dataesr/scientific-paragraphs-categorization huggingface dataset:
Remark. This bound is tight. This can be seen by starting from an arbitrary concept space (X, C) of VC dimension d, and forming the concept space (X 2 , C 2 ) with X 2 = X × {0, 1} and C 2 = {C × {i} : C ∈ C, i ∈ {0, 1}}. It can be checked that the VC dimension of (X 2 , C 2 ) is d, and the VC dimension of (X 2 , C ∆ 2 ) is 2d. We now turn to the proof of Theorem A. 1. The proof is no longer a "generic" reduction to PAC learning. Instead, the proof uses the -net theorem (Theorem 2. 5) directly. Proof of Theorem A. 1. We choose as adversary any adversary that outputs any database DB that is consistent with the observed leakage. Such a database exists, since DB must be consistent with its own leakage. (As with general PAC learning, there is no guarantee that the adversary is efficient. ) Next we pick a sample size m large enough to ensure that the sample is an -net for the concept space (X, C ∆ ).
By Lemma A. 2, the VC dimension of that concept space is at most 2d. By the -net theorem, it follows that m ∈ O( d log d δ ) suffices to ensure that the sample forms an -net with probability at least 1 -δ. We claim that this choice of adversary and m satisfies the conclusion of the theorem. To see this, assume the sample is an -net, which holds with probability at least 1 -δ. Let DB be the database output by the adversary. Assume towards contradiction that there exists j ∈ [R] such that Pr πq [ q(DB[j]) = q(DB [j]) ] >. This last expression is equivalent to saying that the measure of ∆(C DB[j] , C DB [j] ) according to π q is greater than. Since the sample is an -net for C ∆ , it must contain a point in ∆(C DB[j] , C DB [j] ). This point is a (known) query that matches record j in DB but not in DB , or conversely.
Output: Function est-val approximating val. 1: est-symval ← GetEstsymval(Q) Step 1 2: est-val ← GetEstval(Q, est-symval) Step 2 3: return est-val GetEstsymval(Q): 1: for each record r do 2: c(r) ← |{q ∈ Q : r ∈ q}|/|Q| 3: est-symval(r) ← arg min k∈[N/2] |p(k) -c(r)| 4: end for 5: return est-symval GetEstval(Q, est-symval): 1: Q ← |Q| 2: r A ← arg min r |est-symval(r) -N/4| Anchor record 3: est-val(r A ) ← est-symval(r A ) 4: for each record r = r A do 5: c (r) ← |{q ∈ Q : r A , r ∈ q}|/|Q| 6: if c (r) > min{est-val(r A ), est-symval(r)}/N then 7: est-val(r) ← est-symval(r) 8: else 9: est-val(r) ← N + 1 -est-symval(r) 10: end if 11: end for 12: return est-val Finally, we recall that sacrificial -approximate database reconstruction (sacrificial -ADR) is said to succeed iff one of the following two events occur: 1.
e. each value k yields one concept {[x, y] ⊆ [N ] : v A , k ∈ [x, y]}). A straightforward adaptation of the proof of Lemma B. 2 shows that (X, C ) has VC dimension 2. First, we treat the case where = 1/N , which requires special attention. Recall that sacrificial 1/N -ADR is equivalent to full database reconstruction. Lemma B. 5. Let δ > 0. After O N 4 log N + N 4 log 1 δ. queries, GeneralizedKKNO achieves full database reconstruction with probability of success at least 1 -δ. Proof. Using Lemma B. 3 with = 1/N and c 1 = 1, we can ensure est-symval(r) = symval(r) for all r. It remains to show that for each record r, GetEstval correctly determines which side of N/2 the record r is relative to r A , so that GetEstval returns the correct choice for est-val. Fix a record r. Let a = min(symval(r), symval(r A )) and b = max(symval(r), symval(r A )).
Assume that r and r A are on opposite sides of (N + 1)/2 (the other case is very similar). Observe that c (r) converges towards 2ab/(N (N +1)), and the algorithm succeeds if c (r) is less than a/N. Let us compute: a N - 2ab N (N + 1) = a N 1 - 2b N + 1 ≥ 1 N 1 - N N + 1 = Ω 1 N 2. It follows that for the algorithm to succeed, it is enough that c (r) be within Ω(1/N 2 ) of its expected value. Using the concept space (X, C ) (where we recall that each concept corresponds to the set of ranges containing a given value k together with the anchor value v A = val(r A )), a direct application of the -sample theorem with = Ω(1/N 2 ) yields the result. We now remove the assumption N = 1 and treat the general case. We distinguish two cases, based on whether there exists a "good" anchor record or not within the database.
