dataesr/scientific-paragraphs-categorization huggingface dataset:
If we publish that 𝜃 = 0 no party can claim anymore that it liked the idea, so its privacy is lost. Statistical notions of privacy, such as differential privacy  [27] , add noise to guarantee the privacy of the individuals independently of the output. In particular, let 𝜃 be a function mapping datasets on values in X. We say datasets are adjacent if they differ in the data of only one party. Then, we say a randomized algorithm 𝐴 is (𝜖, 𝛿)differentially private (DP) if for any two adjacent datasets 𝐷 1 and 𝐷 2 and for any subset 𝑋 ∈ X, 𝑃 (𝐴(𝐷 1 ) ∈ 𝑋 ) ≤ 𝑒 𝜖 𝑃 (𝐴(𝐷 2 ) ∈ 𝑋 ) +𝛿. 𝐴 is 𝜖-DP if it is (𝜖, 0)-DP. The most common strategy to make information DP before publication is to add noise from appropriately scaled Laplace or Gaussian distributions. For example, consider again the above example where the parties in P want to average their private 𝑥 𝑖.
e. , computing the shared key in CSIDH) and returns the result (e. g. , a hardware security module providing a CSIDH accelerator). We also discuss variants of the attack with weaker access; this includes a hashed version where faulty outputs are not revealed as-is, but passed through a keyderivation function first, as is commonly done for a Diffie-Hellman-style key exchange, and made available to the attacker only indirectly, e. g. , as a MAC under the derived key. Part of the tooling for the post-processing stage of our attack is a somewhat optimized meet-in-the-middle path-finding program for the CSIDH isogeny graph, dubbed pubcrawl. This software is intentionally kept fully generic with no restrictions specific to the fault-attack scenario we are considering, so that it may hopefully be usable out of the box for other applications requiring "small" neighborhood searches in CSIDH in the future.
The labels of the edges of G 1,+ must be positive primes, and all components with a matching label are also positive. Next, all the labels that appear as degrees of edges in G r,+ for any r are necessarily positive. Finally, positively oriented components can only be connected by positive primes, so we  E 1,+ , E 2,+ , E 3,+ , E B , E 3,-, E 2,-, E 1,-) , other faulty curves appearing in the dataset are gray, and white circles are "intermediate" curves discovered while connecting the components. The primes appearing on the connecting path between E i,± and E i+1,± are exactly the primes appearing i times with orientation ±. For example, the primes indexed by 2, 9, 19 appearing between E 1,+ and E 2,+ have exponent +1 in the secret key. can remove from the support all the primes that we know are negative.
The pubcrawl tool The post-processing stage of our attack relies on the ability to reconstruct the graph of connecting isogenies between the faulty CSIDH outputs. We solve this problem by a meet-in-the-middle neighborhood search in the isogeny graph, which is sufficiently practical for the cases we considered. In this section, we report on implementation details and performance results for our pubcrawl software. 7 We emphasize that the software is not overly specialized to the fault-attack setting and may therefore prove useful for other "small" CSIDH isogeny searches appearing in unrelated contexts. Algorithm. pubcrawl implements a straightforward meet-in-the-middle graph search: Grow isogeny trees from each input node simultaneously and check for collisions; repeat until there is only one connected component left.
Size of search space. The number of vectors in Z n of 1-norm ≤ m is [20, § 3] G n (m) = m k=0 n k m -k + n n. Similarly, the number of vectors in Z n ≥0 of 1-norm ≤ m equals H n (m) = m k=0 k + n -1 n -1. Implementation. The tool is written in C++ using modern standard library features, most importantly hashmaps and threading. It incorporates the latest version of the original CSIDH software as a library to provide the low-level isogeny computations. Public-key validation is skipped to save time. The shared data structures (work queue and lookup table) are protected by a simple mutex; more advanced techniques were not necessary in our experiments. We refrain from providing detailed benchmark results for the simple reason that the overwhelming majority of the cost comes from computing isogeny steps in a breadth-first manner, which parallelizes perfectly.
