dataesr/scientific-paragraphs-categorization huggingface dataset:
To this purpose, we have employed the Barabási-Albert synthetic graphs with varying outdegree ( 0 ) and number of nodes () and considered query q2 with  = 3. Table  3  shows the different speedups that the windowed approach offers, when compared to the baseline. We varied  0 from 5 to 25, using increments of 5, and varied  from 32 to 1M in a logarithmic scale with increment factor of √ 10 ≈ 3. 16. In the table, we see that the speedup factor of the windowed approach increases by up to three orders of magnitude as the size of the data and out-degree  0 increase. T/O means that the baseline approach timed out (> 30 minutes). For all entries in Table  3 , the windowed algorithm terminated under 15 minutes. These results show the robustness of our algorithm to variations of dataset size and outdegree as well as its superiority with respect to the baseline.
For general threshold queries, the potential for such optimization is less clear. There, instead of a global limit on the number of answers we have a per-group limit. Consequently, the execution of the subplan can be stopped only when each group has sufficiently many tuples. The level of savings depends on the order in which the subplan produces its results. Such optimization goes beyond the scope of our paper, but is a promising direction for future work. Quantified Graph Patterns. Fan et al. [33]  introduced quantified graph patterns (QGP) that allow expressing nested counting properties like having at least 5 friends, each with at least 2 pets. In contrast to threshold queries, QGPs are unable to count -hop neighbours for  ≥ 2, nor can they count tuples of variables. Moreover, QGPs adopt isomorphism matching, while threshold queries follow the standard semantics of database queries.
Aggregate Queries. In the context of factorized databases, Bakibayev et al. [6]  observed that pushing aggregation down through joins can speed up evaluating queries. These results can be reinterpreted in the context of tree decompositions  [60] , but they optimize different aggregates in isolation and do not investigate the interplay between counting and existential quantification. AJAR (aggregations and joins over annotated relations)  [46]  and FAQs (functional aggregate queries)  [48]  are two very general sister formalisms capturing, among others, CQs enriched with multiple aggregate functions. Because different aggregate functions are never commutative, the evaluation algorithms for both these formalisms require decompositions consistent with the order of aggregating operations. For example, when applied to counting answers to CQs, this amounts to free-connex decompositions, as in our Proposition 4.
CONCLUSIONS AND FUTURE WORK In this paper, we have embarked on a deep theoretical study of a newly identified class of threshold queries. Our extensive empirical study shows that threshold queries are highly relevant in practice as witnessed by their utility in real-world knowledge graphs and their presence in massive query logs. Our theoretical investigation shows that threshold queries occupy a distinctive spot in the landscape of database querying problems. Indeed, our complexity analysis proves that threshold queries allow for a more efficient evaluation than solutions for closely related problems of counting query answers, constant-delay query answer enumeration, and top- querying. As one of the first future steps, we intend to gauge thoroughly the performance of the proposed algorithms.
Designing adequate protocols for experimental evaluation requires a deep understanding of the relationships between evaluation of threshold queries and the related querying problems, which we have already accomplished in the present paper. We intend to carry out a comprehensive implementation of threshold queries in an existing database system similarly to how algorithms of top-k queries have been implemented and evaluated  [55, 55]. More precisely, we will implement dedicated threshold-aware variants of relational operators and then we will introduce them in the query planning stage. Our work has led us to identify remarkable similarities in the query answering methods tackling counting and enumerating answers: they rely on various techniques for compiling out existentially quantified variables.
We plan to pursue this discovery further and give full treatment to the emerging question: is there a unifying framework for assessing threshold queries and the related problems? Further theoretical results about threshold queries can be envisioned, such as establishing a dichotomy of evaluation complexity and identifying a condition under which evaluation is strongly polynomial, rather than pseudopolynomial. We will define a database , a conjunctive query , and a threshold  such that  returns at least  answers on  iff  is valid. The database  uses the binary relations  1 ,. ,   , has Adom() = {,  } ∪ { 1 ,  2 ,. ,   }, and is illustrated in Figure  5. More formally, we put (  , ) in relation   iff assigning   = true is compatible with   , i. e. , does not falsify clause. Similarly, we put (  ,  ) in   iff assigning   = false is compatible with   , i.
