dataesr/scientific-paragraphs-categorization huggingface dataset:
Derivative-free and blackbox optimization Since the 1990's, due to strong demand from industry, optimization methods with proofs of convergence have been developped to address problems involving objective and constraint functions given by costly simulations and/or without any gradient information available. Introductions to blackbox and derivative-free optimization algorithms are given in  [17, 18]. In this paper, we shall use the blackbox optimization software NOMAD  [19, 20]  to solve the machining time minimization problem. NOMAD is considered as the best performer for the type of problem we consider here  [21]. It is a C++ implementation of the MADS algorithm, an iterative method that proposes a new point where to evaluate the objective function (and the constraints) at the next iteration.
The line profiles were included as a source ⋆ Opacity tables are only available at the CDS via anonymous ftp to cdsarc. u-strasbg. fr (130. 79. 128. 5) ⋆⋆ This paper is dedicated to the memory of France  Allard, who initiated this work. of opacity in model atmospheres and synthetic spectra using the  Allard et al. (2001)  atmosphere program PHOENIX. The results were compared to previous models and demonstrated that these improvements are of fundamental importance for obtaining a better quantitative interpretation of the spectra. The far wings play a crucial role for the continuum generated far from the line center. It is then necessary to update all the opacity tables provided in the past for the alkali perturbed by helium and molecular hydrogen using the most recent existing ab initio potentials.
Absolute energies obtained by these two methods for the whole range of distances do not differ by more than 0. 001%, while complexation energies are essentially indistinguishable. Electronic energy grid points have been obtained for 220 internuclear distances, ranging from 0. 5 a 0 to 1000 a 0 , with a higher density at short range and around the potential well. We have paid particular attention to give a correct description at short bond lengths, as energies in this domain change very sharply, especially for the ground state, and line wing intensities are extremely dependent on them. On the other hand, the long range ab initio data are easily connected to a simple inverse even power expansion series form with a leading term in R -6 , expressing dispersion for a neutral-neutral interaction.
We review its key tools for facilitating QC computations (fermionic second quantization, fermion-spin transforms, etc. ). OpenVQE largely extends the QLM's QC capabilities by providing: (i) the functions to generate the different types of excitations beyond the commonly used UCCSD ansatz; (ii) a new Python implementation of the "adaptive derivative assembled pseudo-Trotter method" (ADAPT-VQE). Interoperability with other major quantum programming frameworks is ensured thanks to the myQLM-interop package, which allows users to build their own code and easily execute it on existing QPUs. The combined OpenVQE/myQLM-fermion libraries facilitate the implementation, testing and development of variational quantum algorithms, while offering access to large molecules as the noiseless Schrödinger-style dense simulator can reach up to 41 qubits for any circuit.
In this article, we provide a newly-designed software package named "OpenVQE" that extends the Atos Quantum Learning Machine (QLM). QLM is a quantum computing platform that allows to write hardware-agnostic quantum programs, compile them in compliance with hardware constraints, and either emulate them classically with realistic noise models or execute them on actual quantum hardware. QLM is a mix between commercial tools and noncommercial ones provided by the Atos company. OpenVQE is fully compatible with the freely available open source component of QLM called "myQLM," which is available online. 43 myQLM is a quantum software stack for writing, simulating, optimizing, and executing quantum programs. It provides, through a Python interface: (i) powerful semantics for manipulating quantum circuits, with support for universal as well as custom gate sets, abstract parameters, advanced linking options, and so forth; (ii) a versatile execution stack for running quantum jobs, including an easy handling of observables, special plugins for carrying out NISQ-oriented variational methods (such as VQE or QPE), and an easy application programming interface (API) for writing customized plugins (e.
g. , for compilation or error mitigation), as well as for connecting to any quantum processing unit (QPU); (iii) a seamless interface to available quantum processors and major quantum programming frameworks. 44 The capacity of QLM/myQLM to interoperate with other packages such as Qiskit,  45  Cirq  46  and PyQuil 47 allows researchers from different horizons to communicate, interact, exchange, and work more efficiently and faster. Furthermore, myQLM acts as a universal platform for users who want to access various quantum computers (IBM, Google, etc. ), providing them simple tools to run directly their jobs. myQLM comes with fermionic second quantization tools, which are helpful for solving quantum chemistry problems. These tools are now included in a new specialized open-source module dedicated to quantum chemistry called "myQLM-fermion.