Hence, both time and memory consumption scale almost exactly linearly with the number of nodes visited by the algorithm. Concretely, on a server with two Intel Xeon Gold 6136 processors (offering a total of 24 hyperthreaded Skylake cores) using GCC 11. 2. 0, we found that each isogeny step took between 0. 6 and 0. 8 core milliseconds, depending on the degree. Memory consumption grew at a rate of ≈ 250 bytes per node visited, although this quantity depends on data structure internals and can vary significantly. Example estimates based on these observations are given in Table  1. There is no doubt that pubcrawl could be sped up if desired, for instance by computing various outgoing isogeny steps at once instead of calling the CSIDH library as a black box for each individually. Code. The pubcrawl software is available at https://yx7.
To use precomputation for different rounds, one can replace the starting curve E -B that is fed to the target device by the shift given exactly by the primes in S rmax,s (or, adaptively, by the part of the secret key that is known). This has the same effect as above: shifting all the curves E t with the same orientation closer towards E 0 , hopefully so that the H(E t ) are already in our database. If they are not then likely the opposite orientation appeared when we faulted the computation. Summary. The benefit of using the twist with precomputation is largest for the hashed versions: we need a brute force search from E 0 in any case, and so we would use on average as many steps per round as the precomputation takes. For the non-hashed versions, the expensive precomputation competes with meet-inthe-middle attacks running in square root time.
In 2-point variants, we use Elligreator, which requires two exponentiations instead of one as Elligator does. Thus, the countermeasure is expected to add a more significant, yet relatively small overhead in 2-point variants as in CTIDH. CTIDH uses two calls to Elligreator per round, and both executions contain two pseudo-y checks respectively. We estimate the cost of our countermeasure in CTIDH-512. The software of  [3]  reports an exponentiation by (p -1)/2 to cost 602 multiplications (including squarings). Since CTIDH-512 requires roughly 20 rounds per run, we add two additional exponentiations by (p + 1)/4 per round, and these have almost the same cost of 602 multiplications, the overhead is approximately 2•20•602 = 24080 multiplications. Ignoring the negligible amount of further multiplications we introduce, this comes on top of a CTIDH-512 group action, which takes 438006 multiplications on average.
Sedimentary provenance is a powerful tool for reconstructing convergent margin evolution. Yet single 15 mineral approaches, like detrital zircon, have struggled to track sediment input from mafic and metamorphic sources. Sediment input from these lithologies is especially critical for reconstructing orogenic settings dominated by terrane accretion, ophiolite obduction, and forearc inversion. Rutile can form in metamorphic and igneous rocks and hydrothermal veins, and its U-Pb age and geochemistry often records cooling from the most recent medium to high grade metamorphic event. Thus, detrital rutile complements detrital zircon datasets by offering a path forward in 20 sedimentary provenance reconstructions when metamorphic terranes are potential source regions. However, U-Pb geochronology in rutile can be difficult due to low uranium concentrations and high discordance.
g. ,  Meinhold, 2010). 80 Here, we investigate the limitations of U-threshold filtering with a new dataset from Anatolia inclusive of all rutile, where low-U rutile grains are numerous and diagnostic of specific metamorphic units. We build a new workflow that includes low-U rutile and tests different common Pb correction approaches. Furthermore, we test the sensitivity of resulting U-Pb age spectra to the Pb correction methods and to discordance filters and determine whether these factors alter the overall provenance interpretation. Overall, this new dataset demonstrates that detrital rutile captures 85 sediment input from a subduction accretion complex that is poorly resolved in the detrital zircon record.
However, by nature, the co-genetic grains in detrital samples are unknown. This creates a first-order methodological hurdle for detrital petrochronology: what is the best way to determine the U-Pb age for discordant detrital analyses?; and do different discordance filters influence the resulting age spectra and provenance interpretations or not? This careful methodological step is critical to produce age distributions that can be interpreted confidently. Below we review 208 Pb-based and 207 Pb-based methods for 150 calculating U-Pb dates in discordant grains, then we illustrate this comparison with a new dataset from Anatolia.
To find the intersection, we use the  Schwarz (2022)  intersection function in MATLAB. The 207 Pb-corrected 207 Pb/ 206 Pb* and 206 Pb*/ 238 U dates are calculated from 207 Pb/ 206 Pb* and 206 Pb*/ 238 U, respectively. Note that because the correction forces intersection with the concordia, the two dates are identical. Discordance is calculated in Tera-Wasserburg space, where the percent discordance is defined as the distance between the measured 238 U/ 206 Pb and 207 Pb/ 206 Pb coordinates and the concordia intersection (δ2) along the total 190 discordia line distance (δ1 + δ2) (Figure  1 )  (Vermeesch, 2021) : Concordance = δ 1 /(δ 1 + δ 2 ) (7) This version of discordance, when applied with a stricter filter, is more forgiving for dates younger than 1000 Ma where the slope of the concordia curve is shallow  (Vermeesch, 2021).