The database  is constructed in the same way as in Proposition 3. 2, except that we add a unary relation Node(•) that contains all elements in Adom(). Boolean evaluation of the at-most query 𝑡 (𝑣 1 ,. , 𝑣 𝑛 ) = 𝑛 𝑖=1 Node(𝑣 𝑖 ) ∧ ∃ ≤𝑘 𝑢 𝑛 𝑖=1 𝑋 𝑖 (𝑢, 𝑣 𝑖 ) checks if there exists an assignment that satisfies at most  clauses in the DNF formula. For the dual CNF formula, this means that there is an assignment that falsifies at most  of its clauses. This means that this assignment satisfies at least  - of its clauses. For at-least queries, we reduce from MINSAT, which is also NP-complete  [51]. Boolean evaluation of the at-least query 𝑡 (𝑣 1 ,. 𝑣 𝑛 ) = 𝑛 𝑖=1 Node(𝑣 𝑖 ) ∧ ∃ ≥𝑘 𝑢 𝑛 𝑖=1 𝑋 𝑖 (𝑢, 𝑣 𝑖 ) checks if there is an assignment that satisfies at least  clauses in the DNF formula. For the dual CNF / SAT formula, this means that there is an assignment that falsifies at least  of its clauses.
If  is a project node, then it has exactly one child, and because  is not a  -leaf, this child must belong to. □ Proposition 4. 3. Counting answers grouped by  for conjunctive queries of  -rooted tree-width  and star-size  over databases of size  can be done in time Õ   •. Proof. Let  be a conjunctive query of tree-width  and star-size  , and let  ⊆ FVar() be a set of grouping variables. Let  be an  -rooted tree decomposition of , of width. Because ss() =  , we can equivalently write  as the conjunction of CQs  1 ,  2 ,. ,  ℓ , where |FVar(  )| ≤  or QVar(  ) = ∅ for each. Without loss of generality we can assume that QVar(  ) are pairwise disjoint and if QVar(  ) = ∅ then   consists of a single atom. Let us rewrite  as 𝑞 ′ = 𝑉 1 ( x1 ) ∧ 𝑉 2 ( x2 ) ∧ • • • ∧ 𝑉 ℓ ( xℓ ) using views 𝑉 𝑖 ( x𝑖 ) ← 𝑞 𝑖 ( x𝑖 ) where, for each , the tuple x lists each variable from FVar(  ) exactly once.
We note that blank nodes are the least frequent and, when used, occur only once per query in 99. 96% of cases. Conversely, IRIs, which provide a mechanism for globally identifying resources, are much more common. We also observed that timeout queries usually contained more variables and blank nodes. This relationship does not apply to almost IRIs and literals. Another potential purpose for threshold queries we identified is data monitoring, exemplified by the following Boolean query from the Wikidata logs. TQ5 Are there at least 67 language versions of Wikipedia pages for the movie The Matrix?.
Proposition 3. 2. Given an acyclic conjunctive query , a threshold  in binary representation, and a database , testing if  returns at least  tuples on  is coNP-hard. Proof. We reduce from the well-known VALIDITY problem. Consider a Boolean formula  in disjunctive normal form with clauses  1 ,  2 ,. ,   over variables  1 ,  2 ,. ,. VALIDITY asks if  is valid, i. e. , if  evaluates to true under every possible truth assignment  : { 1 ,. ,   } → {true, false}.
Õ | |. Because | ′If  is a join node with children  1 and  2 , then   can be obtained as the set of records 1 ⊲⊳  2 ,  for ( 1 ,  1 ) ∈   1 , ( 2 ,  2 ) ∈   2 such that  1 is compatible with  2 and  =  1 •  2 if  1 ⊲⊳  2 satisfies all atoms of  ′  that not present in  ′  1 ∧  ′  2 , 0 otherwise. To compute   we materialize the relevant views, as explained above, and then apply a variant of the merge-join algorithm. All this can be done in Õ | |  •. □ Proposition 4. 4. Counting answers grouped by  for conjunctive queries of  -rooted free-connex tree-width  over databases of size  can be done in time Õ.
for each  either QVar(  ) = ∅ and   is a single atom or |FVar(  )| ≤ |   )| ≤. Thus, we are in a situation entirely analogous to the one in Proposition 4. 3, except that the role of star-size  is now played by the  -rooted free-connex tree-width. Continuing like in Proposition 4. 3 we would obtain an algorithm evaluating  on database  with running time Õ | |  2. But it is easy to improve this complexity. Let.