First, we will assume that every record in the database has values within N/4 of 1, N and (N + 1)/2. This is the case where no good anchor record exists. Note that the adversary does not know that fact, but that is immaterial: what we will show is that the same algorithm GeneralizedKKNO succeeds whether a good anchor record exists or not. The following lemma handles this first case. Lemma B. 6. Let δ > 0. Assume all records r satisfy val(r) ∈ [1, 1 + N/4] ∪ [(N + 1)/2 -N/4, (N + 1)/2 + N/4] ∪ [N -N/4, N ]. Then after O 1 4 log 1 + 1 4 log 1 δ. queries, GeneralizedKKNO achieves sacrificial -ADR with probability of success at least 1 -δ. Proof. First, note that the definition of sacrificial -ADR makes no claim about records within N/4 of 1 or N , so we can focus purely on those records whose values lie within N/4 of (N + 1)/2.
Then |symval(r) - N/4| < N/4 + 1/2 -N/4. Using Lemma B. 3 with c 1 = 1/16, we get |est-symval(r) -N/4| < N/4 + 1/2 -(1/4 -1/16) N. Since r A is chosen such that est-symval(r A ) is closest to N/4 , the same inequality applies to r A. Finally, because we have applied Lemma B. 3 with c 1 = 1/16, we can deduce that |symval(r A ) -N/4| < N/4 + 1/2 -N/8. First, consider the case that N ≤ 16. In that case = N/16, so O( -4 log -1 + -4 log δ -1 ) is the same as O(N 4 log N + N 4 log δ -1 ), and we can apply Lemma B. 5 to achieve full database reconstruction within that query complexity. In particular we achieve sacrificial -ADR, so we are done. Hence in the remainder we are free to assume N > 16. In that case the inequality |symval(r A ) -N/4| < N/4 + 1/2 -N/8 from earlier implies 1 + Ω( N ) ≤ symval(r A ) ≤ N 2 -Ω( N ).
2. Let < 1/4. Assume the database under attack satisfies hypotheses h 2 and h 3. Then after O 1 log 1 + 1 log 1 δ. queries, Algorithm 7 succeeds with probability at least 1 -δ. The proof of Theorem D. 2 is given in the next section. Remark. Intuitively what we are showing is that when building a PQ-tree from uniform ranges, assuming some fairly mild hypotheses expressed by h 2 and h 3 about the database not being overly sparse or overly concentrated on a few values, then quite quickly the PQ-tree contains a Q-node near the root that provides a considerable amount of information about the order (each of its children has small diameter, their order is known since it is a Q-node, and collectively they contain all values save a small fraction near 1 and N ). Moreover that Q-node can be located easily because it is the deepest node containing a strict majority of records.
Notation. Throughout [n] denotes the set of integers {1,. , n}; [a, b] denotes the set of integers within the given interval; and open brackets such as [a, b[ denote that the corresponding endpoint is excluded. (If b ≤ a, [a, b[ is empty. ) We model a database as a set of R records where each record has a single attribute that takes an integer value in [N ]. We let val(r) ∈ [N ] denote the value of the record r.
[1, ep 1 ,. , ep |B| , N ] of[N ]  where the records in group b i are between ep i and ep i+1 , so we need only choose a value in [ep i , ep i+1 ] to assign to the records in b i. Since we are concerned with minimizing the absolute value of the difference between the true value and the guess, the natural choice is the median of the database distribution π, conditioned on the range [ep i , ep i+1 ]. In Algorithm 4 this is written as RangeMedian(π, ep i , ep i+1 ).
r) < (p( w L ) + p( w R ))/2 then 12: est-val(r) ← w L 13: else 14: est-val(r) ← w R 15: end if 16: end for Finally, we recall that sacrificial -approximate database reconstruction (sacrificial -ADR) is said to succeed iff one of the following two events occur: 1. For every record r such that val(r) ∈ [1, N [∪]N + 1 -N, N ], |est-val(r) -val(r)| < N. 2. For every record r such that val(r) ∈ [1, N [∪]N + 1 -N, N ], |est-val(r) -(N + 1 -val(r))| < N.
Acknowledgments Portions of this work were written while the first author was visiting  Royal Holloway, University of London. This work was supported by  NSF   Graduate Research Fellowship   DGE-1650441 , the  European Union's Horizon 2020  grant  ECRYPT-NET (H2020 643161 ),  ERC  Project  aSCEND  ( H2020 639554 ), and  EPSRC  Grant  EP/M013472/1.
