dataesr/scientific-paragraphs-categorization huggingface dataset:
In Section 3 we show a lower bound to the bit complexity of any (1ε)-locality-preserving MPHF that depends on a parameter 0 < ε < 1. The complexity is below the well-known bound of n log 2 e bits for a "classic" MPHF, for sufficiently small ε. We then give in Section 4 a construction using random minimizers  [43, 41]  whose space approaches the lower bound by increasing k. The construction approximates a LP-MPHF for ε = 2/(w + 1), for a sufficiently-large minimizer length m ≤ k, where w = km + 1. The data structure is built in linear time in the size of the input (number of distinct k-mers). In Section 5 we present experiments across a breadth of datasets to show that the construction is practical too: the functions can be several times smaller and even faster to query than the most efficient, albeit general-purpose, minimal perfect hash functions.
Locality-Preserving Minimal Perfect Hashing of k-mers Let X be a set of strings over an alphabet Σ. Throughout the paper we focus on the DNA alphabet Σ = {A, C, G, T } to better highlight the connection with our concrete application but our algorithms can be generalized to work for arbitrary alphabets. A sub-string of length k of a string S ∈ X is called a k-mer of S. Definition 1 (Spectrum). The k-mer spectrum of X is the set of all distinct k-mers of the strings in X. Formally: spectrum k (X ) := {x ∈ Σ k | ∃S ∈ X such that x is a k-mer of S}. Definition 2 (Spectrum-Preserving String Set). A spectrum-preserving string set (or SPSS) S of X is a set of strings such that (i) each string of S has length at least k, and (ii) spectrum k (S) = spectrum k (X ). In particular, we are interested in a SPSS S where each k-mer is seen only once, i.
e. , for each kmer x ∈ spectrum k (S) there is only one string of S where x appears once. We assume that no k-mer appearing at the end of a string shares and overlap of k -1 symbols with the first k-mer of another string, otherwise we could reduce the number of strings in S and obtain a smaller SPSS. In the following, we make use of this form of SPSS which is suitable for the minimal perfect hashing problem. We remark that efficient algorithms exist to compute such SPSSs (see, e. g. ,  [40, 9, 25, 24] ). The input for our problem is therefore a SPSS S for X with |S| strings and n > 1 distinct k-mers. Without loss of generality we assume an order S 1 , S 2 , S 3 ,. of the strings of S is fixed, so that also an order between the k-mers is fixed and we indicate with x i the i-th k-mer in S for i = 1,.
, n. Definition 3 (Fragmentation Factor). Given a SPSS S with |S| strings and n = |spectrum k (S)| distinct k-mers, we define the fragmentation factor of S as α := |S|- 1  n. The fragmentation factor of S is a measure of how much contiguous the k-mers in S are. The minimum fragmentation α = 0 is achieved for |S| = 1 and, in this case, x i shares and overlap of k -1 symbols with x i+1 for all i = 1,. , n -1. This ideal scenario is, however, unlikely to happen in practice. On the other hand, the worst-case scenario of maximum fragmentation α = 1 -1/n is achieved when |S| = n and k-mers do not share any overlap. This is also unlikely to happen given that k-mers are extracted consecutively from the strings of X and, as a result, many overlaps are expected. A more realistic scenario happens, instead, when |S| n, resulting in ε α.
Then P[E 1 and E 2 ] = 1 -ε ⇐⇒ ε = 1 -P[E 1 and E 2 ] = P[¬E 1 or ¬E 2 ] by De Morgan's laws. Therefore we have ε = P[¬E 1 or ¬E 2 ] = P[f (x i+1 ) = f (x i ) + 1 or x i , x i+1 are not from the same string of S]. Lemma 1. Let S be a SPSS with fragmentation factor α and f be a (1ε)-locality-preserving MPHF for S. Then ε ≥ α. Proof. ε = P[¬E 1 or ¬E 2 ] ≥ P[¬E 2 ] = P[x i , x i+1 are not from the same string of S] = (|S| -1)/n = α, since there are exactly |S| -1 consecutive pairs (x i , x i+1 ) of k-mers in S that are not in the same string (x i at the end of some string S j and x i+1 at the beginning of the string S j+1 ). Lemma 1 says that any LP-MPHF for S is at best (1α)-locality-preserving 1 and how small ε can be actually depends on the input SPSS (and on the strategy used to implement f in practice, as we are going to illustrate in Section 4).