Õ | |. Because | ′If  is a join node with children  1 and  2 , then   can be obtained as the set of records 1 ⊲⊳  2 ,  for ( 1 ,  1 ) ∈   1 , ( 2 ,  2 ) ∈   2 such that  1 is compatible with  2 and  =  1 •  2 if  1 ⊲⊳  2 satisfies all atoms of  ′  that not present in  ′  1 ∧  ′  2 , 0 otherwise. To compute   we materialize the relevant views, as explained above, and then apply a variant of the merge-join algorithm. All this can be done in Õ | |  •. □ Proposition 4. 4. Counting answers grouped by  for conjunctive queries of  -rooted free-connex tree-width  over databases of size  can be done in time Õ. | ≤  •  , we can compute the join in time Õ | | •. If  is a project node with child , then we let   =   ′  ;sum(witnessCount)   ; that is, we group records (, ) in   by   ′  () and for each group return   ′  () and the sum of all 's in this group.
17 9] [20] [21] [22]  Concerning ceramic materials, only a few studies comparing numerical model/experimental results have been found in the literature. However, we can cite the work of Mahmood et al. , who developed a mathematical model using MATLAB software to study the temperatures reached during laser sintering on a bulk substrate of silicon nitride (Si 3 N 4 ) and on a alumina powder bed (Al 2 O 3 ). 23 With their numerical model, they can predict the temperature distribution during the laser radiation-matter interaction with 8% accuracy. Thus, numerical modeling is appropriate to simulate the thermal diffusion inside metallic or polymer layers during the SLS process. Nevertheless, this technique faces significant challenges because this technique is dependent on a large number of parameters and remains under development for ceramic material.
Code The source code of our attacks and experiments on Falcon's reference implementation can be found on this git repository: https://github. com/mguerrea/ FalconPowerAnalysis. It has been made openly accessible online for easy reproducibility. Acknowledgements We thank Hugues Randriam and Jérôme Plût for the useful discussions throughout this project and the anonymous reviewers for their suggestions and corrections that helped improving the presentation of this paper. This work was supported in part by the European Union Horizon 2020 Research and Innovation Program Grant 780701 (Project PROMETHEUS).
We wrote a simple SageMath script to call the Leaky LWE / NTRU tool. For our very low values of the experimental standard deviation, we had to increase the precision of the intermediate computations inside the tool. The tool returns the estimated BKZ block-size β. This value gives an idea of the remaining work though the so-called cost models (See [ACD + 18] for more details). In a nutshell, most models suggest a security increase of one bit every 2 to 4 increase of β. Note that the block size for a key recovery on Falcon-512 is estimated around β = 480.
2. 3. We improved the search in the following way. When we get a first approximation of a b i , the seven remaining ones are almost free: we can use the first found vector as a starting point for the gradient descent, resulting in very fast convergence (few dozens of iterations). The only costly step that remains is the computation of the Gram matrix. We focus our experimental measurements on Falcon-512 parameters. We generated a database of 10 millions of signatures and the associated values of the z i 's. This precomputation took one week of computations on a standard computer. The obtained database is around 40 Gigabytes. This database allowed us to extensively analyze the resources of the attack. We performed our parallel HPP attack on a server with 80 cores and were able to finish the gradient descent of the HPP within a few days or weeks depending on the number of traces.
Experiments on other n We also performed our attack on modified instances of Falcon with smaller n (32, 64, 128 and 256), several experiments are provided in appendix in Table  4. One interesting fact is that the attack behaves better when the n increases. Indeed, the standard deviation of the error between (f , g ) and (f, g) decreases with the dimension. This may be explained by the fact that the norm (f, g) is bounded by 1. 17 √ q and is very close to this value for every n. The direct consequence is that, when n increases, the values of the coefficients of f, g decrease, easing the recovery. This behavior is favorable for the attacker, since the complexity of correcting noisy vectors increases with the dimension. For Falcon-1024, we did not generate a database of signature measurements and thus we cannot provide experimental data, though  [DN12]  claimed the number of required signatures to be polynomial in the dimension.
