dataesr/scientific-paragraphs-categorization huggingface dataset:
The text size was not counted as part of the index size for any implementation. The construction space was measured by recording the maximum resident set size in kilobytes (KB) using the /usr/bin/time -v command. Results. In Sections 6. 2 to 6. 7 we present the results for the datasets of Table  1. In Section 6. 8 we present the results for the HUMAN dataset but only for the FM-index, the r-index, and the BDA-index I and II (all the other indexes were not competitive).
Computing Bd-anchors Figure  5  shows the time required to compute the reduced bdanchors for the five datasets of Table  1. The Θ(𝑛ℓ) line represents the simple Θ(𝑛ℓ)-time algorithm of  [68]. The results show that for all five datasets, all 𝑏 values, and all ℓ values, BDA-compute outperforms the Θ(𝑛ℓ)-time implementation. In particular, BDA-compute becomes more than two orders of magnitude faster as ℓ increases. As suggested by Theorem 4. 4, the runtime of BDA-compute should not be affected by ℓ in the case of a uniformly random input string. Even if our datasets are real and thus not uniformly random, we observe that the runtime of BDA-compute in Figure  5  is not affected too much by the value of ℓ; an exception to this is the case of SOURCES, which is explained by the fact that this dataset, in particular, is very far from being uniformly random, which is assumed by our theoretical findings.
Specifically, in this dataset, the number of (𝑤, 𝑘)-minimizers is much larger than what is expected on average with increasing ℓ. Thus, more ties need to be broken (Lemma 4. 3), and this is why the runtime increases with ℓ. Nevertheless, even in this bad case, BDA-compute is up to 8× faster than the implementation of the simple Θ(𝑛ℓ)-time algorithm  [68]. Figure  6  shows the space required to construct the reduced bdanchors for the five datasets of Table  1. For all datasets, all 𝑏 values, and all ℓ values, BDA-compute performs similarly to the Θ(𝑛ℓ)time implementation, using just slightly more space as 𝑏 increases. This is expected because the latter implementation uses only Θ(ℓ) space  [68]  and 𝑏 ≫ ℓ in our experiments. These space-time results establish the practical usefulness of our Theorem 4.
Index Size Figure  7  shows the index size for the five datasets of Table  1  when using the implementations of Section 5. As expected, the index size of BDA-index I and II decreases with increasing ℓ. Notably, for all datasets and ℓ ≥ 64, BDA-index I and II are smaller than all other indexes except for the FM-index. When ℓ ≥ 512, BDA-index I and II outperform all indexes for all datasets.
Query Time Figure  8  shows the average query time for all datasets when using the implementations of Section 5 with ℓ = |𝑃 |. For all datasets and |𝑃 | ≥ 64, BDA-index I and II are up to several orders of magnitude faster than the compressed indexes, especially for large alphabets, which is consistent with the observations made in  [29, 40]. Notably, for all datasets and ℓ values, BDA-index I and II are even faster than the SA. FM-index did not finish for |𝑃 | = 16 within 24 hours for XML. CST did not finish within 24 hours for |𝑃 | ≥ 64, in the case of SOURCES and ENGLISH.
Index Construction Space Figure  9  shows the index construction space required for the five datasets of Table  1  when using the implementations of Section 5. As expected, the construction space required by BDA-index I and II decreases with increasing ℓ. For all datasets and ℓ values, BDA-index II outperforms BDA-index I (as expected). Notably, for all datasets when ℓ ≥ 128, BDA-index I and II outperform all other indexes.
Index Construction Time Figure  10  shows the time required to construct the index for the five datasets of Table  1  when using the implementations of Section 5. We set 𝑏 = 25K for BDA-index I and II. For all datasets and ℓ values, BDA-index I and II outperform CSA and are outperformed by the FM-index, SA, r-index, and CST. This is, however, expected due to the construction of SA and LCP array in EM. BDA-index I and II are around 8× slower than the fastest to construct FM-index.
Index Construction in Internal Memory Figure  11  shows the index construction space required for the five datasets of Table  1  when using an internal memory implementation to compute the SA and LCP array for BDA-index I and II. We set 𝑏 = 25K for both BDA-index I and II. The results generally show that BDA-index I and II are outperformed by the existing indexes. This is, however, expected; it in fact highlights the motivation for this work and, in particular, one of our main contributions: the index construction in small space. As mentioned in Section 4. 2, if one would like to have a near-linear-time construction in small space using only internal memory, sparse suffix sorting could be directly employed to replace the current external-memory construction. Figure  12  shows the time required to construct the index for the five datasets of Table  1  when using an internal memory implementation to compute the SA and LCP array for BDA-index I and II.