195  Like the 208 Pb correction method, the 207 Pb correction method assumes U-Pb concordance and no Pb loss. Because Pb loss is not considered, all calculated dates are obtained from lower intercepts are (possibly) minimum ages. The method here is modified for detrital samples with unknown cogenetic minerals based on methods in  Faure (1986) ,  Chew et al. (2011) , and the semitotal-Pb/U scheme of  Ludwig (1998)  and  Vermeesch (2020). We illustrate the difference between these different Pb correction methods and the issue raised by low-U 200 screening with a new dataset from Anatolia.
Influence of Pb Corrections on Date Spectra All the U-Pb results are displayed together in Figure  4  in Tera-Wasserburg space. A substantial number of analyses plot close to non-radiogenic common Pb values. This is evident in the convergence of data toward y-intercept 280 values close to known common Pb values: from 1000 Ma to present, the 207 Pb-206 Pbcommon ratio evolves from ~0. 88 to 0. 83  (Stacey and Kramers, 1975). Therefore, this section explores the sensitivity of U-Pb date spectra to 208 Pb-and 207 Pb-correction methods and to discordance filters in order to determine whether these factors change the overall provenance interpretations. The uncorrected and corrected data are shown in Figure  5  as kernel density estimates (KDEs) and cumulative 285 distributions. Resulting date distributions for each sample are shown in Figure  A3 , but due to small sample sizes, interpretations are based on the cumulative dataset.
The difference in date significantly increases for grains that are less than 40% concordant. This result is replicated in statistical comparisons included in the data repository (i. e. , similarity, likeness, cross-correlation, Kolmogorov-Smirnov;  Mueller et al. , 2023). For this reason, we prefer the date distributions that include all grains 100-40% concordant, excluding grains below 40% concordant. However, the similarity in the 207 Pb with t208 cumulative date distribution for the 100-40% and 40-0% groups is notable, which could warrant the inclusion of 300 those low concordance grains. Ultimately, the prominent date modes are the same across 207 Pb-and 208 Pb-corrected groups, meaning that provenance interpretations are not affected by the choice of Pb correction method. This may not be the case for other datasets where the Pb correction method and concordance filter may influence the final date distribution and in cases where the KDE amplitude is important.
Influence of Low-U Rutile on Age Spectra 305 A common analytical workflow for detrital rutile is to first analyze trace elements then only collect U-Pb data on rutile above a given U concentration threshold (ca. > 4-5 ppm;  Zack et al. , 2004a; Okay et al. , 2011; Rösel et al. , 2019). Elemental concentrations are calculated based on the measured count rate (i. e. , counts per second, CPS), which is inherently dependent on the individual mass spectrometer and laser ablation parameters (e. g. , spot size, fluence). The concentration in an unknown is calculated based on the known concentration in the primary reference 310 material and measured CPS of the primary reference material. Hence, if sensitivity is increased or decreased proportionally for reference materials and unknowns across various ICP-MS instruments and analytical parameters, the resulting concentration (ppm) will be the same.
Thus, the U-threshold filter does not seem to impart a bias toward older dates. The two filtering methods produce date spectra with the same 330 dominant modes, yet the amplitude of peaks vary between methods. For example, the 190 Ma mode is more prominent with the concordance filter than with the U-threshold filter. Furthermore, the predominant date modes contain rutile of both metapelitic and metamafic origin (cf. next section and Figure  8 ). Even though the two filters do not yield different provenance interpretations in this case, most mafic-classified grains have U contents below 4 ppm and are in the 190 Ma population. Hence, the U-threshold filter is likely biasing results toward pelitic sources. In this dataset, all 335 grains more than 40% concordant are above 0. 1 ppm, which could be a more suitable U-threshold.