Indeed, they require a large amount of sequencing data and a follow-up period long enough to allow the diagnosis of a sufficient number of cases, which is not yet available. To overcome this limit, methods have been developed to combine data from large prospective cohorts with large case/control studies and evaluate with more accuracy the lifetime risks or penetrance associated with genetic risk variants  [3, 17]. Another option is to resort to family-based study designs. Indeed, focusing on families where the proband carries a specific variant of interest enriches the dataset in rare variant carriers. However, the downside is the risk of bias resulting from this ascertainment scheme, which could even be compounded by a selection on AAO. To overcome this issue, methods based on retrospective  [18]  or prospective  [19, 20]  likelihood were developed such as to condition the phenotype observation on the ascertainment process.
Here, we further extended this method to (i) a digenic scenario combining a rare and a common risk factor and (ii) the integration of previously published data to robustly stratify for the common risk factor. We applied this strategy to assess the penetrance of AD associated with SORL1 rare loss-of-function (LoF) variants in pedigrees where the AD-affected proband carries such a variant, with a baseline model stratified for common APOE-ε4 alleles derived from the Rotterdam Study  [25]. We thus provide here the first penetrance estimates for SORL1 rare variants stratified on the number of APOE-ε4 alleles. variant identified in a whole-exome sequencing (WES) dataset, generated from patients with a diagnosis of probable AD  [26, 27]  among patients referred to the National Reference Center for Young Alzheimer Patients (Centre National de Référence Malades Alzheimer Jeunes, CNRMAJ-Rouen, Rouen, France) in the context of a nation-wide recruitment.
Genetic data processing and SORL1 variants selection All variants were detected in the context of WES performed in the National Center for Research in Human Genomics sequencing center (CNRGH, Evry, France) using Agilent Sureselect all exons human kits and Illumina sequencing technology, as described before  [6]. Sequencing data were processed as previously described in Nicolas et al. [6] , based on BWA, GATK, and SNPeff tools. We considered exome data from 1295 unrelated AD probands remaining after quality control as previously performed in our case-control association studies  [9]  and after exclusion of patients carrying a likely pathogenic or a pathogenic variant in a Mendelian dementia gene  [6]. Minor allele frequencies (MAF) were annotated from the gnomAD database, non-Finnish European population  [28].
We extracted germline (allelic ratio [0. 25-1], all were eventually heterozygous) rare (MAF < 1%), non-synonymous, and splice region SORL1 variants (NM_003105. 6). We considered as PTV all nonsense, frameshift, and canonical splice site variants, in addition to splice region variants with a demonstrated effect on splicing (one described in Le Guennec et al. [29]  and one following unpublished patient blood mRNA analysis). We also considered missense variants that were predicted damaging by all three software tools among Polyphen-2  [30] , Mutation Taster  [31] , and SIFT  [32] , referred to as Mis3 variants, as candidates for the analysis. To lessen the heterogeneity of the set of variants under analysis, we restricted our analysis to the selection of SORL1 loss-of-function variants, namely (i) high confidence PTVs (i.
These probabilities are computed using an ad hoc C++ implementation of belief propagation in pedigrees (bped)  [36]  extended from Alarcon et al. [23]  to the specific case of APOE×SORL1 genotypes. Indeed, the bped program was initially designed for a single bi-allelic locus. The program takes as input a pedigree structure and an evidence file and returns both the w m i (a, s) = P Genotype combination of i is a, s | ev m i (a, s) log-likelihood and the marginal posterior genotypic distribution of all individuals. The evidence file can incorporate any kind of data (binary outcome, time-to-event outcome, etc. ) as long as the conditional probabilities P(outcome | genotype) are provided as real numbers. The marginal posterior probabilities are all we need to implement an EM algorithm. For the present application, bped had to be extended to two loci (one with 3 alleles, the second with 2 alleles, bped3alleles2alleles) which is a straightforward extension of the initial program  [36].
Assessing ages of SORL1-LoF variant carriers per APOE genotype in a case-control study To verify that our penetrance estimates per APOE genotype were consistent with large datasets of unrelated individuals, we interrogated the discovery dataset of the largest exome/genome case-control series, combining data from the Alzheimer Disease European Sequencing (ADES) and American Alzheimer Disease Sequencing Project (ADSP) consortia  [11, 37] , to which we added more recent cases from the ECASCAD study from France (N = 545), reaching a total of 13,007 cases and 10,182 controls. We then extracted carriers of SORL1-LoF variants as defined above and sorted them based on their case/control status and their APOE genotypes. Ages at last examination of controls and AAO for cases were then compared to the expected penetrance identified in our family-based study.
