dataesr/scientific-paragraphs-categorization huggingface dataset:
1% values including minimum, maximum and fluctuations, based on an oxygen desaturation of 2-4%; pulse rate; cycling time and cycling severity; and motion artifact detection via actigraphy and the SatScreen algorithm, which identifies and discards physiologically impossible recordings due to movement (Figure  4 ). The SatScreen algorithm and the 300i's 0. 1 s data collection speed permits near elimination of movement error, which is not possible with standard oximetry recordings. The algorithm provides interpretation of the slope of the SpO2 waveform, giving a stable monitoring method for titration. It was noted that movement reduced as the patient's OSA severity improved, which was a helpful indicator of treatment outcomes. The averaged data from the three-night recordings were evaluated to guide the decision as to whether further titration and additional 300i/SS studies were warranted.
The reason for three nights of 300i/SS study included the ability to exclude an anomalous night due to loss of power (battery failure); detachment of the finger probe; factors such as alcohol/substance use or abuse; medications; environmental allergies; or any other potential documented disturbances in the bedroom or sleep during any of the three nights. All technically acceptable data were then averaged and summarized. Subjects kept sleep diaries during the oximetry testing, to match objectively noted anomalous readings on the SS reports with subjectively logged contributing factors, such as illness, medication, or substance ingestion. Polysomnogram is the gold standard to assess sleep physiological parameters but was born in the laboratory. It is difficult, if not impossible, to use for a clinical/home based application, and the issue of cost and insurance coverage is of obvious importance as well.
The decision to utilize the Minolta 300i and SatScreen could be implemented at any point according to the progress of an individual's MAD titration. The 300i eliminated the need to schedule an appointment with the sleep laboratory, and alleviated the concern for cost or insurance reimbursement. The loss rate of data from the three-night oximetry protocol averaged 37%. If two nights with an error detection rate <10% were not achieved, testing was repeated. SatScreen calculates the amount of time lost due to patient movement or probe malfunction and recommends that the study be repeated with >10% error. As the patient approached ideal treatment position (that is, horizontal protrusion of 5-7 mm and vertical dimension of 4 mm) for the MAD, desaturations became much more subtle  (29). SatScreen measures respiratory effort-related arousals (RERAs) in the 2-4% range to record milder events, which would be detected on a polysomnogram, but missed on other oximetry reporting systems.
Titration of the MAD has only two data points for titration that were discoverable in this study. First, the 300i/SS sleep study reports and second the digital "One Shot" lateral cephalometric radiographic imaging capturing the entire oropharyngeal area in a single pulse of radiation. The cephalometric radiograph was employed as an adjunct to 300i/SS during the MAD adjustment process. One of the authors (JM) developed a protocol for the reproducibility of the cephalometric image. In this protocol, the patient stands perfectly straight with ear posts of the cephalometric unit properly inserted, teeth closed together maximally; inhales, then exhales, taking care not to forcibly exhale past the end-expiratory point; does not swallow; and maintains an ideal head posture by looking straight ahead into his/her own pupils in a mirror mounted at eye level.
Despite improvement of SatScreen parameters, some patients were still symptomatic, and required longer duration of interventions or additional interventions for their resolution. Polysomnogram (PSG) is considered the gold standard for diagnosis and efficacy testing of OSA  (34) , but the home sleep testing via portable unattended cardiorespiratory monitors may provide accurate diagnosis and efficacy data and is increasingly utilized  (34, 35). HST offers the benefits of cost-efficient testing in the home sleep environment  (36, 37)  as well as being recognized as non-inferior to PSG  (38, 39). For analysis purposes and continuity of the sleep data collected all pre-and post-treatment respiratory indices were blindly converted to the REI, based on total monitoring time (MT) [(number of respiratory events)/MT in hours] (40).
Statistical Analysis Statistical analyses were conducted in Stata software (version 14) (Statacorp LLC, College Station, TX). All data were scored and analyzed in a blinded fashion. The data were analyzed using means and frequencies to examine sample characteristics. Then, frequencies were used to determine the percentage of MAD complete responders (complete response [CR]-[REI] < 5), partial responders (partial response [PR]-REI ≥ 50% reduction), and non-responders (non-response [NR]-REI < 50% reduction or increase). T-tests for independent means and chi-square tests for proportions were used to examine differences in demographics and disease characteristics [REI, body mass index (BMI)] among subjects with CR, PR, and NR. Logistic regression models were also constructed to evaluate the independent effects of age, sex, obesity, amount of protrusion, and vertical component of mandibular advancement on the odds of MAD CR, PR or NR.