Source Metamorphism The Zr-in-rutile temperature results are displayed alongside U concentration (Figure  9 ). In this dataset, Zr 350 concentrations range from 2 to 1934 ppm, yielding a range in source rock minimum peak temperatures from 359 °C to 824 °C. Even though many studies only acquire U-Pb dates on rutile with U > 4-5 ppm, 87% of rutile in this study are below 4 ppm (n=517/592). This commonly accepted strategy has important implications for provenance interpretation. In our dataset, the majority of rutile with U > 4 ppm are classified as pelitic and generally have higher Zr contents (Figure  8  and Figure  9 ). Whereas low-U rutile in this study generally correlates with lower Zr contents 355 (lower temperature) and includes the majority of mafic-classified grains (Figure  9 ). Therefore, the exclusion of low-U rutile in provenance studies likely misses sediment sourced from lower grade metamorphic units and metamafic sources.
Principal Component Analysis 370 Principal component analysis (PCA) was conducted on the detrital rutile trace element compositions (V, Cr, Zn, Ga, Zr, Nb, Mo, Sn, Sb, Hf, Ta, W) using OriginPro statistical software and the results are given in Appendix B. PCA is a multivariate statistical procedure that identifies the variables that explain the most amount of variance within Figure  11  shows that the variance between samples can largely be explained by Hf, Zr, Sn, Cr, V, Nb and Ta. Because Cr, Nb and Ta are protolith dependent (PC 2) and Hf and Zr are temperature dependent (PC 1), the variance in detrital rutile trace element chemistry is best explained by both protolith and metamorphic grade, allowing us to track these two properties of source rocks.
The Karakaya Complex is composed of metamafic and metapelitic rocks, and the rutile dataset demonstrates that low-U rutile are sourced from mafic and pelitic units (Figure  7  and Figure  8 ). The contribution of Karakaya Complex to the basin would be underrepresented without including low-U rutile. Additionally, the U threshold is dependent on the spot size and sensitivity of the ICP-MS used and does not adequately delineate interpretable data in a way that merits continued use. Lastly, the presence of 580 Ma grains means that those grains 435 escaped younger high-T events, such as Variscan-related Carboniferous metamorphism (Figure  10 ). This supports the interpretation that the 580 Ma grains are recycled from sedimentary units, rather than derived from primary Pontide basement sources that underwent Carboniferous metamorphism.
Conclusion Sedimentary provenance analysis plays a crucial role in understanding the geodynamic, magmatic, structural, and topographic evolution of convergent margins. Detrital zircon U-Pb geochronology is a widely used technique, however, it has several limitations and can struggle to capture significant events in a convergent margin lifecycle (e. g. , low grade metamorphism, mafic protoliths). Detrital rutile provides one opportunity to overcome these limitations. 455 This study provides methods for using detrital rutile U-Pb and trace element analysis in tracking sediment input from metamorphic units using a new dataset from the Central Sakarya and Sarıcakaya Basins in Anatolia. We present a workflow for evaluating discordance and common Pb, which is critical for confidently interpreting age distributions.
Acknowledgements 580 We thank  Çelik Ocakoğlu ,  Jan Westerweel ,  Kate Huntington ,  Alison Duvall ,  Sean Mulcahy ,  Scott Braswell ,  Joel DesOrmeau ,  Scott Dakins , and  Eric Steig  for support in the field and lab. We thank  Andrew Kylander-Clark ,  Francisco Apen , and  Peter Downes  for reference materials and  Margo Odlum  and  Eirini Poulaki  for discussions on U-Pb data reduction. We thank the iolite team for student access. Financial support 585 This work was funded by the  University of Washington Department of Earth and Space Sciences  and  NSF   EAR-1543684  and  EAR-2141115. https://doi. org/10. 5194/egusphere-2023-1293 Preprint. Discussion started: 28 June 2023 c Author(s) 2023. CC BY 4. 0  License.
Data availability 565 The detrital rutile trace element and U-Pb raw data, results and Pb correction methods; rutile U-Pb reference material raw data and results; and statistical comparison of Pb correction methods are stored in an Open Science Framework data repository that can be accessed at https://doi. org/10. 17605/OSF. IO/A4YE5 (Mueller et al. , 2023). Analyses and plots were performed in MATLAB (The MathWorks Inc. , 2021).
https://doi. org/10. 5194/egusphere-2023-1293 Preprint. Discussion started: 28 June 2023 c Author(s) 2023. CC BY 4. 0 License. a dataset. The principal components are ranked based on the amount of variance they explain. Plots of principal component 'loadings' display the distribution of the trace element variables with respect to the principal components. 375.