We set 𝑏 = 25K for BDA-index I and II. The results generally show that as ℓ increases BDA-index I and II become competitive to the existing indexes (expected). An exception to this is with SOURCES (see Section 6. 2 for an explanation). Figure  13  shows the time required to construct BDA-index I and II for the five datasets of Table  1  for varying size of internal memory. An internal memory size ranging from 128MB to 2048MB was used. We set 𝑏 = 25𝐾 and ℓ = 128 for both implementations. The results show that in general for all datasets, the construction time decreases as the size of the internal memory used increases.
DISCUSSION We have shown that our implementation of the bd-anchors index should be the practitioners' choice for long patterns. When ℓ ≥ 512, our index outperforms all indexes for all datasets in terms of index size. When ℓ ≥ 64, our index outperforms all indexes for all datasets in terms of query time. When ℓ ≥ 128, our index outperforms all indexes for all datasets in terms of construction space. The construction time of our index is between 4 and 8× slower than the state of the art. However, we believe that this does not make our index less practical; the construction time of the bd-anchors index can be improved in practice in at least two ways, which we describe below as future work (see the Future work paragraph). An obvious criticism against our index is that its theoretical guarantees rely on the average-case model and on the assumption that we have at hand a lower bound on ℓ.
First, we have shown, using real-world datasets (and not using synthetic uniformly random ones), that our index generally outperforms the state of the art for long patterns, which is the main claim here. Second, in most real-world applications we can think of, we do have a lower bound on the length of patterns (see Section 1. 2). For example, in longread alignment, this bound is in the order of several hundreds. Last, the state-of-the-art compressed indexes also have a crucial                  assumption, which is implicit and thus oftentimes largely neglected. The assumption is that the size 𝜎 of the alphabet is much smaller than the length 𝑛 of the text. In the worst case, i. e. , when 𝜎 = Θ(𝑛), the state-of-the-art compressed indexes have no advantage compared to the suffix array: they occupy 𝑛 log 𝜎 = Θ(𝑛 log 𝑛) bits.
g. [39]  for FM-index or  [11]  for suffix array, we have based our implementations on sdsl-lite as much as possible for fairness. Likewise, in the implementation of our index, we have used sdsl-lite as much as possible, and no particular low-level code optimization was conducted. Future Work. Our immediate goal is to improve the construction time of the bd-anchors index in the following two ways. In our current implementation, we use the standard lexicographic order to compute minimizers. However, for an alphabet size 𝜎, there are 𝜎! lexicographic orders that we could choose from. For large alphabets, like the one in SOURCES, a different lexicographic order could result in significantly fewer minimizers, and thus in a significantly faster bd-anchors computation. Second, as mentioned above, given the set of bd-anchors, we could replace the suffix array external-memory construction with an existing sparse suffix sorting algorithm.
ACKNOWLEDGMENTS This research is supported in part: by the  PANGAIA  and  ALPACA  projects that have received funding from the  European Union 's  Horizon 2020 research and innovation programme  under the  Marie Skłodowska-Curie  grant agreements No  872539  and  956229 , respectively; and by  UKRI  through  REPHRAIN  ( EP/V011189/1 ).
Note that the terms appearing in (8) and (  9 ) are computed integrating the distributed variables element-by-element according to the selected shape functions, which play the role of the kinematic map, while the position of each element in the mesh is ensured by the assembly process. Since nodal coordinates are of absolute nature, the nonlinearities appears in F int (q, v). They are named geometric or material, depending whether they come from the large displacements (and namely the rotations) of the elements, or from the constitutive laws. To overcome the geometric non-linearity, corotational approaches are used in three-dimensional FE softwares. One other solution to represent the non-linearities is the employment of an absolute nodal coordinate formulation  [23]. The FEM represent a standard for many popular simulation software, such as Abaqus, ANSYS, Comsol.
The main advantage of these software is that they provide a powerful and general tool that can be applied to a wide spectrum of physical problems ranging from structural dynamics, fluid-structure interactions, contact and thermodynamics. They provide a ready made and user-friendly framework that can be easily used for specific studies on multiphysics systems. They have been widely used to model soft robots  [24] ,  [25]  (Abaqus),  [26]  ANSYS. At the same time, their generality intrinsically entail an increased computational cost and the simulations, especially in dynamics, can take a lot of time to converge, sometimes even days. There are also some popular examples of ad-hoc Finite Element approaches (and softwares) that have been specifically proposed for (soft) robotics applications. In 2007  [27] , a group of researchers from different institutes released Sofa (Simulation Open Framework Architecture) an open-source C++ library which was originally presented as a computational environment for medical simulations  [28] ,  [29].