Fleury et al. used a Nonin 8500M oximeter, which records SpO 2 to the whole number. Our protocol is novel due to the use of the Minolti 300i/SatScreen software. The 300i records to the 0. 1%, giving more detailed SpO 2 data. An algorithm can then be applied to the data wave to screen out physiologically impossible data, mostly as a result of movement artifacts. Cheyne-Stokes and hypoventilation patterns can also be detected. The extent of information is what allowed for more precise titration than has been previously described in the dental/medical literature, allowing for the discovery of the previously unreported anatomic norms. The initial starting horizontal protrusion described by Fleury et al. is greater than our final point of protrusion with titration utilizing the 300i/SS. One of the primary morbidities with MAD therapy is the untoward movement of teeth.
CONCLUSION Obstructive sleep apnea (OSA) at any level of severity can be effectively treated with a MAD, even in the presence of obesity or severity > REI of 30/hour. Age and horizontal protrusion emerging as the only two predictive factors associated with CR. Attention to the titration process with a combination of carefully standardized lateral cephalometric images and 300i/SS testing are important to guide the adjustment of MAD and optimize CR rates. The RDI indicator on the SatScreen report indicated even milder desaturation events as the MAD titration changed events frequency and severity, and as such resulted in no further MAD changes being necessary after the second, clearing PSG or HST. The Minolta 300i with SatScreen software is a simple and low-cost method that allows multiple nights of home study and the SatScreen RDI indicator correlates with the final device efficacy.
Finally, we give a abstract view of our constructions. By simply changing a fundamental building block called the phase, we can obtain FHE cryptosystems based not only on LWE, RingLWE, Module-LWE, but also scale-invariant versions based on the approx-GCD, or on the NTRU function. We show how to instantiate a canonical version, based on RingLWE, directly from the two user parameters: security parameters, and depth of circuit in the case of LHE. We reduce the number of parameters to avoid dependency loops between them, and we keep the remaining ones as intrinsic as possible, to ease their setup: for example, scale invariant versions of lattice problems are expressed on the torus, Gaussian noises are represented by their standard deviation or their variance, the size of the key is measured in bits.
TLWE In this section, we present a generalization of the LWE problem, following the footprint of  [12]  (that defined the General LWE problem) and  [34]. We call this generalization TLWE. In the previous example, the phase was derived from the settings of the LWE cryptosystem. In TLWE, the phase becomes the central building block. All other notions are deduced from the algebraic properties of this linear function: message space, ciphertext space, encryption, decryption. In particular, this abstraction allows to unify every scale-invariant FHE scheme, based not only on LWE, RingLWE, Module-LWE  [39] , but also on other problems like Approx-GCD or NTRU. Definition 3. 1 (Abstract TLWE problems). Let I be an ideal of Z[X], we call R = Z[X]/I and T I [X] = T[X]/I. A phase function is a Lipschitz morphism from a R-module M to T I [X].
Setting M = T n+1 and the phase as ϕ s (a, b) = b -sa, we retrieve the previous scale-invariant LWE. By choosing instead M = (Z/qZ) n+1 with phase ϕ s (a, b) = (b -sa)/q and discrete Gaussian error, we retrieve the well known LWE mod q. If we set M = T and take ϕ s (x) = p. x where p is a secret integer, then the TLWE problem consists in recognizing approximations of multiples of 1/p, so the TLWE abstraction can express cryptosystems based on the (dual) approx-GCD problem. Now, if we take a different ideal, for instance I = (X N + 1), then the canonical choice for a phase: ϕ s (a, b) = b -sa expresses RingLWE and Module-LWE  [39] , depending on the dimension of a. But again, other choices of phases are possible, for instance ϕ (f,g) : T N [X] 2 → T N [X] , (x, y) → f x -gy for small secret polynomials f, g, would allow to build FHE over scale invariant version of NTRU.
