg peak measurements. A key feature of our method is the fact that the forward model we developed to reconcile multiple Bragg peak measurements from a single originating crystal does so by emulating the native measurement space associated with BCDI rocking curve data sets. We also note that our reconstruction approach obviates the need for trial-and-error fixed point projection recipes and reduces the need for intermittent support updates via the shrinkwrap algorithm  4.
Our formulation of MR-BCDI offers another potential advantage in that it permits the analytical interrogation of the high-dimensional solution space in the neighborhood of the true solution, opening the door to rigorous uncertainty analysis where fixed-point-iteration-based methods fall short. In implementing our MR-BCDI method, we have demonstrated successful reconstructions of the 3D electron density and displacement field for both numerical and experimental data. Crucially, we have shown that crystals with both smoothly varying displacement fields as well as ones with discontinuities in lattice displacement due to, for example, the presence of dislocations, are reconstructable with our approach. In addition, this work brings coherent diffraction methods further into the scope of global optimization techniques  15, [39] [40] [41] [42]  , thereby enabling the use of highly optimized software packages capable of handling large data volumes and running on seemingly ever-improving high-performance computing hardware.
Sequential optimization plans In Tables 1-3 we specify the optimization plans used in the three reconstructions corresponding to the simulated crystal without  Bragg peak of the crystal with screw dislocations, using the recipe in Section B of the Supplementary Information. The cross section shown displays prominent fluctuations in electron density that are not present in the MR-BCDI reconstructions by virtue of the coupling effect of multiple data sets in a single optimization of the object. Note that the aspect ratio of the central slice of the object is not as it appears in Fig. 5a  because the output of standard single-peak BCDI phase retrieval is not shear corrected. 3  of the Supplementary Information. b Final estimated SiC nanocrystal electron density A, from a highly permissive mask threshold of 0.
ACKNOWLEDGEMENTS The development of the MR-BCDI forward model and inversion approach, experimental demonstration, and design and fabrication of the SiC nanoparticles was supported by the  U. S. Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Science and Engineering Division. Additional support for materials preparation came from the  Q-NEXT Quantum Center , a  U. S. Department of Energy, Office of Science, National Quantum Information Science Research Center , under Award Number  DE-FOA-0002253. Silicon carbide deterministic nanoparticle fabrication and SEM characterization work was performed under proposals 72483 and  775514  in the  Center for Nanoscale Materials  clean room. Work performed at the  Center for Nanoscale Materials , a  U. S. Department of Energy Office of Science User Facility , was supported by the  U.
S. DOE, Office of Basic Energy Sciences , under Contract No. DE-AC02-06CH11357. Refinement of the geometric, computational and optimization concepts was supported by the  European Research Council (European Union 's  Horizon H2020 research and innovation program  grant agreement No. 724881 ). Generation of the simulated structures and the BCDI data acquisition was supported by the  Laboratory Directed Research and Development (LDRD)  funding from  Argonne National Laboratory , provided by the  Director, Office of Science , of the  U. S. Department of Energy  under Contract No. DE-AC02-06CH11357. This research uses the resources of the Advanced Photon Source, a  U. S. DOE Office of Science User Facility  operated for the  DOE Office of Science  by  Argonne National Laboratory  under contract No.
form a basis of 3D sampling vectors in real space in the frame k1 , k2 , k3 of the detector (see Fig. 1). The elements of fB ðiÞ real g M i¼1 are determined by the corresponding reciprocal basis matrix fB ðiÞ recip g M i¼1 which depends on the detector pixel size, detector orientation, the angular increments of the rocking curve, sample rotation axis, and the signal-space array size chosen to encompass the Bragg peak. It is important to note that fB ðiÞ real g M i¼1 for every Bragg peak scan is unique. • Dataset-dependent scaling factors fχ i χ i 2 R j g M i¼1 for the scattering amplitude A that rescales the sample exit wave amplitude of the model to correspond to the relative intensities of the set of 3D Bragg peak measurements.
The information generated from structural biology research has applications in many areas beyond structural biology itself, such as medicine, biotechnology, and agriculture. The first protein structure (for myoglobin) was published in 1958  [1]. This endeavor took more than 20 years and required the development of a new method for protein crystallography, the isomorphous replacement method to solve the phase problem. Each step was manual, laborious, and time-consuming and involved the isolation of a protein of interest from native sources, its crystallization, collection of diffraction data on photographic films, and computational analysis on computers with a fraction of the processing power of a typical modern mobile phone. In 1971, the Protein Structure Database (PDB) was established as the central archive for experimentally determined macromolecular structure data.
There are two main approaches for modern protein modelling: template-based and neural network (deep learning)-based. Template-based modelling, including fold recognition and homology modelling, uses available resembling structures as templates to generate structure models and has been used for decades, as implemented in the software suites Modeller and Phyre2. Some deep learning methods have been used to aid template-based modelling to produce better results  [3]. In 2021, AlphaFold2 and RoseTTAFold were the first to use deep learning approaches  [4, 5]  for protein modelling. This brought about a sensational breakthrough in protein structure prediction and ignited a new revolution in structural biology. The Protein Data Bank was the source of the training data for Alphafold2, which at the time consisted of more than 170,000 protein structures.
DeepMind and the EMBL's European Bioinformatics Institute partnered to create AlphaFold DB to make structure predictions freely available to the scientific community  [6]. The most recent database release comprises approximately 200 million entries with extensive coverage of the UniProt database and has transformed the way experimental structural biology is performed and democratized access and use of information about protein 3D structure. Importantly, the reliability of models is estimated at the level of individual amino acids by the predicted local distance difference test. This enables the user to detect potentially uncertain structural regions, such as those caused by conformational disorder. Excellent follow-up advances in the prediction of protein-protein interactions and automatization of pipelines have been made with AlphaFold-Multimer  [7]  and AlphaPullDown  [8] , respectively, as well as on generation of models loaded with their ligands with AlphaFill  [9] , which "transplants" small molecules and ions from experimentally determined structures to predicted protein models.
Not surprisingly, these predictions have been challenged on numerous fronts. Some consider them suboptimal because they are based on statistics rather than first physicochemical principles, while others say that, at least for the time being, the accuracy of experimental structures cannot be reached. Careful comparison of AlphaFold2 models with a recently redetermined set of crystal structures revealed that the differences are greater than those between high-resolution structure pairs containing the same components but determined in different space groups  [10]. Due to the nature of the prediction and the available training dataset, AlphaFold2 does not accurately model protein aggregation, macromolecular complexes (in particular protein-nucleic acids interactions, macromolecule-ligand interactions, and structural rearrangements triggered by, e.
FPGAs also require less power than traditional microprocessors, which makes them ideal for ADAS because they can be used to reduce system power consumption  [6]. In addition, FPGAs are cost-effective and can be adapted to meet the needs of different ADAS applications. Our research aims to evaluate the robustness and effectiveness of YOLOv4 on large autonomous driving datasets. Comprehensive analysis, performance evaluation, and dedicated FPGA architecture design will advance ADAS technologies and facilitate efficient and accurate object detection. The main contributions of this paper are outlined as follows: • Comprehensive analysis: We conduct a thorough investigation of the algorithmic complexity of YOLOv4 on the KITTI and Self Driving Car datasets, considering various input sizes. This analysis provides a detailed understanding of the algorithm's computational requirements and helps identify potential areas for optimization.