In the following years, Sofa became a comprehensive high-perfomance library that have been widely implemented for different application fields, and a SoftRobots plugin was also created for the design  [30] , modeling and control  [31] ,  [32] , of soft robots, including self-collision scenarios  [33]. Moreover, a model combining the FEM and the discrete Cosserat approach described in Section III-B is presented in  [34]. A discussion on the architecture of the software is addressed in Section VII, while here we mostly focus on the modeling part for the soft bodies. In Sofa, a deformable continuum is modeled using a dynamic or quasi-static system of simulation nodes. The node coordinates are the independent DOFs of the object, and they are typically governed by equations of the type (  8 ) and  (9).
The GE character, then imposes to apply the FEM without resorting to any simplifications on finite rotations, except the unavoidable space and time discretizations required by the numerical resolution. The GE-FEM was particularly developed for shells  [41] ,  [42] [43]  and rods  [47] ,  [48] ,  [49] ,  [50] , where microstructures are rigid transverse fibers, and rigid cross-sections respectively. The method's tour de force was to generalize all the key operations of the FEM (interpolation, space and time-integration. ), from the linear vector space of positional fields to the curved manifold SO(3). This approach, which is probably the most advanced for modeling mechanisms of rods subject to rigid motions and finite deformations, is today used as a reference for others, and commercialized in the SAMCEF software through its plugin MECANO.
It is then possible to define an additional strain variables Ξ(X) = Υ -1 Υ (X) where Υ(X) = ||q(X)|| 2 , which model the inflation of the rod and its space-rate, respectively. These can then be related to the other strain variables to obtain the kinematics, in the quaternion algebra, incorporating bending, twisting, extension, shear and inflation. In this way, the configuration is isophormic to a subspace of 7D functions. Then, the weak form of the static equilibrium is provided and solved employing a off-the-shelf FEM software (COMSOL). Nevertheless, a geometrically-exact finite element approach for the modeling of soft robots is presented in  [53]. Taking the cue from  [50] , a helical shape function is employed in terms of an exponential map to express the shape of the flexible manipulator, which is given in terms of the initial position and orientation at the base (X = 0) and the strain ξ(X).
In  [58] , the PVS approach is further extended to the modeling of concentric tube robot systems, including the modeling of the tube's insertion motion. Finally, the PVS approach has been implemented in a Matlab Toolbox, SoRoSim, for the simulation of soft, rigid and hybrid robots  [57]. A special case of the PVS is the Piecewise Constant, Approach (PCS)  [59] ,  [60] , where the strains in the sections are assumed to be constant, which was also extended to closed-chain geometries in  [61]. 3) Shooting Methods: Depending on the considered external forces and initial conditions, the equations describing a Cosserat rod  (19)  and its kinematics (15) represent a boundary value problem (BVP). Here, we gather all the approaches that employ standard numerical techniques, such as the shooting method, to solve this problem.
Because of their simplicity, lumped mass models are particularly suited for large robotics simulations library, such as the one presented in  [136]. Titan is a GPU-accelerated C++ software library for the modeling of soft bodies and multiagent robots at massive scales. The soft robotic body structure is represented through spring-mass lattices and an interactive approach is employed. In particular, the first iteration is applied to all the springs to compute, with Hooke's Law, the forces acting on each corresponding mass and then a second iteration is performed over all masses to update their accelerations and positions. The main benefit of this approach is the possibility to perform parallel computing, resulting in great computational performances.
In  [139]  the forward kinematic modeling of a bionic assistant trunk is obtained through Multilayer Perceptron (MLP) and Radial Basis Function (RBF) neural networks, which are both class of FNNs. The input neurons propagate the input variables to the following layers, while each neuron in the hidden layer is associated with a RBF kernel (usually Gaussian). The data are obtained experimentally, measuring the arm's tip position at varying the actuation pressure, using a trilateration algorithm. In one other paper by the same authors  [140] , the same handling assistant trunk is modeled, both with a data-driven and a pseudo-rigid modeling approach. With regards to the latter, the trunk is modelled as a series of rigid vertabrae connected by a total of four prismatic joints. For the data-driven approach, a modified Elman neural network is employed.