Definition 3. 2 can be viewed as the analogue of the General-LWE problem of  [12]  over the torus. It considers a continuum among anticyclic Module-LWE instances, between LWE (for N = 1) and RingLWE (for k = 1). However, we restrict the definition of canonical TLWE problem to only these particular cyclotomic instances, because they are the most efficient to implement with fast fourier transform. Also, the Gaussian error distribution can be sampled directly on the coefficients of the polynomials, rather than the general definition on the Lagrange basis. If for all secret s, the distributions U ker ϕs + ξ is concentrated, Regev's cryptosystem can be abstracted as follow: -The message space is the image T I [X] of ϕ s , -The ciphertext space is the domain M of ϕ s. -The encryption of µ is an approximation of a random preimage ϕ -1 s (µ).
This way, elementary additions or products can be performed simultaneously on N independent slots, and thus, packing is in general associated to the concept of batching a single operation on multiple datasets. These techniques can have some limitations, especially if in the whole program, each function is only run on a single dataset, and most of the slots are unused. This is particularly true in the context of GSW evaluations, where functions are split into many branching algorithms or automata, that are each executed only once. In the rest of the paper, packing refers to the canonical coefficients embedding function, that maps N TLWE messages µ 0 ,. , µ N -1 ∈ T into a single TRLWE message µ(X) = N -1 i=0 µ i X i. This function is a Z-module isomorphism. Messages can be homomorphically unpacked from any slot using the (noiseless) SampleExtract procedure, described in Section 4.
The final weight is the result of the multiplication. For the generic multiplication of two d-bits integers, we can upper bound the number of states by 4d 3 , instead of Θ(d 4 ) with one classical automata per output bit. Indeed, each column of the multiplication holds a partial sum that ranges between 0 and 2d. It takes less than d multiplications to update each column sum, so the WFA needs 2d 2 states per column, so 4d 3 states in total. For a more precise number of states we wrote a C++ program to eliminate unreachable states and refine the leading coefficient, but the average behaviour is still in O(d 3 ). The depth is 2d 2 and the noise evaluation can be easily deducted by previous results. The same principle can be used to construct the multiaddition, and its det-WFA is slightly simpler (one transition per bit in the sum instead of two).
Security analysis On the asymptotical side, TLWE samples can be equivalently rescaled and rounded to their closest binLWE representative, which in turn can be reduced to standard LWE with full secret using the modulus-dimension reduction  [13]  or group-switching techniques  [31]. Therefore, the semantic security of TFHE is asymptotically equivalent to worst case lattice problems. At the time of writing, there is still no reduction between the RingLWE and the binary-RingLWE instances. There is instead an asymptotic equivalence between ring  [51, 41]  and module LWE  [39]  problems for large modulus  [5]. In this section, we will rather focus on the practical hardness of TFHE, and express its effective security parameter λ directly as a function of the entropy of the secret n and the error standard deviation α.
Practical blockwise lattice reduction algorithms have an intrinsic quality δ > 1 (which depends on the blocksize and is usually called the root Hermite Factor ), and given a m-dimensional real basis B of volume V , they compute short vectors of norm δ m V 1/m. 3. Different approaches to evaluate the running time of BKZ-2. 0 have been proposed in the literature  [4, 17, 6, 7, 3]. In this section, we use the following estimation in seconds: log 2 (t BKZ )(δ) = 0. 009 log 2 (δ) 2 -27 according to the extrapolation by Albrecht et al  [3]  of Liu-Nguyen datasets  [40]. 4. The coordinates of vectors produced by lattice reduction algorithms are balanced. Namely, if the algorithm produces vectors of norm v 2 , each coefficient has a marginal Gaussian distribution of standard deviation v 2 / √ n. Provided that the geometry of the lattice is not too skewed in particular directions, this fact can sometimes be proved, especially if the reduction algorithm samples vectors with Gaussian distribution over the input lattice.