| A quantum programming environment and a powerful simulator QLM is a complete environment designed for quantum software programmers, engineers and researchers. 82 4] [85] [86] [87]  These tools come in the form of so-called "plugins" that can be combined or stacked upon another to construct a quantum compilation chain. QLM can simulate quantum circuits in a noiseless or noisy fashion. The noiseless simulators come in different flavors, with "Schrödinger style" simulators (storing the wavefunction either in a dense fashion or using Matrix Product States  88  ), a "Feynman-style" simulator,  89  a binary decision diagram simulator,  90  a Clifford simulator, and so forth. The Schrödinger-style dense simulator can reach up to 41 qubits for any circuit, while the other simulators can reach much larger qubit counts depending on the circuit properties (entanglement, gateset, etc.
Such "variational plugins" handle the update of the variational parameters based on the result of the previous steps. They can optionally generate jobs to compute the gradient of a given expectation value if gradient-based optimization is asked for. In practice, the QLM environment is composed of software modules and a powerful classical HPC hardware appliance, as described in Figure  2. Among the software modules, some are available and downloadable for free as Python packages. They come under the name of myQLM. 43 myQLM includes modules for programming quantum circuits, with quantum libraries (for performing, e. g. , quantum arithmetic operations, etc. ), for describing quantum observables and analog quantum schedules. It also comes with a basic noiseless simulator for quantum circuits, basic plugins (e.
g. , for splitting observables depending on the commutation relations of the Pauli operators), and modules for interacting with other quantum frameworks like Qiskit, Cirq, and so forth. Finally, myQLM contains the aforementioned myQLM-fermion module. myQLM can be installed on a laptop or on a local cluster. The size of the circuits that can be simulated with the QPU simulator of myQLM is limited by the available Random Access Memory (RAM) (for a standard laptop, this corresponds to about 25 qubits). The quantum learning machine is also a powerful HPC appliance. It comes with extra software in addition to myQLM: advanced noiseless simulators, modules for describing hardware models, noisy simulators (both gatebased and analog), advanced compilers, tomography and error mitigation modules, among others.
| THE OpenVQE PACKAGE OpenVQE facilitates the development of new algorithms on quantum computers. It consists of a couple of new modules that extend the main myQLM/myQLM-fermion implementations (see Section 3). Those modules allow to build normal UCCSD algorithm, its variants and ADAPT-VQE algorithms as reviewed in Section 2. To explain in another fashion, OpenVQE allows to perform calculations using new types of UCC methods that are different from the QLM predefined ones such as the regular UCCSD ansatz. OpenVQE consists of two main modules that are inside the "openvqe" folder: • UCC Family denoted in the code by "ucc_family": this module includes different classes and functions to generate the fermionic cluster operators (fermionic pool) and the qubit pools, and to get the VQE optimized energies in the cases of active and non-active orbital selections.
• ADAPT denoted by "adapt": it includes two sub-modules: Fermionic-ADAPT: containing functions performing the fermionic-ADAPT-VQE algorithmic steps in the active and non-active space selections; Qubit-ADAPT: containing functions that perform the qubit-ADAPT-VQE algorithmic steps calculation in the active and non-active space orbital selections. Additionally, "openvqe" contains a subfolder named "common_files" that stores all the internal functions needed to be imported for executing the two modules. OpenVQE also contains a "notebooks" folder that allows the user to run and test the above two modules (which are theoretically described in the review Section 2). A brief sketch of the OpenVQE implementation is explained in the flow chart presented in Figure  3. We remind the reader that we will describe below the code of OpenVQE for the full space selections and some internal function examples such as those related to "gen-erator_excitations" and "fermionic_adapt_vqe.
| CONCLUSION AND FUTURE WORK In this article, we discussed in detail our newly introduced open source package, OpenVQE. OpenVQE allows one to perform quantum chemistry computations based on the quantum learning machine (QLM) thanks to the newly introduced myQLM-fermion open-source library that gather the key QLM resources that are important for quantum chemical developments. The OpenVQE/myQLM-fermion combined quantum libraries facilitate the implementation, testing and overall development of variational quantum algorithms dedicated to quantum chemistry problems and provide state-of-the-art quantum computing methods (see Table  3  which summarizes the GitHub links of the open-source quantum chemistry packages available to the community). We have shown that OpenVQE enables users to construct modules in a few lines of Python code using simple class structures related to the adaptive UCC family ansätze that we reviewed in the article.