This network is also trained using the experimental results based on a trilateration system. FNNs are also employed in  [141]  and  [142] , which deal with the inverse kinetics of a cable driven soft manipulator. While the kinematical model describes the configuration of the robot without considering the involved loads, the kinetics model relates the motion of the robot with its actuation forces. In the above mentioned papers, the direct kinetics model is obtained using a geometrically-exact model that follows the approach described in  [143] , which uses the continuous Cosserat rod model  (12). Thus, a FFN, taking the tip position as an input and giving the cable tension as an output, is employed. After fabricating the considered 3-cable driven manipulator, a data collection phase is carried out, using a set of cable tensions and obtaining the tip position with an infrared vision system.
These data were used for the optimization and training of the FNN. After the training phase, the performance of the FNN are measured on test sets, using the output of the FNN as the input of the direct kinetics model. One other example of a machine learning formulation for the global inverse kinematics of continuum manipulators was presented in  [144]. The data samples are generated by continuous motor babbling and a single hidden-layer artificial neural network is employed to learn directly the mapping (x i+1 , q i ) → q i+1 , where x is the pose of the end effector. In one other work by the same authors  [145] , a dynamic model for open-loop control of soft robotics manipulators is presented. The PCS model described in III-B2 is employed to obtain the dynamics of a cable driven robot operating underwater.
Given an initial design, different objective functions are defined (motion-tracking, ease of actuation, resilience to failure) and the optimization is performed using a sensitivity analysis. Development and use of modeling software and toolboxes for soft robotics are essential to avoid the reinvention of the wheel. They could potentially avoid the need to write a custom code script in a programming language (C/C++, Python, MATLAB, etc. ) for each robot design, optimize the robot design for a particular task, or be used for the modelbased control of a specific robot. The modeling framework should be user-friendly (necessary for the multi-disciplinary soft robotic community), accurate, fast, and reliable. There The SoftRobots plugin of SOFA, one of the earliest opensource platforms for physics-based simulation, uses FEM to model, simulate, and control soft robots  [28].
SOFA employs a multi-model representation of a deformable body, allowing the presence of several representations (mechanical, thermal and visual) of the same object. The representations are then connected together through a mechanism called "the Mappings". This multi-modal representation allows the simulation of scenarios where different bodies, such as different rigid and/or deformable bodies or fluids, are interacting together. In particular, deformable bodies are modeled employing FEM with different constitutive laws. In general, a simulation in SOFA is described as a scene which is composed by different nodes organized as a tree or as a Directed Acyli Graph (DAG). PyElastica, which is the python implementation of Elastica, employs Discrete Geometry and the Cosserat rod theory of section V-A to model soft bodies with a finite number of lumped degrees of freedom  [123].
SoRoSim and TMTDyn are MATLAB toolboxes that use geometrically exact piecewise variable strain models  [57]  and discretized lumped systems with reduced-order models  [162] , respectively. SoMo (Soft Motion) toolbox couples the pseudo-rigid model discretization of section V-B with a rigid body physics engine of python to model soft robots  [163]. ChainQueen, and IPC-Sim (Incremental Potential Contact Simulator) are simulators oriented towards computer graphics rather than mechanical systems. ChainQueen is a python toolbox that uses the Moving Least Square Material Point Method, a hybrid Eulerian/Lagrangian FEM which uses both particles and grids to simulate soft bodies  [164]. IPC-Sim solves extreme non-linear volumetric elastodynamic models using FEM (section III-A1)  [165]. Particular toolboxes are developed for a specific soft robotic problem, such as the DiffAqua, an optimization toolbox for soft underwater swimming robots  [166] , and Vine Simulator, a toolbox dedicated to growing soft robots  [167].
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"Epidemiology and prevalence of extended-spectrum β-lactamase-and carbapenemase-producing Enterobacteriaceae in humans, etd. aau. edu. et Internet 20 words -1 % jglobalbiosecurity. com Internet 11 words -< 1 % Crossref 36 words -1 % wwwnc. cdc. gov Internet 18 words -< 1 % www. scidev. net Internet 11 words -< 1 % biofarmaka. ipb. ac. id Internet 9 words -< 1 % 17 28 37 animals and the environment in West and Central Africa", International Journal of Antimicrobial Agents, 2020 Crossref zenodo. org Internet 18 words -< 1 % hal. archives-ouvertes. fr Internet 10 words -< 1 % trace. tennessee. edu Internet 9 words -< 1 % dokumen. pub vdoc. pub Internet Melina Heinemann,.