In fact, for the worst-case input -a SPSS with maximum fragmentation factor -we immediately obtain the following Corollary. Corollary 1. Let S be a SPSS with maximum fragmentation factor. Then any LP-MPHF for S is 0-locality-preserving. Intuitively, the "best" LP-MPHF for S is the one having the smallest probability ε, so we look for practical constructions with small ε. On the other hand, note that a "classic" MPHF is obtained when the locality-preserving property is almost always not satisfied and, as a consequence, P[f (x i+1 ) = j + 1|f (x i ) = j] = P[f (x i+1 ) = j + 1] ≈ 1 n for any j ∈ [n] , regardless of the overlap between x i and x i+1. Corollary 2. Let S be a SPSS with fragmentation factor α. Then any "classic" MPHF for S is (1-α)locality-preserving for a very small ≥ 0.
Theorem 2. Given a random minimizer scheme (k, m, h) with m > (3 + ) log 4 (w + 1) for any > 0 and w = km + 1, there exists a (1ε)-LP MPHF for a SPSS S which takes n • 2 w + 1 • log 2 4e • (w + 1) 2 + o(1) bits (6) with ε = 2 w+1 and n = |spectrum k (S)|. Comparing the space bound in Theorem 2 with the lower bound in Formula 5 and omitting lower order terms, it is easy to derive that our construction costs 2 w+1 • (3 + log 2 ( w+1 e )) bits/k-mer more than the theoretic minimum. However this surplus diminishes as w grows; for example, when m is fixed and k grows. Next we show how to improve the result of Theorem 2.
Algorithm 2 shows the evaluation for this partitioned representation of f (x). Also this algorithm executes in O(w) time. Intuitively, if the fraction of left-right-max super-k-mers and that of left/right-max super-k-mers is sufficiently high, we can save significant space compared to the previous data structure which stores both L and P for all minimizers. Indeed, we obtain the following Theorem (see the supplementary material for the proof). Theorem 3. Given a random minimizer scheme (k, m, h) with m > (3 + ) log 4 (w + 1) for any > 0 and w = km + 1, there exists a (1ε)-LP MPHF for a SPSS S which takes n • 2 w + 1 • log 2 e 16 • 2 1/4 3 • (w + 1) + o(1) bits (7) with ε = 2 w+1 and n = |spectrum k (S)|. Comparing this space bound with the lower bound in Formula 5 and omitting lower order terms, we see that this construction costs 2 w+1 • log 2 ( 32•2 1/4 3e ) bits/k-mer more than the theoretic minimum.
Ambiguous Minimizers Let G µ be the set of super-k-mers whose minimizer is µ. The rank computation in Equation 3 can be used as long as |G µ | = 1, i. e. , whenever one single super-k-mer g has minimizer µ and, thus, the single p g,1 unequivocally displace all the k-mers x g,1 ,. , x g,|g|-k+1. When |G µ | > 1 we say that the minimizer µ is "ambiguous". It is a known fact that the number of such minimizers is small for a sufficiently long minimizer length m  [34, 23, 11]  (for example, on the datasets used in Section 5, the fraction of ambiguous minimizers is in between 1% and 4%). However, they must be dealt with in some way. Let ξ be the fraction of k-mers whose minimizers are ambiguous. Our strategy is to build a fall-back MPHF for these k-mers. This function adds ξ log 2 e bits/k-mer on top of the space of Theorem 2 and 3, making our functions be (1ξ)(1ε)-locality-preserving.
Experiments Implementation Details. We report the major implementation details for LPHash. The arrays L and P are compressed with Elias-Fano  [16, 14]. Both the function f m and the fall-back MPHF are implemented with PTHash using parameters (D-D, α = 0. 94, c = 3. 0), unless otherwise specified. We do not compress the bit-vectors in the wavelet tree and we add constant-time support for rank queries using the Rank9 index  [22, 46]. Testing Machine. The experiments were executed on a machine equipped with a Intel i9-9900K CPU (clocked at 3. 60GHz), 64 GB of RAM, and running the Linux 5. 13. 0 operating system. The whole code (LPHash and competitors) was compiled with gcc 11. 2. 0, using the flags -O3 and -march=native. Datasets. We use datasets of increasing size in terms of number of distinct k-mers; namely, the wholegenomes of: Saccharomyces Cerevisiae (Yeast, 11.
