dataesr/scientific-paragraphs-categorization huggingface dataset:
An eigenvalue problem We end up this section by showing an example of a 3D problem, namely, the computation of the first eigenvalues/eigenvectors of the Laplace operator in the parallelepipedic volume [0, 1]×[0, 1  2 ]×[0, 1  2 ], with Dirichlet boundary conditions. Mathematically speaking the problem writes as finding couples (λ, u) that are solutions to the eigenvalue problem -∆u = λu on Ω , u = 0 on ∂Ω , (3) where Ω = [0, 1] × [0, 1  2 ] × [0, 1  2 ]. Now the problem is posed in 3D, and we need to force (homogeneous) Dirichlet boundary conditions. The corresponding Matlab listing becomes % C r e a t e mesh o f t h e cube + boundary N = 1 e4 ; mesh = mshCube (N, [ 1 0. 5 0. 5 ] ) ; meshb = mesh. bnd ; % I n t e g r a t i o n domains Omega = dom( mesh , 4 ) ; % F i n i t e e l e m e n t s p a c e Vh = fem ( mesh , ' P1 ' ) ; Vh = d i r i c h l e t (Vh , meshb ) ; % Matrix and RHS K = i n t e g r a l ( Omega , grad (Vh) , grad (Vh) ) ; M = i n t e g r a l (Omega , Vh , Vh) ; % R e s o l u t i o n Neig = 1 0 ; [ V,EV] = e i g s (K,M, Neig , 'SM ' ) ; Notice the enforcement of Dirichlet boundary conditions on the finite element space (line 9), the assembling of the rigidity and mass matrices (lines 11-12).
Finite element programming in Matlab Programming the finite element method in Matlab is very attractive and has already been considered by many people (see for instance  [1, 16, 25, 7, 10, 5, 23] ), probably because the language is easy to use and already contains the most recent linear solvers. It is important to notice that Matlab is usually very powerful when one uses its vectorial capabilities. Therefore, the traditional assembling of the matrices that come from finite element discretizations, which uses a loop over the elements with indirect addressing, might lead to prohibitive execution times. This problem was identified a long time ago and several ways have already been proposed to circumvent it. In particular, we refer the interested reader to  [10] , where different alternatives that lead to very efficient assembling are given and compared.
Many languages are also compared (C++, Matlab, Python, FreeFem++), and it is shown that the C++ implementation only brings a slight improvement in performance. Other Matlab implementations are proposed in the literature (see e. g. [1, 25, 7, 5, 23] ), but they all suffer from the lack of generality. The problem solved is indeed very often the Laplacian with piecewise linear finite elements and one needs to adapt the approach for any different problem. We have followed yet another strategy that has the great advantage to be very general and easily adaptable to a wide variety of possible operators to build and solve, and which also enables the user to assemble matrices that come from the coupling between different finite elements. Moreover, we will see that the method also leads to reasonably good assembling times.
Notice that the approximation is coming from the fact that a quadrature rule has been used instead of an exact formula. In particular, we emphasize that if the quadrature formula is exact in  (5) , then the approximation (  7 ) is in fact an equality. From the preceding considerations the procedure that enables to assemble the sparse mass matrix can be summarized as: • Knowing the triangulation (resp. tetrahedral mesh), and a quadrature formula on a reference triangle (resp. tetrahedron), build the set of quadrature points/weights (x k , ω k ) 1≤k≤M. (This is done in the package open-DOM. ) • Knowing the finite element used (or, equivalently, the basis functions (φ j ) 1≤j≤N ) and the quadrature points (x k ) 1≤k≤M , build the matrices W and B. (This is done in the package openFEM. ) • Eventually, compute A = B t W B.
The domain The domain is a geometric object on which one can furthermore integrate. Numerically speaking, this is the concatenation of a mesh and a quadrature formula. This formula is identified by a number, that one uses with the simplices of the corresponding mesh, in order to integrate functions. The default choice is a quadrature formula with only one integration point located at the center of mass of the simplices. This is usually very inaccurate, and it is almost always mandatory to enhance the integration by taking a higher degree quadrature formula. A domain is defined using the dom keyword. For instance, the command 1 Omega = dom ( myMesh ,4) ; defines an integration domain Omega from the mesh myMesh, using an integration formula with 4 integration points. If such an integration formula is not available, the program returns an error.