Finally, for close binaries, measuring the precession rate also provides information on the stars' internal structure  (Claret & Gim énez 2010 ). In this paper, we first we describe a binaries-specific radial velocity model applied in the kima package in Section 2. This new model (which we will occasionally refer to as kima-binaries when comparing it with the old model) mo v es be yond fitting pure Keplerian orbits (as done in  Faria et al. 2018 ) , by including an apsidal precession parameter to the fitted model. The section details those changes and describes the inclusion of other tidal and relati vistic ef fects that are kno wn to af fect orbital solutions. In Section 3 , the new model is used on both simulated and observed data. The ability to accurately reco v er the apsidal precession rate is demonstrated, and we show how fitting for apsidal precession can impro v e a surv e y's sensitivity to circumbinary planets by producing Bayesian detection limits.
Adding in a double-lined binary model The vast majority of spectroscopic binaries are double-lined (e. g. Kov ale v a et al. 2016 ), and although the detection of circumbinary planets in double-lined system is problematic (as in  Konacki et al. 2009 Konacki et al. , 2010 ) ) , new methods to disentangle both spectral components accurately enough to detect circumbinary planets are being developed (e. g. Lalitha et al. in prep). To prepare for the time when circumbinary planets can be searched for, and be detected in double-lined binaries, we add a feature to kima to model such a configuration. As an input, the software requires files containing radial-velocities for each component of the binary. The sets of data are fit simultaneously, each with an independent γ parameter to account for differing zero-point calibrations.
C O N C L U S I O N S We have shown that fitting for the apsidal precession of a binary's orbital parameters impro v es the radial velocity sensitivity to circumbinary planets. Our conclusions are in line with previous work such as  Konacki et al. ( 2010 )  and  Sybilski et al. ( 2013 ) , but extend theirs to a fully Bayesian framework. The impro v ement in the detection limits can be of up to an order of magnitude in some configurations, but in most cases, impro v ements are expected to be marginal as in the case of Kepler-16. Accounting for precession can also give improvements in the precision of the parameters recovered from a fit, as well as the potential to unco v er planets that were hidden by precession (or instead require less data to detect the same planet). We hav e deriv ed a formula for calculating the theoretical precession induced in a binary (equation A11 ) and have discussed the potential use of a measurement of the apsidal precession rate as a way to constrain the mutual inclination of the planetary and binary orbital planes using this formula.
The theoretical and observed values of precession for Kepler-16 are in slight tension, this may be because of undetected planets or some other unknown mechanism. The longer the baseline of radial velocity observations, the more important it is to account for apsidal precession. As the field progresses, and the number of data from surv e ys like BEBOP increases, fitting the apsidal precession of the binaries will become vital. To prepare for that time, we have presented an updated version of the kima package which is more adapted to fitting radial velocities for single and double-lined binaries. The code is made public on github.
Experiments We built a prototype implementation of our algorithm in Scala, using the TTT automata learning algorithm  [30]  from the learnlib library  [31] , and the associated automatalib for manipulating finite automata. We used the TChecker  [29]  model checker for implementing membership and inclusion oracles. For the latter, we complement H into H c , and check the emptiness of the parallel composition of T with H c. We use the NuSMV model checker for finite-state model checking. The implementation is available at https://github. com/osankur/compRTMC. The overall input consists in an SMV file describing A, and of a TChecker timed automaton describing T. We use define expressions in SMV to define the labels Σ, while TChecker allows us to tag each transition with a label. We compare our algorithm on a set of benchmarks with the model checkers Uppaal  [8]  and nuXmv which has a timed automata model checker  [16].
Experiments Our tool accepts instances G T where G is given as a Verilog module, and T as a TChecker timed automaton. Some of the inputs of the Verilog module are uncontrollable (chosen by Environment), some others are controllable (chosen by Controller). We use outputs of the Verilog module to define the synchronization labels Σ; while TChecker models tag each transition with such a label. Membership, inclusion, and containment queries are answered by TChecker. For the synthesis oracle, we used the game solver Abssynthe  [12]. Abssynthe's input format is the and-inverter graphs format (AIG). For translating Verilog modules to AIG circuits, we use berkeley-abc and yosys. Abssynthe is able to compute the winning strategy S for the winning player; it also computes the system controlled by S in this case as an AIG circuit.