6 × 10 6 k-mers), Caenorhabditis Elegans (Elegans, 95×10 6 k-mers), Gadus Morhua (Cod, 0. 56×10 9 k-mers), Falco Tinnunculus (Kestrel, 1. 16×10 9 k-mers), and Homo Sapiens (Human, 2. 77 × 10 9 k-mers). For each dataset, we obtain the corresponding SPSS by first building the compacted de Bruijn graph using BCALM2  [12] , then running the UST algorithm  [40]. At our code repository https://github. com/jermp/lphash we provide detailed instructions on how to prepare the datasets for indexing. Also, all processed datasets are available at https://zenodo. org/ record/7239205. Space Effectiveness. Figure  4  shows the space of LPHash in average bits/k-mer, by varying k from 31 to 63 with a step of 4, for both un-partitioned and partitioned data structures. We report the actual space usage achieved by the implementation against the theoretical space usage computed using Formula 6 (un-partitioned) and Formula 7 (partitioned).
We also plot the theoretic minimum computed with Formula 5. For each combination of k and dataset, we choose a suitable value of minimizer length (m) as reported in Table  1. For all datasets we use c = 3. 0 the PTHash f m and fall-back, except on the largest Human where we use c = 5. 0 to lower construction time at the expense of a larger space usage. As expected, the space lowers for increasing k and the partitioned data structure is always considerably smaller than the un-partitioned counterpart. The net result is that the achieved space is much better than that of the classic MPHFs traditionally used in the literature and in practice. To make a concrete example, partitioned LPHash for k = 63 achieves 0. 54, 0. 65, 0. 83, 0. 58, and 0. 87 bits/k-mer on Yeast, Elegans, Cod, Kestrel, and Human respectively.
LPHash is as fast as PTHash for streaming queries on the smaller Yeast dataset, but actually up to 2 -2. 5× faster on the larger Elegans, Cod, Kestrel, and Human. Compared to BBHash, LPHash is 2× faster on Yeast and up to 4 -5× faster on the larger datasets. Random lookup time is, instead, slower for LPHash compared to PTHash and BBHash: this is expected because the evaluation of LPHash is more complex (it involves computing the minimizer, accessing several arrays, and computing a rank using a wavelet tree). However, we do not regard this as a serious limitation since, as we already motivated, the streaming query modality is the one used in Bioinformatics tasks involving k-mers  [1, 7, 31, 42, 34]. We also see that: the slowdown is more evident on the smaller datasets while it tends to diminish on the larger ones; lookup time for k = 31 is substantially better than that for the other values of k since 31 bases fits into a single 8-byte integer whereas any 31 < k ≤ 63 requires the double of the size, making hash calculations more expensive.
Building Time. Lastly in this section, we consider building time. Refer to Table  3. Again, we report that the building time for un-partitioned and partitioned LPHash is the same. LPHash is competitive with the fastest BBHash and significantly faster than PTHash on the larger datasets. Specifically, it is faster than PTHash over the entire set of k-mers since it builds two smaller PTHash functions (f m and fall-back). The slowdown seen for Cod is due to the larger fall-back MPHF, which is built with PTHash under a strict configuration (c = 3. 0) that privileges space effectiveness (and query efficiency) rather than building time. One could in principle use BBHash instead of PTHash for the fall-back function, hence trading space for better building time. For example, recall that we use c = 5.
Conclusion and Open Questions In this paper, we initiate the study of locality-preserving minimal perfect hash functions for k-mers. We illustrate a theoretic minimum lower bound of the space complexity of these functions and propose a construction that approaches the minimum when k increases. We show that a concrete implementation of the method is practical. Before this paper, one used to build a BBHash function over the k-mers and spend (approx. ) 3 bits/k-mer and 100-200 nanoseconds per lookup. This work shows that it is possible to do significantly better than this when the k-mers come from a spectrum-preserving string set (SPSS): for example, less than 0. 9 bits/k-mer and 30-60 nanoseconds per lookup. Our code is open-source. As future work, we plan to carefully engineer the current implementation to accelerate construction and streaming queries even more.