An accelerometer having a mass of m = 41 g, is placed on the top of the rod since it has been proved to be the optimal location  [25]. The accelerometer records the transient dynamic response of the sensor corresponding to its first bending mode of vibration. The scour process is taken into account by the progressive increase of the exposed length H of the sensor. Table  3  summarizes the range of the exposed length H for each rod. This length is limited on the one hand by the tank dimensions, and on the other hand by the stability of the rod-sensor. The scour depth is increased step by step with increments of 50 mm. For each exposed length H, the impulse force is applied and the vibratory response of the rod is recorded. The data samples are recorded with a sampling frequency of 512 Hz. The transient response of the system is then post processed using SCILAB to measure the first natural frequency from the Fast Fourier Transform (FFT).
Model description A 3D finite elements model is developed using the finite element software Code-Aster  [32]. The proposed model is based on the following hypothesis: 1) the soil medium and the rod-sensor are elastic, 2) all displacements and strains remains small and 3) the soil and the sensor are perfectly bounded at the interface. For the boundary conditions, the lateral faces of the soil are fixed against displacement in the normal direction and the base is fixed against displacement in all directions. The weight of the accelerometer is not negligible and is modeled as a nodal mass placed at the top of the rod-sensor. In this model, the soil and the sensor are meshed with 10 nodes tetrahedron elements. The mesh was refined near the sensor with a progressive transition to a coarser mesh away from the sensor.
, 1997). This vegetation cover is forced by climatic inputs from ECBilt, and in turn, VECODE calculates land surface albedo and passes it back to ECBilt. By activating VECODE in iLOVECLIM, we already include in a crude way the impact of vegetation changes in our climate simulations. However, note that our goal for the iLOVECLIM simulations was to obtain 8. 2 ka BP climate anomalies that are as close as possible to proxy-based evidence, to be used as forcing for LPJ-GUESS, so that we could evaluate the impact of this abrupt climate change on vegetation in considerable detail. We thus only consider the climatic output of iLOVECLIM, and do not evaluate the results of VECODE in this study. Because cloud cover is prescribed in iLOVECLIM, the transient climatic forcing of LPJ-GUESS consists only of varying temperature and precipitation.
Acknowledgements. We thank  Yurui Zhang  for providing the 8. 5 ka Bp initial climate conditions. We thank  Heikki Seppä  for helpful discussion on the comparisons between reconstructed and simulated vegetation. We appreciate the valuable comments and suggestions provided by the three anonymous reviewers which helped improve an earlier version of the manuscript. This work was supported by the  China Scholarship Council. P. A. M. acknowledges this as a contribution to the  Strategic Research Area MERGE  and is grateful for financial support from the  Swedish Research Council (VR).
, 2000) , restricted to Poaceae  (Jang et al. , 2007)  or Solanaceae  (Liu et al. , 2010). Around 200 nsLTPs have been identified in wheat, rice and Arabidopsis genomes and classified into nine different types according to sequence similarity  (Boutrot et al. , 2008). More extensive studies including ancestral plants indicate that nsLTPs are also present in liverworts, mosses and ferns, but not present in algae  (Edstam et al. , 2011; Wang et al. , 2012). -From a structural point of view, the nsLTP family belongs to the all-alpha class in the SCOP database  (Murzin et al. , 1995) , as these small proteins contain four or five helices organized in a right-handed superhelix. To date, only 30 three-dimensional redundant structures corresponding to 8 different proteins have been experimentally determined.
According to SCOP, the protein fold called "Bifunctional inhibitor/lipid-transfer protein/seed storage 2S albumin" is found in at least six distinct plant nsLTPs for which the 3D structure has been solved (from five species Triticum aestivum, Hordeum vulgare, Zea mays, Oryza sativa and Triticum turgidum), and one soybean hydrophobic protein. In the RCSB Protein Database  (Berman et al. , 2000)  we listed four more plant nsLTP 3D structures (from Nicotiana tabacum, Phaseolus aureus, Prunus persica and Arabidopsis thaliana). According to the CATH database  (Orengo et al. , 1997) , nsLTPs belong to the "Mainly alpha" class. They display the "Orthogonal Bundle" architecture and the "Hydrophobic Seed Protein" topology. At this level, only one homologous superfamily called "Plant lipid-transfer and hydrophobic proteins" can be found.