The same technique can be applied to the bootstrapping key, on which the size is only reduced by a factor k + 1 = 2. The source code of our implementation is available on github https:// github. com/tfhe/tfhe. We implemented the FHE scheme in C/C++, and run the bootstrapping algorithm on a 64-bit single core (i7-4910MQ) at 2. 90GHz. This seems to correspond to the machine used in  [29]. We measured a running time of 13ms per bootstrapping, and of 34µs per external product, both using the Lagrange half-complex representation. Profiling the execution shows that the FFTs and complex multiplications are taking 66% of the total time. The remaining time is mostly taken by the keyswitch operation, and the decomposition in base h. As a consequence, all binary gates are executed in 13ms, and the native bootstrapped MUX (also described in Section 6.
Circuit Bootstrapping Starting from all these considerations, we implemented our circuit bootstrapping as a proof of concept. The code is available in the experimental repository of TFHE  [25]. We perform a Circuit Bootstrapping in 0. 137 seconds. One of the main constraints to obtain this performance is to ensure that all the computations are feasible and correct under 53 bits of floating point precision, in order to use the fast FFT. This requires to refine the parameters of the scheme. We verified the accuracy of the FFT with a slower but exact Karatsuba implementation of the polynomial product. In our three levels, we used the following TRLWE and TRGSW parameter sets (Table  5 ), which have at least 152-bits of security, according to the security analysis from Section 7. Table  5. Parameters for levels 0, 1 and 2.
Acknowledgements This work has been supported in part by the  CRYPTOCOMP  project. The authors would like to thank the anonymous reviewers of this paper and of the papers [22] and [24], as well as the Asiacrypt 2016 committee for rewarding [22] with the best paper award and for the invitation to submit at Journal of Cryptology. The authors would also like to thank  Damien Stehlé ,  Fernando Virdia  and  Matthias Minihold  for the discussions and for their helpful comments.
| Environmental predictor variables Coordinates of each site were recorded in the field using handheld GPS devices (Supporting information Appendix S3, Table  S3. 1). We extracted data on all 19 bioclimatic variables for each site from the WorldClim database  (Hijmans, Cameron, Parra, Jones, & Jarvis, 2005). Since bioclimatic variables are often correlated, we performed a principal component analysis on the correlation matrix for temperature and precipitation variables separately (i. e. , temperature: BIO 1 -11; precipitation: BIO 12 -19). The first two principal components explained most of the variation in both datasets (temperature: 75%; precipitation: 91%; Supporting information Appendix S3, Table  S3. 2) and were subsequently used as a proxy for bioclimatic conditions at the sites. The first principal components represented a gradient in mean temperature or precipitation with high values indicating sites with overall high temperature or sums of precipitation, respectively.
The second principal components represented a gradient in seasonality with high values for sites displaying high temperature or precipitation seasonality, respectively. To obtain a proxy for landscape-scale habitat amount and anthropogenic pressure, we calculated the proportion of forest cover surrounding the sites for radii from 100 to 5,000 m (100-m steps). Forest cover within a radius of 700 m around sites had the highest independent effect on alpha diversity, and thus, this radius was chosen for further analyses (Supporting information Appendix S3, Figure  S3. 1). We used data based on Landsat satellite images from the database on Global Forest Change  (Hansen et al. , 2013) , which is available with a spatial resolution of approximately 25 metres per pixel, with values ranging from 0 to 100 per pixel encoding the proportion of canopy closure for all vegetation taller than 5 m in height.
| Statistical analyses All statistical analyses were carried out using R version 3. 3. 2 (R Core  Team, 2016). The main analyses included beetles identified taxonomically and all other arthropods identified by metabarcoding and were thus restricted to the 52 sites for which metabarcoding data were available. Additional analyses were conducted for beetle data from all 61 sites with beetle abundances (see Supporting information Appendices S4 and S5). To estimate the overall species pool, we calculated the Chao2 estimator, as implemented in the vegan package version 2. 4-3  (Oksanen et al. , 2018). The Chao2 estimate is a function of species occurring once or twice in the dataset and offers robust lower bound estimation for species richness based on incidences under the assumption that rare species have similar detection probabilities  (Chao, 1987).