Other strategies for sampling the strings could be used other than random minimizers  [19, 47]. For example, the Miniception by Zheng et al. [47]  achieving ε = 1. 67  w +o(1/w). Evaluating the impact of such different sampling schemes is a promising avenue for future research. Lastly, we also plan to investigate other strategies for handling the ambiguous minimizers. A better strategy is likely to lead to improved space effectiveness and faster construction. We conclude with some questions that remain open from this work, in the hope of spurring further research on the topic. (i) Given a SPSS with fragmentation factor α, what is the lowest ε that can be achieved in theory? And in practice? We know for Lemma 1 that ε ≥ α. Can we improve this lower bound or prove that it is tight? (ii) Does exist a MPHF for a SPSS which is not locality-preserving and, yet, has a lower bit-complexity than a classic MPHF? Or do our results suggest that any MPHF built for a SPSS features the locality-preserving property for some ε ≥ α? (iii) In Table  4  we report the lower bounds for other minimal perfect hashing problems, such as r-wise, monotone, and order-preserving minimal perfect hashing.
All of them are tight as they can be matched, at least in theory. We must be careful in comparing such lower bounds with that from Theorem 1 because those results are valid for arbitrary k-mer sets, not for k-mer spectra. Thus, a natural question is: What is the bit-complexity of the other MPH problems in Table  4  when applied to a SPSS? For example, we know that SSHash  [34, 33]  is an order-preserving MPHF for a SPSS (and (1α)-locality-preserving): in fact, its space usage is well below Ω(log n) bits/k-mer even with the ability of rejecting alien k-mers. Funding. This work was partially supported by the project MobiDataLab (EU H2020 RIA, grant agreement N o ¯101006879) and by the French ANR AGATE (ANR-21-CE45-0012).
In our case, we are using metal nanowires that have a cylindrical shape with a diameter of 35 nm and a length of 25 µm based on our previous investigation showing an experimental increase of the efficiency of an organic solar cells despite its thick active layer  [13]. Later in this article, we'll look at the modes that are predominant in this type of structure. In this work, we will first explore the concept of plasmonic resonance, followed by the study of plasmonic resonance in silver nanowires using Finite-Difference Time Domain (FDTD) simulation software, in which a ZnO/AgNWs/ZnO (ZAZ) electrode model will be constructed with the different materials used. We will observe the spatial distribution of the electric field as a function of wavelength and the type of plasmonic resonance. The ZAZ electrode was modeled according to the structure described in Figure  2.
Modeling a ZAZ electrode with multiple silver nanowires The aim of this numerical study is to propose a numerical model of the ZAZ electrode that approximates that of the experimental one, in order to demonstrate plasmon resonance. To this end, we have used a script to generate a semi-random array of ZnO-coated silver nanowires. The numerical model structure closest to the filling factor of an experimental ZAZ electrode is that with five AgNWs. The electric field is maximum at 454 nm, close to the peak of the waveguide mode. The two modes of plasmon propagation (SPP and waveguide) are also present for several AgNWs through the ondulation of the electric field along the wires. For example, in Figure  7. b. we show both propagation modes, with the slightly vertical nanowire showing waveguide mode propagation and the slightly horizontal nanowire showing the superposition of both propagation modes.
High-resolution accurate mass instruments represent the current state-of-the-art analysers for quantitative proteomics  (11). The bottom-up approach is referred to as peptide-centric, as identification and quantification is J o u r n a l P r e -p r o o f carried out at the peptide level  (11). Protein inference is then performed to obtain a cumulative signal representative of the quantitative levels of the proteins analysed. Data acquisition is currently based on two main paradigms: data-dependent acquisition (DDA) and dataindependent acquisition (DIA). In DDA, the most abundant signals (Top N) are recorded in each MS scan whereas in DIA, for each MS scan, a set of acquisition windows is used to record all theoretical signals and subject them to further fragmentation and detection  (12). These methods require different search strategies for peptide/protein identification.
For DDA the mass signals of each peptide fragment are matched to theoretical masses coming from an "in silico" digestion of a protein database. In DIA MS, the complex data pattern is deconvoluted using experimental spectral libraries, i. e. , a collection of real spectra usually built from the same sample type analysed or pan-libraries including spectra collected from different biological fluids or tissues  (12). With libraries, the search space is limited to the peptide fragments included in the libraries, but the information about fragment intensity is retained whereas it is usually lost in DDA methods. New approaches can also use specialised computational methods to match and quantify DIA experiments without the use of spectral libraries  (13). Depending on the acquisition methods, several quantification workflow methods have been developed over the years; some are based on spectral counts (i.
The limit of detection depend on the specific reagents used but generally range between low pg to low ng/ml  (88). Standard curves can be included for singleplex assays, allowing for absolute quantification estimations and combination of datasets generated over long periods of time. Protein panels can be specifically defined for each research question and study. It is also possible to convert from the J o u r n a l P r e -p r o o f multiplexed and exploratory study setup to more focused validation studies using the same setup of reagents.