Both cases are respectively (and similarly) handled by the two following commands. 1 B = integral ( Sigma1 , y_j , Phi , G ) ; 2 C = integral ( x_i , Sigma2 ,G , Psi ) ; In all the preceding commands, G should be a Matlab function that takes as input a couple of 3 dimensional variables X and Y of respective sizes N X × 3 and N Y × 3. It should also be defined in order to possibly handle sets of such points in a vectorized way. As a sake of example, G(x, y) = exp(ix • y) can simply be declared as 1 G = @( X , Y ) exp (1 i * X *Y ') ; where it is expected that both X and Y are matrices that contain 3 columns (and a number of lines equal to the number of points x and y respectively).
Namely, for a given tolerance tol, the commands A = integral ( Sigma1 , Sigma2 , Phi ,G , Psi , tol ) ; B = integral ( Sigma1 , y_j , Phi ,G , tol ) ; C = integral ( x_i , Sigma2 ,G , Psi , tol ) ; return the same matrices as before, but now stored in a hierarchical H-matrix format, and approximated to the desired tolerance. In particular, this enables the user to use the +, -, * , \, lu or spy commands as if they were classical Matlab matrix objects. These generalizations, together with the possibility of directly assemble Hmatrices using the same kind of syntax, seem to us one of the cornerstones of the Gypsilab package. To our knowledge, there is, at the moment, no comparable software package which handles BEM or compressed BEM matrices defined in a way as general and simple as here.
Acoustic scattering As a matter of example, we provide hereafter the resolution of the acoustic scattering of a sound soft sphere and the corresponding program in Gypsilab. For this test case, one considers a sphere of unit radius S 2 , and an incident acoustic wave given by p inc (x) = exp(ikx • d) ( 15 ) where k is the current wave number and d is the direction of propagation of the wave. It is well-known that the total pressure p tot outside the sphere is given by p tot = p inc + p sca where the scattered pressure wave obeys the formula p sca (x) = S 2 G(x, y)λ(y) dσ(y). The preceding program follows the traditional steps for solving the problem. Namely, one recognizes the spherical mesh and domain (lines 11-12), the radiative mesh on which we want to compute and plot the solution, here a square (lines 14-15), the incident plane wave (line 21), the Green kernel definition (line 23), the finite element space (line 25), the assembling of the operator (line 27-28), the construction of the right-hand side (line 30), and the resolution of the problem (line 32).
The rest of the program consists in computing from the solution λ of (  17 ), the total pressure on the radiative mesh, and plot it on the square mesh. Notice that due to the presence of the tol parameter in the assembling of the operator (and also of the radiative operator), the corresponding matrices are stored as H-matrices. Notice also that the key part of the method (assembling and resolution) are completely contained between lines 21-32. The figures of the total pressure are given in Fig. 3  for the two cases N = 10 4 and N = 9 • 10 4. The H-matrix produced in the former case is shown in Fig. 4. Figure  3 : Magnitude of the pressure produced in the acoustic scattering by a unit sphere of a plane wave coming from above, using Gypsilab. On the left, the sphere is discretized with 10 4 vertices and the frequency is 10 3 Hz.
Performances 6. 1 Performances in FEM In this section we compare Gypsilab with FreeFem++. The machine that we have used for this comparison is equipped with Xeon E5-2643-V1 processors with a frequency of 3. 3 GHz and 128 GB of memory. Although the machine possesses two such processors, meaning that up to 8 cores could be used for the computation, we only chose a single core to run the test, both for FreeFem++ and Matlab which is therefore launched using the -singleCompThread option. For the test, we have used FreeFem++ version 3. 61 and Matlab R2018a. We have chosen to solve the Dirichlet problem -∆u = 1 in Ω , u = 0 on ∂Ω , (19) where Ω = (0, 1) 3 is the unit cube of R 3 meshed regularly, with (N + 1) 3 points and N ranges from 20 up to 100 depending on the case. Both linear P 1 and quadratic P 2 elements are considered.