The superfamily appears to contain ten distinct protein sequences, lacking the A. thaliana nsLTP, but including the soybean hydrophobic protein found in the SCOP database. Of the known nsLTP 3D structures, only Boutrot's type I, II and IV are represented. An interesting point to be noted is that two different cysteine pairing patterns have been observed (which correspond to a single cysteine switch between two disulfide bridges): C1-C6 and C5-C8 in type I structures; C1-C5 and C6-C8 in type II and IV structures. However, C2-C7 and C3-C4 bridges are common to all known nsLTP structures and the overall fold is conserved among the whole family. -From a functional point of view, plant nsLTPs are classified into different families depending on the scope of interest and their properties  (Liu et al.
Definition of the protein sequence set A first pool of plant nsLTPs sequences was retrieved from the UniProtKB (Swiss-Prot + TrEMBL) (http://www. uniprot. org), Phytozome (http://www. phytozome. net) and NCBI databases (http://www. ncbi. nlm. nih. gov), using either Blast or keyword queries ("Plant lipid transfer protein", "viridiplantae lipid transfer protein", "plant A9 protein", "A9 like protein", "tapetum specific protein", "tapetum specific", "anther specific protein", "A9 Fil1"). Original data obtained on the Theobroma cacao genome were also investigated  (Argout et al. , 2011). From this large pool of proteins, the plant nsLTP dataset was defined according to a new set of criteria: (i) sequences from 60 to 150 residues long, including signal peptide; (ii) containing strictly eight cysteine residues after removal of the signal peptide; (iii) cysteine residues distributed in the 8CM pattern (C-Xn-C-Xn-CC-Xn-CXC-Xn-C-Xn-C).
Sequence alignments and phylogenetic analysis In order to achieve the best alignment, the pool of 797 sequences was aligned using both the MAFFT  (Katoh et al. , 2002; Katoh & Toh, 2010)  and MUSCLE  (Edgar, 2004)  programs with respective parameters of 1. 53 for gap opening, 0. 123 for gap extension and BLOSUM62 matrix; maximum iteration 16. The two resulting multiple alignments were compared and conflicts between the two were highlighted. To discriminate between the two different cysteine patterns suggested (see Results section), a restricted analysis was carried out using only the 10 nsLTPs for which at least one structure had previously been experimentally determined. Two new 10-sequence alignments were calculated, one by MUSCLE and one by MAFFT. Using the ViTo program  (Catherinot & Labesse, 2004) , each alignment was projected on type I, II and IV nsLTP 3D structures, and the spatial distance of equivalent cysteine residues was evaluated.
2/ NsLTP three-dimensional structures Three-dimensional structure modeling For 10 out of the 797 nsLTP dataset, one or more experimentally determined 3D structures were available and downloaded from the Protein Data Bank (http://www. rcsb. org/pdb). Theoretical structures were calculated for the other 787 proteins using the @tome2 suite of programs to perform homology modeling (Pons & Labesse, 2009) (http://atome. cbs. cnrs. fr). The quality of each final structure model was evaluated using Qmean  (Benkert et al. , 2008). Structures with low quality (i. e. for which the cysteine scaffold could not be fully modeled) were discarded from further analysis (see Table  1 ).
Structural classification All the remaining good-quality theoretical structures, together with the 10 experimental structures composed the 3D structure pool of the study. Except for the cysteine pattern analysis by ViTo, this structural pool was used in all further structural analysis. The structures were compared to each other in a sequence-independent manner, using the similarity matching method of the MAMMOTH program  (Ortiz et al. , 2002). The RMSD was calculated for each pair of structures, using the superposition between matched pairs that resulted in the lowest RMSD value. This superposition was computed using the Kabsch rotation matrix  (Kabsch, 1976; Kabsch, 1978)  implemented in the MaxCluster program (Herbert, http://www. sbg. bio. ic. ac. uk/maxcluster, unpublished). We used the RMSD score matrix calculated by MaxCluster as input for the FastME program  (Desper & Gascuel, 2002)  to calculate a structural distance tree.
3/ NsLTP functional annotation Extensive bibliographic work was carried out to collect and classify functional information available in the literature about the nsLTPs of the dataset. Gene Ontology (GO), Plant Ontology (PO) and Trait Ontology (TO) terms were collected from the Gramene Ontologies Database (http://www. gramene. org/plant_ontology) and organized in a dedicated database, together with the bibliographic references when available. The database was also enriched with additional information, such as methods used for gene expression studies (northern, RT-PCR or microarray data, in situ hybridization), protein purification, in vitro or in planta antifungal and antibacterial activity, lipid binding or transport (fluorescence binding assay or in vitro lipid transfer). Information about tissues and organs used in cDNA libraries was collected from the NCBI databases (http://www.