Single Molecule Array (Simoa) Single molecule array, Simoa, is a bead-based ELISA run on the automated HD-X/HD-1 or manual SR-X instruments, provided by Quanterix (Billerica, MA, USA). Simoa sandwich immunocomplexes are formed by incubation of: 1) a bead-conjugated capture antibody, 2) samples containing the target protein, and 3) an enzyme-labelled detector antibody. The mixture J o u r n a l P r e -p r o o f of bead-conjugated immunocomplexes and an enzyme substrate is transferred to microarray discs with 50-femtoliter wells that are sized to confine only one bead. Once the bead-coupled immunocomplexes are loaded to wells and sealed, fluorescence of single beads is read, as the enzyme converts the substrate into a fluorescent reaction product. The Simoa software calculates the fluorescent measurements as average number of enzymes per bead (AEB), which can be further translated to concentration units using a calibration curve.
Strengths An indisputable strength of Simoa is its sensitivity, often being 1000x higher than a conventional ELISA, which is crucial for the field of neurodegenerative dementias, where many target proteins are present at extremely low concentrations (119, 120). A clear illustrative example of this, is that in a platform comparison study for the neurodegenerative biomarker neurofilament light (NfL), where all three platforms employed the same antibody pair, only with the Simoa NfL assay a significant difference in plasma levels was observed between healthy controls and patients with multiple sclerosis (120). Thanks to the combination of digital and analogous read-outs, Simoa provides also a wide dynamic range. Among other strengths of Simoa is that the technology provides high throughput (up to 288 data points per single run when run on the HD-X/HD-1), which is essential when considering the platform for large batch analyses.
More and more students and researchers are willing to get their hands on battery modeling in some universities where commercial solutions are not always easily accessible. We believe that SoftwareX open-access papers can give them the opportunity to play their role in battery innovation  [12]. Since there is not yet any battery model available in SoftwareX, we want to bring our contribution to the community with a code developed on Scilab ® , which is the free alternative to Matlab ® since 1980  [13]. This project started over a decade ago, while developing from scratch a lead-acid battery model that ultimately ended up in the Batteries and Fuel Cells Module of COMSOL Multiphysics ® 4. 2a  [14].
There are also a dozen of physical relations characterizing parameters which evolve in time with the electrode state (see Supplementary Material). The choice of implementing these parameters in the form of analytical expressions instead of data tables is dictated by code compactness and computation time, the latter being significantly shorter when you do not have to interpolate the data for each time step. Most of the thermodynamic data come from the seminal work of Hans Bode  [15]. To illustrate the accuracy of our analytical functions compared to the experimental data available, we present some of the newly developed expressions of the relative molar Gibbs free energies of water (Fig. 1a ) ḠH 2 O = ∆G 0 H 2 O -m A (16. 9 m A + 90. 7) (1) and sulfuric acid (Fig. 1b ) ḠH 2 SO 4 = ∆G 0 H 2 SO 4 + 12 900 √ m A -79 200, (2) as well as the partial molar entropies of water (Fig.
Software functionalities NEOLAB offers the possibility to study the impact of discharge rate on the voltage curve through a robust and optimized model. For instance, the solver used and its tolerance parameters have been meticulously selected based on their performance (execution time and reliability of the solution). Two standard Scilab solvers are applicable for our model: DAE (implicit method) and ODE (explicit method). Because of the stiffness of the problem, DASSL (DAE sub-solver) and STIFF (ODE sub-solver) offer the best compromise accuracy/speed. Both of them approximate the derivative using the BDF (Backward differentiation formula), but differ on the computation of the Jacobian matrix  [17]. Applying the quasi-Newton's method, DAE and specially DASSL are much faster than ODE and STIFF for a similar solution accuracy (Fig.
However, the use of dimensionless expressions does not allow to reduce the execution time (Fig. 3c ). Furthermore, a simplification of the system of DAEs is proposed to the user who has the choice of deleting some terms that have very little influence on the model's performance. Therefore, NEOLAB is the promising result of a simple, fast, and efficient software allowing the simulation of the negative electrode behavior. Simulation data of the interfacial voltage, electrode porosity, and acid concentration are saved and plotted so it is possible to observe their evolution in space and time. Comparisons between simulation and experimental data can also be made to validate the model adjustable parameters.