Conclusion The package Gypsilab is a numerical library written in full Matlab that allows the user to solve PDE using the finite element technique. Very much inspired by the FreeFem++ formalism, the package contains classical FEM and BEM functionalities. In this latter case, the library allows the user to store the op-erators in a H-matrix format that makes it possible to factorize the underlying matrix and solve using a direct method the linear system. We are not aware of any comparable software package that combines ease of use, generality and performances to the level reached by Gypsilab. We have shown illustrative examples in several problems ranging from classical academic Laplace problems to the Combined Field Integral Equation in electromagnetism. Eventually, a short performance analysis shows that the library possesses enough performance to run problems with a number of unknowns of the order of a million in reasonable times.
Weak-constraint assimilation We present in this Section the results of experiments that have been performed in the 'weak-constraint' case when the deterministic model I-6 is no longer considered as being exact. Following a standard 165 approach, we now assume that the truth is governed by the equation x k+1 = M(x k ) + b k , (1) where b k is a white-in-time stochastic noise with probability distribution N (0, Q k ) at time k. A typical experiment is as follows. A reference 'truth' x r k , k = 0, • • • , K is created using (1) for a particular realization of the noise b k. Noisy observations y k are extracted from that reference truth 170 in the same way as in Part I (Eq. I-7). The data to be used in order to reconstruct the whole sequence of states x r k now consist of the observations y k and of the a priori estimates w k = E(b k ) = 0 of the noise b k.
However, in the weak-constraint case, QSVA has not been necessary, providing new evidence as to the favourable effect, on numerical efficiency of assimilation, of introducing a weak constraint. At the same time, the comparison of the results shown in the right bottom panels of Figures  3  and 5 , shows that EnsVAR, even when it has as high a degree of reliability as in purely linear and Gaussian situations, is not Bayesian. Comparison with two other standard ensemble assimilation filters, namely Ensemble Kalman Filter and Particle Filter, made at constant ensemble size, shows a superior or equal performance for EnsVAR, at least as concerns the dispersion of the ensembles. If a code for variational assimilation is available, EnsVAR is very easy (if costly) to implement. It possesses the advantages and disadvantages of standard variational assimilation.
Advantages are easy propagation of information both forward and backward in time (smoothing) and easy introduction of observations of new types and of temporal correlations between data errors. What is usually considered to be a major disadvantage of variational assimilation is the need for developing and 9 Nonlin. Processes Geophys. Discuss. , https://doi. org/10. 5194/npg-2018-6 Manuscript under review for journal Nonlin. Processes Geophys. Discussion started: 24 January 2018 c Author(s) 2018. CC BY 4. 0 License. maintaining an adjoint code. Concerning that point, it must however be stressed that algorithms are being developed which might avoid the need for adjoints while keeping most of the advantages of variational assimilation. EnsVAR, as it has been implemented here, is very costly in that it requires a very large number of 305 iterative minimizations.
Experiments are carried out on a home made chimeric (own made) benchmark dataset with 34 users (fingerprint and biometric pattern) and show the benefit of the proposed solution face to the literature. This paper is organized as follows. Section 2 provides a literature review on existing solutions for user authentication on smartphone. The proposed method is described in Section 3. We present its general principle of user, the concept of feature transformation template protection schemes and the Biohashing algorithm. The computation of biometric features from pattern drawing is also described. Section 4 illustrates through experimental results the benefit of the proposed solution. Finally, we conclude and give some perspectives in Section 5.
BioHashing A feature transformation is a function F using a key K (that is typically a random seed or a password), applied to a biometric template T. The transformed template F K (T ) is stored in a database or in a personal   device. The Biohashing algorithm, described below, belongs to this class of transformation. During the authentication step, the same transformation is applied to the query template T with the same key K and a comparison is realized between F K (T ) and F K (T ). It is generally considered that, given the transformed template F K (T ) and the key K, it is not possible to recover the original template T (or a close approximation) as presented in  (Nagar et al. , 2010)  (mainly because the transformation is not invertible). The key constitutes an important secret. The performance of the authentication system is generally estimated with FMR (False Match Rate computing the ratio of false positive verification) FNMR (False Non Match Rate calculating the ratio of false negative verification) rates and the feature transformation should not decline the performance of the system.