Calculations were based on data for all species and separately for fungi specialists and each trophic guild (i. e. , consumer, predator and parasitoid) on the 52 sites. In addition, we used the rarefaction-extrapolation framework based on species incidences across all sites  (Chao et al. , 2014). We used Hill number of the orders 0 (species richness), 1 (the exponential of Shannon's entropy) and 2 (the inverse of Simpson's concentration) to analyse the diversity of rare and common species within one framework. We used 999 replicated bootstraps to calculate confidence intervals around the species-accumulation curves using the iNEXT package  (Hsieh, Ma, & Chao, 2016). Alpha diversity was calculated as the number of species per site. To estimate the relative importance of the predictor variables, we performed hierarchical partitioning-as implemented in the hier.
| RE SULTS In total, we identified 216 arthropod species emerging from fruitbodies of F. fomentarius from 52 sites. Species belonged to 13 orders, with highest species richness found in Diptera (n = 72) and Coleoptera (n = 71; Figure  2 ; Supporting information Appendix S2). The majority of taxa (n = 179) could be assigned to species by the taxonomist or by alignment of operational taxonomic units (OTUs; see Supporting information Appendix S1) with existing databases. The remaining 37 OTUs not assigned to a species were mostly members of the Cecidomyiidae (Diptera), for which barcodes were not available in the databases. We identified 74 species as fungi specialists. Concerning trophic guilds, we classified 131 species as consumers, 68 species as predators and 17 species as parasitoids. Genetic analysis of F.
6 and Table  S3. 7). Additionally, we found a significant increase in overall beta diversity as well as in dissimilarity due to turnover with increasing dissimilarity of sample size for predators. Our analyses for beetles from all 61 sites included abundance data for 123 species (Supporting information Appendix S5). Here, alpha diversity was strongly affected by sample size (Figure  5 ; Supporting information Appendix S4, Table  S4. 1). The number of beetle species increased with fungal sample size as the range in sample size was considerably higher across all 61 sites (Figure  5b ) than across the subset of 52 sites (Figure  5a ). Beetle community composition was F I G U R E 3 Rank-incidence plot of all 216 arthropod species reared from fruitbodies of Fomes fomentarius from 52 beechdominated forest sites across Europe F I G U R E 4 Relative contribution of predictor sets in explained deviance of alpha and beta diversity and its components turnover and nestedness.
Snow Spectral Albedo The spectral planar albedo products derived from OLCI scenes were compared to ground measurements of surface albedo. In a first step, the accuracy of the OLCI albedo product and its ability to capture the temporal evolution of the surface, and thus seasonal trends, was assessed using a dataset of sub-hourly observations of spectral surface albedo obtained at a fixed location at Dome C, Antarctica (75 • 06 00"S, 123 • 19 58"E, 3233 m elevation). Instrumentation details are provided below. In a second step, the evaluation of the OLCI spectral planar albedo retrievals at multiple locations spreading across the Antarctic plateau with varying snow surface properties was performed using portable spectral albedo measurements obtained along a 1371 km transect south of Dumont d'Urville (66 • 39 47"S, 140 • 00 10"E, 202 m).
Data Processing and Instrumentation An OLCI database was created for the different validation sites, applying the following steps. For each of the validation datasets, the OLCI L1c full-resolution products overlapping the location of the field measurements for the dates corresponding to the ground-based acquisitions were gathered. The Snow Properties Processor was run for all the remaining OLCI scenes, and the values for the pixels overlapping the field sites were extracted from the product. For all OLCI scenes, the SPP was run for the 21 OLCI bands, using band 21 (1020 nm) as the reference wavelength. In this study, the OLCI SVC gains (described in Section 3. 3, see Figure  7 ) were not applied. For the scenes in Antarctica, the SPP was run without applying the snow pollution algorithm, whereas for the Col du Lautaret scenes, the snow pollution algorithm was used.
For the validation purposes of this study, the datasets of the 2016-2017 and 2017-2018 summer seasons were used. The comparison between the ground observations and the satellite retrievals of spectral albedo was performed in several steps. Over the two summers, 1151 OLCI scenes were available at the Dome C location. For each scene, the closest Autosolexs albedo measurement in time was selected. To avoid a bias due to the albedo changing with the SZA and possibly changing snow physical properties, Sentinel-3 scenes more than 15 min apart from an Autosolexs measurement were automatically discarded. A second filter was applied to remove the measurements performed with a SZA larger than 75°, as it was shown in  [22]  that large SZA values introduce significant variations in the Autosolexs measurements.