Discrimination diagrams of Cr versus V and V versus Zr can verify that analyzed grains are rutile. The grains from this study are plotted alongside the polymorph dataset of Triebold et al. (2011) which were classified using Raman spectrometry (Figure A4). All samples from this study plot within the range of rutile grains. 520 https://doi. org/10. 5194/egusphere-2023-1293 Preprint. Discussion started: 28 June 2023 c Author(s) 2023. CC BY 4. 0 License.
3x3 SKONN PCB We designed a 3x3 SKONN on PCB with fully-connected capability and 81 synapses (Fig. 6a ) as a proof of concept for the SKONN architecture. Due to area constraints, we only implemented negative weights that we program by placing discrete capacitors C ij manually. Fig. 6b  shows the oscillating neuron based on a Schmitt trigger (U1) with feedback resistor R 3 that charges/discharges a load capacitor C L , producing a triangular-like waveform with 720 mVpp amplitude. The neuron output is a square-like waveform oscillating between V DD = +0. 9V and V SS = -0. 9V. Using an FPGA, we set the initial phase state by delaying the oscillator's starting time (Q1). The FPGA measures the neurons' output voltages and allows phase post-processing with a maximum precision of ϵ = 360 • f 0 /f F P GA.
Weighted Max-cut of random graphs To assess how SKONN's computational performances scale, we run large-scale simulations of random Weighted Max-cut problems for N=8, 16, 32, 64, 128, 256, 512, and 1024 nodes. For each graph density d=0. 25, 0. 5, and 0. 75, 10 random graphs G(N, d) are generated such that the total number of edges m = d N (N -1)/2. The graph edges are randomly weighted with positive values from 0 to 15 that correspond to the ASIC synaptic range. We use the ASIC parameters and solve SKONN's dynamics  (7)  with MATLAB using the built-in ODE solver ode15s. For each graph instance, we run 10 trials with random phase initialization, for a total of 100 trials per graph size and density. As a ground truth, we consider the best solution Cut GW provided by the Goemans-Williamson algorithm, out of 100 random projections defining the cut  [36]  and computed with the CVX solver on MATLAB  [47].
G-set benchmark The previous study concerned random graphs. Here, we benchmark SKONN for solving Max-cut using the G-set benchmark that includes various graph topologies  [48]. Table  5  shows the cuts obtained for a single trial with SKONN and Kuramoto using the same random phase initialization, and considering the first oscillator as the phase reference. The cuts are compared against the state-of-the-art GW  [36]  and the Kuramoto-CirCut scheme  [37]. GW's cut is the best cut obtained out of 100 random projections and computed with the CVX solver on MATLAB  [47]. For graphs with N > 3000, GW values are taken from another state-of-the-art SDP solver  [49]  due to memory constraints. The Kuramoto-CirCut values correspond to the best cut extracted from the Kuramoto dynamics, out of N possible reference oscillators.
Discussion SKONN mixed-signal architecture facilitates scaling up the ONN size thanks to the separation between analog computation and digital propagation. While the neurons exchange information in the digital domain, SKONN architecture ensures that the sensitive analog computation remains within modules and can be shielded from the outside. However, it remains some design challenges that are currently being investigated: 1. Any delay added to the digital propagation is equivalent to a synaptic phase shift. This must be considered for a high-frequency operation when buffers' delays become non-negligible and can be an issue for advanced technologies. 2. Large synaptic values can induce large voltage jumps at the analog input that can decrease the frequency for recurrent synapses, as highlighted in Fig.
Specifically, the OHNN acts like a rotation to transform the original speaker vectors into anonymized speaker vectors, which are constrained to follow the distribution over the original speaker vector space. A basic classification loss is introduced to ensure that anonymized speaker vectors from different speakers have unique speaker identities. To further protect speaker identities, an improved classification loss and similarity loss are used to push original-anonymized sample pairs away from each other. Experiments on VoicePrivacy Challenge datasets in English and the AISHELL-3 dataset in Mandarin demonstrate the proposed anonymizer's effectiveness.