At the end of the enrollement phase, the biometric raw data is discarded and the BioCode (with the associated seed) is stored. The biohashing algorithm can be applied on any biometric modalities, that can be represented by a real values vector of fixed length. The Biohashing algorithm transforms the biometric template T = (T 1 ,. T n ) in a binary template B = (B 1 ,. B m ), with m ≤ n, as follows: 1. m pseudorandom orthonormal vectors V 1 ,. ,V m of length n are generated from the random seed K typically with the Gram Schmidt algorithm. 2. For i = 1,. , m, compute the scalar product x i =< T,V i >. 3. Compute the binary template B = (B 1 ,. , B m ) with the quantization process: B i = 0 if x i < τ 1 if x i ≥ τ, where τ is a given threshold, generally equal to 0. The performance of this algorithm is ensured by the scalar products with the orthonormal vectors, as detailed in  (Teoh et al.
Implementation The traditional approach to Android development is to use the native SDK published by Google. If this is an efficient approach at first sight, it does not allow further reuse for a different mobile platform from Android because the code is tightly connected to this SDK. As we may want to be able to later evaluate the authentication performance on any platforms the proposed application is developed using Xamarin framework. Android touch screen raises touch events every 10 to 30ms based on the gestures. Each event defines raw values such as horizontal X and vertical Y coordinates, pressure and size of the touch on the screen, an orientation indicator dedicated to stylus use and a time stamp. These values highly depend on mobile model used during the acquisition process: • (X,Y ) position depend on screen resolution when the velocity vector (X ,Y ) also depend on screen size.
Protocol In this work, we first used a biometric dataset of data captured when users draw a single pattern: • Data have been collected on a Nexus 4 mobile phone with a touch screen having a resolution of 800 x 1280 pixels, • The pattern was the same for all users and is defined by the following pattern code "1235987". This experimental setup can be considered as the worst case where an attacker knows the pattern to draw. 34 users participated to this experiment, • Each user provided 15 samples described by 4 signals undersampled to 200 values (time normalization). Four more signals have been computed by cnsidering the first and second derivative of X and Y signals. We also added the total time to draw the secret path as additional parameter. Figure  4  presents the data of the first sample for user 1.
The x-axis corresponds to the time and the y-axis to feature value. So, the template size is 1601 (by concatenating all undersampled signals) and the single time value, In total, we have a subset of 34 × 15 = 510 biometric templates of size 1601 real values for biometric pattern. Considering the BioHashing setup, we set the parameter values as following: • Template size: n=1601, • BioCode size: m=750 for the Reference BioCode and Capture BioCode, • As the pattern is the same for all users, in the computation of the Reference BioCode, the secret K for all users is randomly drawn, • Matching algorithm: Hamming distance. Concerning fingerprint, we extract a subset of well known datasets namely FVC2002 DB2, FVC2004 DB1 and FVC2004DB3  (FVC, 2002). We can see that fingerprints are quite different and representative of the different types of fingerprint (acquired with sensors using different technologies).
These datasets have fingerprints from 100 individuals with 8 samples per individual. In order to constitute a chimeric multi-biometric dataset (synthetic database), we took into account the fingerprints from the 34 first individuals. For each FVC dataset, we use so 34 × 8 = 272 fingerprint samples. In order to evaluate the performance of the proposed method, we use the following methodology: • We use the first sample of each user as reference template, for the biometric pattern, we use this data to compute the Reference BioCode, • As we do not have access to the fingerprint sensor hardware (i. e. the value of the matching score) on a mobile phone, we simulate the result of the matching score by considering the Bozorth3 algorithm provided by the NIST. This algorithm does not provide as good results as commercial on card comparison (OCC) algorithms, it can be considered as an estimate of the worst performance, • We compute genuine scores as follows.