InTreeGreat: an integrative tree visualization tool We developed an integrative tree visualization tool called InTreeGreat in order to display the whole or some parts of either sequence or structure distance trees. InTreeGreat was implemented using PHP and Javascript, in order to generate and manipulate an SVG graphical object. The main objective of this tool is to graphically highlight correlations between 3D structures, evolution, functional annotations or any available heterogeneous data. In the context of this study, the interface was able to retrieve information from the nsLTP database to annotate the tree. InTreeGreat includes functionalities such as tree coloration, fading, and collapsing. Heterogeneous data related to sequences (e. g. annotations, nsLTP classification) can be displayed in colored boxes, aligned to the tree.
Structural Trace calculation A structure-based sequence alignment was carried out on the nsLTP structures by Mustang software  (Konagurthu et al. , 2006). For each previously selected structural cluster, the corresponding set of protein sequences was extracted from the multiple structural alignment of the nsLTPs. The Evolutionary Trace (ET) method  (Lichtarge et al. , 1996)  was applied: the partial multiple sequence alignment was submitted as input for the ETC program (locally installed, http://mammoth. bcm. tmc. edu/ETserver. html) together with the representative structure of the cluster (selected as described in the previous paragraph). The "evolutionary" traces based on the structural alignments corresponding to the three nsLTP clusters were then compared to each other. To that end, the 30% top-ranked residues of the defense cluster trace were considered as constitutive of the reference trace (i.
NsLTP dataset Over the last four decades numerous proteins, whose ability to transfer lipids has not always been demonstrated, have been annotated as nsLTPs on the basis of sequence homology. In order to understand more clearly the functional characteristics and the inner variability of this family, we focused the study on the monodomain proteins, which present the strict and only nsLTP domain, i. e. the eight-cysteine residues arranged in four disulfide bridges. In total, including the wheat, rice and Arabidopsis sequences previously identified  (Boutrot et al. , 2008) , together with sequences from the UniProt (Swiss-Prot/TrEMBL), NCBI and Phytozome databases, 797 nonredundant mature nsLTP sequences belonging to more than 120 plant species were kept for analysis. This first step allowed the selection of a relevant set of proteins covering variability in the nsLTP family.
Sequence alignment and Cysteine pattern The alignment of all non-redundant protein sequences for which the 3D structure was experimentally determined (10 sequences) was carried out twice, using the MUSCLE program on the one hand, and the MAFFT program on the other hand. The resulting alignments obtained with standard settings are shown on Figures  1A1  and 1B1. In both cases, cysteine residues of the 8CM aligned quite well among the three represented types of nsLTPs (types I, II and IV), except for the Cys5-X-Cys6 (CXC) pattern region (where X stands for any amino acid residue). MUSCLE did align type I Cys5 with types II and IV Cys5', as well as type I Cys6 with types II and IV Cys6' (Figure  1A1 ), just as previous studies typically showed  (Liu et al. , 2010; Siverstein et al. , 2007). However, in the alignment carried out by MAFFT (Figure  1B1 ), Cys5 of type I nsLTPs was equivalent to Cys6' of type II and IV nsLTPs, and not to the corresponding Cys5'.
NsLTP sequence classification Our dataset was mainly composed of nsLTPs from angiosperm species (19 monocotyledonous species and 83 eudicotyledonous species) plus five gymnosperm species (35 sequences), one lycophyte species (34 sequences) and two bryophyte species (17 sequences). The monocot sequences were mainly represented by Poales nsLTPs (256 out of 270 sequences) whereas Rosid nsLTPs were the most abundant (364 out of 436 sequences) within eudicots. The phylogenetic analysis showed that the pool of proteins clustered into nine different types, all highly supported (branch support >0. 84). This result mostly confirmed Boutrot's classification, defined on A. thaliana, T. aestivum and O. sativa nsLTP sequences, in nine types  (Boutrot et al. , 2008). The main differences were the identification of a new group (named type XI), including 23 sequences, and that Boutrot's type VII nsLTPs disappeared from our dataset.
Indeed, the latter did not satisfy the 8CM criteria as they have only seven cysteine residues in their sequences. For the same reason, Wang's A, B, C and D types  (Wang et al. , 2012)  were not represented in our classification. Type I nsLTPs formed a well-supported monophyletic group (branch support of 0. 879) and predominated over the other types, as they accounted for more than half of our dataset (417 out of 797 sequences). This was also observed by Wang  (Wang et al. , 2012)  with a set of 595 nsLTPs. Conversely, in Solanaceae, the most abundant nsLTPs belong to a type referred to as type X by Wang (70 out of 135 sequences) and which seems specific to that plant family  (Liu et al. , 2010)  but was not present in our dataset. To avoid any confusion, we did not used type X denomination in this work.