The strategy containment oracle is implemented using NuSMV; since H is deterministic, one can complement it, and check whether the intersection with (G H) S is empty. The tool uses two Java threads to implement both learning phases, which are interrupted and continued while switching phases. Note that the very first learning step of H and H can be parallelized since the first underapproximation conjecture H does not depend on S. We evaluate our algorithm with two classes of benchmarks. The only tool to which we compare is Uppaal-TIGA  [6]  since Synthia  [45]  is not available anymore, and we are not aware of any other timed game solver. In the scheduling benchmarks, there are two sporadic tasks that arrive nondeterministically, but constrained by the timed automaton. The controller must schedule these using two machines which have internal states, modeled either by a simple 8-bit counter, or by a genbuf circuit from the SYNTCOMP database.
Multivariate analysis is becoming central in studies investigating high-throughput molecular data, yet, some important features of these data are seldom explored. Here, we present MANOCCA (Multivariate Analysis of Conditional CovAriance), a powerful method to test for the effect of a predictor on the covariance matrix of a multivariate outcome. The proposed test is by construction orthogonal to tests based on the mean and variance, and is able to capture effects that are missed by both approaches. We first compare the performances of MANOCCA with existing correlation-based methods and show that MANOCCA is the only test correctly calibrated in simulation mimicking omics data. We then investigate the impact of reducing the dimensionality of the data using principal component analysis when the sample size is smaller than the number of pairwise covariance terms analysed.
We then describe the challenges faced when analysing highdimensional data, and present a robust solution based on principal components analysis. We next investigate the power of MANOCCA conditional on alternative parametrizations, providing guidelines for real data application across various settings. Finally, we illustrate the method by studying health, lifestyle and genetic factors associated with variability of blood biomarkers and flow cytometry-based immune phenotypes using data from 1,000 healthy subjects from the Milieu Intérieur cohort.
Power simulation To investigate power, we drew a series of 50 replicates with sample size of 1,000 including a binary exposure 𝑋 with frequency of 0. 5 and a multivariate outcome 𝐘 including 50 to 169 variables (Fig. 4 ). For each replicate, we used two covariance matrices, one for the exposed (𝐶 1 ), and the other for the unexposed (𝐶 2 ), and tested the association between 𝑋 and 𝐘 using MANOCCA. We generated the outcome from a multivariate normal and real covariance matrix (𝐶) derived from the Milieu Interieur flow cytometry data under three scenarios. In scenario (i), 𝐶 1 = 𝐶 and 𝐶 2 = |𝐶| 𝛾 × 𝑠𝑖𝑔𝑛(𝐶), inducing a covariance with similar pattern among exposed but variability in the magnitude of covariance. In scenario (ii), 𝐶 1 = 𝐶 and 𝐶 2 = 𝛿𝐶 + (1 -𝛿)Δ, where Δ is a random covariance generated using the R randcorr package  16  , thus inducing random noise between exposed and unexposed.
Efficient implementation The MANOCCA approach requires multiple steps that can be computationally expensive in largescale data. The main limiting step is the computation of the product matrix followed by the PCA transformation, but it is a one-time cost regardless of the number of predictors tested. With 𝑁 the sample size, 𝑘 the number of outcomes and 𝑞 the number of predictors to test, the computation time is divided in 𝑂(𝑁𝑘 2 ) for the computation of the product matrix, 𝑂(𝑚𝑎𝑥(𝑁, 𝑘 2 ) 2 * 𝑚𝑖𝑛(𝑁, 𝑘 2 )) for the computation of the PCA, and 𝑂(𝑁𝑞) for the test of 𝑞 predictors (Fig. 5 ). Most steps were implemented with limited usage to exterior libraries, but ground proofed against multiple existing tools. The approach is implemented in a Python package with dependencies to numpy, scipy for the fisher distribution, scikit-learn for the PCA and pandas for dataframe integration, but all computations are performed under numpy array to increase performance.
Application to Milieu Intérieur omics data We applied MANOCCA in 1,000 healthy individuals from the Milieu Intérieur (MI) cohort to screen for factors associated with changes in the covariance of 33 blood biomarkers and 169 flow cytometrybased immune phenotypes (Table  S1 -3). Both datasets display high correlation, ranging from -0. 71 to 0. 99 for the flow cytometry data, and from 0. 08 to 0. 98 for the biomarkers (Fig. S6 ). We first investigated the effect of 49 health-related and lifestyle factors using a subset of 992 participants with complete data. We applied the proposed PCA reduction, and investigated power when using 5 to 200 top PCs with a step of 5, resulting in 40 tests per variable. As showed in Figure  6a -b, multiple features were associated at a stringent Bonferroni corrected significance level (P < 2.