We consider all reference fingerprints and we compare them with each available samples belonging to the same individual. We consider two times these scores because biometric pattern has 14 samples. For biometric pattern, we compare the Reference Biocode with all other BioCodes from the same individuals. We obtain 14 × 34 = 476 fingerprint and biometric pattern genuine scores for each FVC dataset. • We have a similar process to simulate impostor attack by considering all biometric samples belonging to another user. We obtain 14 × 34 × 33 = 15708 fingerprint and biometric pattern impostor scores for each FVC dataset, • Given these two sets of scores, we can compute their distribution in order to estimate in which measure impostor scores are different than legitimate ones. Second, we compute the Equal Error Rate (EER) value that is a well known metric in biometrics that measures the behavior of the biometric system when the decision threshold is set to have the same number of false rejected users and false accepted ones.
The worst case scenario (the secret is known by the impostor) with a performance similar to raw features performance. This error could be considered as too high but without using the biometric pattern, impostors would be able to enter the system knowing the pattern (used as password). We limit this attack by considering biometric features. Figure  5  provides the score distribu-   (Stokkenes et al. , 2016)  eyes and face yes -best case 1. 8%  (Galdi et al. , 2016)  iris and sensor fingerprinting no 0. 05% Contribution fingerprint and biometric pattern yes -best case 0% Contribution fingerprint and biometric pattern yes -worst case 2. 3% Figure  5 : Distribution of scores for the multi-biometric system while using a fingerprint database. tion by combining the fingerprint and biometric secret path in the best case scenario (where the secret used in the BioHashing algorithm is unknown by impostors).
We obtain for each a perfect recognition for all fingerprint databases. This is of course an excellent result and improves results given by applying only the fingerprint system. Now, we have to consider the worst case scenario when the impostor obtained the secret K associated to the BioHashing algorithm. We assume here the threshold set for the fingerprint system is the one associated to the EER value (it could be more strict). As for example, for the FVC2004DB1, we obtain a FAR equals to 8%. We assume to set the threshold value for the biometric secret path following the same approach at the EER value. We computed the FAR in the worst case scenario and it is 28. 7%. That means if the impostor knows the secret, he has 28. 7% chances to break the system. By considering the multi-biometric system, he has 8% chances to break the fingerprint system (on FVC2004DB1) and 28.
7% to break the secret path one. As these events are independent, we can estimate the FAR of the multi-biometric system by using fingerprints from FVC2004DB1 to 8%×28. 7% = 2. 3%. For all fingerprint datasets, the FAR is between 1. 5% to 2. 3% for the multi-biometric system if the impostor knows the secret K associated to the BioHashing algorithm. Once again, this is an upper bound estimate of the proposed method as the performance of the fingerprint comparison would be much better. Nevertheless, we can consider this result as very low considering all the information needed by the impostor.
CONCLUSION AND PERSPECTIVES In this paper, we propose a multi-biometric system for mobile devices by combining the fingerprint recognition using its embedded sensor and a behavioral biometric system. The proposed system is very fast (a few seconds for the capture and about 200 miliseconds for comparison) and practical for users as all these verification systems are commonly used. The combination of fingerprint recognition and biometric pattern allows to limit the possible attack and increase the security of user authentication. The privacy protection of biometric templates is ensured by using at the same time a secure element and template protection schemes. In the best case, we obtain a perfect recognition on our own made database and a FAR lower than 2. 3% in the worst case (the impostor needs the mobile devices, knows the secret path and the secret key K associated to the BioHashing algorithm).
In addition, the researcher must define the rate of temperature data recordings during the period when the data logger will be used. In some cases, data loggers may have high resolution but low accuracy, or limited flexibility in the rate of data collection. Ordering a set of data loggers can be a Cornelian dilemma: should the priority be optimization of accuracy, of resolution, or the sampling rate? An important first step is to clearly conceptualize the difference between resolution and accuracy. Resolution refers to the level of specificity that the data logger will record temperature in its memory. For example, a resolution of 0. 5°C indicates that temperatures will be recorded by bins of 0. 5°C, even if the electronic chips can read internally the temperature with better resolution. The number of possible temperature records that can be stored during a session is positively related to the available memory but negatively related to the resolution and the range of temperatures that can be recorded.