For the baseline scenario, we generated 27 families mimicking what we observed in our dataset in terms of SORL1-LoF variant effect, ascertainment, and available genotypes. Then, the model was challenged through three additional scenarios: (i) Unbalanced phenotype information: if one of the parents was affected, we removed all the phenotypic information of the parental branch with the unaffected parent. (ii) Relatives' genotypes 100% missing: we removed all information about relatives' genotypes. (iii) Heterogeneous variant effect: instead of generating age at onset based on a constant variant effect, we generated age at onset based on a normal distribution of the variant effect with a variance equaling to 1. A bias greater than 0 indicates an overestimation and a bias lower than 0 indicates an underestimation of the risk associated with SORL1-LoF variants 17.
02], Welch-test p-value = 0. 004). The case-control dataset did not include any SORL1-LoF and APOE-ε4 homozygous patients (respectively control) with AAO (respectively age at last examination) > 70 years, nor APOE-ε4 heterozygous patients (resp. control) with AAO (resp. age at last examination) > 80 years, which would be inconsistent with our penetrance curves. Finally, based on likelihood, our penetrance model computed from pedigree better fits the observations of all SORL1-LoF carriers in the case-control study (Log-likelihood = -327, AIC = 662, BIC = 671) than the null model considering no effect of SORL1-LoF variant (log-likelihood = -606, AIC/BIC = 1213). Thus, all these observations are fully compatible with the estimates from our family-based study.
In our study, we generated familial data based on a nation-wide recruitment that is probably amongst the largest datasets on SORL1-LoF families, as this gene is not systematically screened in a clinical setting. Despite this, the number of families remained limited, especially after restriction to families with a non-ambiguous LoF variant. However, the EM approach allowed us to reach sufficient power to provide meaningful estimates. A limitation of our study may be the absence of possible replication in a large number of pedigrees as there is no comparable series of extended pedigrees, to our knowledge. We thus assessed the compatibility of our curves in the largest dataset of exomes/genomes of AD patients and controls available. AAO for cases and age at last visit for controls were all consistent with our penetrance curves.
Thus, the haplotype context Fig. 4  Age-dependent penetrance for carriers and non-carriers of a SORL1 LoF variant. The penetrance is displayed with its 95% confidence interval according to the number of APOE-ε4 allele from 65 to 85 years of age. Curves for non-carriers and their confidence intervals were obtained from our estimation of λ nc (t | a) based on the Rotterdam Study. Data from pedigrees were censored at 85 years. Confidence intervals for SORL1-LoF variant carriers were obtained from the 2. 5th and 97. 5th quantiles of 500 bootstrap iterations. Penetrance values at 65, 70, 75, 80, and 85 years of age for carriers of the SORL1-LoF variant are displayed below the figure of the rare LoF variant could theoretically influence AAO. However, ORs remain rather modest (OR = 0. 84, [0. 81-0.
Conclusions We propose here digenic penetrance estimations for SORL1-LoF variants together with APOE-ε4 alleles. Our estimation is based on recruitment likely closer to that of genetic counseling requests in families than to the general population, and our estimates may thus be taken into account when an asymptomatic relative may request information following the identification of a SORL1-LoF variant found in a proband. We consider that SORL1 presymptomatic testing should not be performed regardless of APOE genotyping, given the large modifying effect in these families. funded by the National Institute on Aging. The ADSP umbrella contains data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (adni. loni. usc. edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in the analysis or writing of this report.
Funding This work was supported by grants from  Fondation pour la Recherche Médicale  (Equipe FRM  DEQ20170336711 ),  Fondation Alzheimer  (ECASCAD study),  France Alzheimer association  ( AAPSM2019 -grant  # 1957 ), CNRMAJ, and  Clinical Research Hospital Program  from the  French Ministry of Health  (GMAJ,  PHRC 2008/067 ). CS is supported by the  Fondation pour la Recherche Medicale  ( ARF201909009263 ). This work is a collaboration between  CEA-DRF-Jacob-CNRGH-CHU de Rouen. This work did benefit from the support of the  France Génomique National  infrastructure, funded as part of the  "Investissements d' Avenir" program  managed by the  Agence Nationale pour la Recherche  (contract  ANR-10-INBS-09 ).