5 x 10 -5 accounting for 1,960 tests). Flow cytometry-based phenotypic covariance was associated with age (P < 6. 0 x 10 -9 ) and all smoking variables: smoking status (P < 2. 1 x 10 -12 ), smoking frequency (P < 1. 2 x 10 -11 ), number of years smoked (P < 3. 8 x 10 -10 ), number of years since last smoke (P < 7. 5 x 10 -9 ). Likewise, blood biomarkers covariance was strongly associated with age (P < 3. 5 x 10 -33 ) and sex (P < 1. 3 x 10 -30 ), and to a lesser extent with BMI (P < 1. 6 x 10 -7 ) and smoking variables (minimum P < 5. 5 x 10 -12 , for smoking status). Except for the age-flow cytometry association, the maximum association signal was almost reached when including the top 50 PCs and display only modest improvement when including more PCs (Fig. 6 ). Thanks to a limited number of outcomes, the blood biomarker dataset could also be analysed by applying MANOCCA directly on the 528 pair-wise products.
To investigate the value of using the PCA in such situations, we applied MANOCCA on the product and compared results against the PCA-based approach. Note that the product-based test should be approximately equivalent to the test of all PCs, which was confirmed for these data (Fig. S7 ). Comparing the minimum P-value across the 40 PCAbased test (𝑃 𝑃𝐶𝐴 ) against the P-value from product-based test (𝑃 𝑝𝑟𝑜𝑑 ), we observed a substantial gain for the PCA-based approach, even when accounting for the multiple testing cost of the PCA approach. The product-based test identified only five of the seven signals from the PCA-based approach (Fig. 7 ). For the strongest signals, the association P-value from the best PCA-based test was several orders of magnitude larger than for the product-based test (e. g.
, for age, P= 3. 5 x 10 -33 and 2. 6 x 10 -11 , respectively). This suggests that the benefit of testing multiple sets of PCs can strongly outpace the statistical cost of multiple testing. When comparing the MANOCCA results to a standard MANOVA applied to both datasets, MANOVA identified significant associations (P < 1. 0 x 10 -3 to account for the 49 tests conducted) with 8 and 13 predictors associated in the flow cytometry data and the blood biomarkers data, respectively (Table  S4 ). These associations included all associations detected by MANOCCA. More generally, while the two tests are expected to be independent, we observed a strong correlation between association signal as measured by the -log10(P-value) (𝜌 𝑏𝑖𝑜𝑚𝑎𝑟𝑘𝑒𝑟𝑠 = 0. 88, 𝜌 𝑐𝑦𝑡𝑜𝑚𝑒𝑡𝑟𝑦 = 0. 65), suggesting that many of the predictors are associated with effects on both the mean and variance of the outcome studied (Fig.
S8 ). However, several predictors display discordant associations, with a significant effect on the mean but no effect on the covariance. This includes, for example, systolic blood pressure (𝑃 𝑀𝑎𝑛𝑜𝑣𝑎 = 2. 6 x 10 -11 , 𝑃 𝑀𝐴𝑁𝑂𝐶𝐶𝐴 = 0. 14), and heart rate (𝑃 𝑀𝑎𝑛𝑜𝑣𝑎 = 4. 9 x 10 -24 , 𝑃 𝑀𝐴𝑁𝑂𝐶𝐶𝐴 = 0. 001) effect on blood biomarkers. On the other hand, one predictor, the number of years of second-hand smoking, display suggestive significance with MANOCCA on the flow cytometry data, but did not display mean effect (𝑃 𝑀𝑎𝑛𝑜𝑣𝑎 = 0. 31, 𝑃 𝑀𝐴𝑁𝑂𝐶𝐶𝐴 = 3. 0 x 10 -5 ). Finally, we conducted genome-wide association studies (GWAS) for both blood biomarkers and flow cytometry datasets, testing 5,699,237 genetic variants with a minor allele frequency (MAF) > 5% in up to 894 samples where both genetic and phenotypic data were available.