dataesr/scientific-paragraphs-categorization huggingface dataset:
Conclusion and perspectives FIFRELIN is a Monte Carlo code which fully describes fission fragment characteristics. It involves different models to simulate a fission de-excitation and the entry zone given by the fission process. Both experimental and calculated data are used. Impact of input parameters on fission observables were highlighted. It gives insight on the current limits of the code. New development are under progress in order to better control the sensitivy on the input parameters and improve the prediction power of FIFRELIN.
We demonstrated the accuracy of our algorithm to detect the SPT-window. The value of this algorithm lies in studies such as UK Biobank where a sleep diary was not used. Wrist-worn raw-data accelerometers are increasingly used for the assessment of physical activity in large population studies such as the Whitehall II study or mega-cohorts such as UK Biobank 1-3. The decision to use raw-data accelerometers is motivated by the improved comparability of output across different sensor brands 4,5 , and better control over all steps in data processing 6. Accelerometers are commonly worn for 24 hours per day, thus providing information over the day and night; making them potentially valuable for sleep research. A major challenge in accelerometer-based sleep measurement is to derive sleep parameters without additional information from sleep diaries  1, 3, 7.
Methods Study population. In order to assess the validity of our algorithm in different settings and against both data from sleep diary and polysomnography, data are drawn from three different study populations described below. The Whitehall II cohort study  12  : full details on data collection were previously described  11. Briefly, accelerometer measurement was added to the study at the 2012/2013 wave of data collection for participants seen at the central London clinic and for those living in the South-Eastern regions of England who underwent a clinical evaluation at home  2. Of the 4879 participants to whom the accelerometer was proposed in the Whitehall II Study, 388 did not consent and 210 had contraindications (allergies to plastic or metal, travelling abroad the following week). Of the remaining 4281 participants who wore the accelerometer, 4204 (98.
All 28 patients recruited for the polysomnography study (11 female) had complete accelerometer data for the left wrist and 27 had complete data for the right wrist and were aged between 21 and 72 years (mean ± sd: 45 ± 15 years). Diagnosed sleep disorders included: hypersomnia (N = 2), insomnia (N = 2), REM behaviour disorder (N = 3), sleep apnoea (N = 5), narcolepsy (N = 1), sleep apnoea (N = 4), parasomnia (N = 1), restless leg syndrome (N = 5), and sleep paralysis (N = 1), and nocturnia (N = 1). Three patients had more than one sleep disorder. Healthy good sleepers: these data come from 22 adults who underwent a one-night PSG assessment at the University of Pennsylvania Center for Sleep. Twenty-two participants recruited for the polysomnography study (68% female) had complete accelerometer data for the non-dominant wrist and were aged between 18 and 35 years (mean ± sd: 22.
Instrumentation. Participants in the Whitehall II Study were asked to wear a tri-axial accelerometer (GENEActiv, Activinsights Ltd, Kimbolton, UK) on their non-dominant wrist for nine (24-h) consecutive days. They were asked to complete a simple sleep diary every morning which consisted of two questions: 'what time did you first fall asleep last night?' and 'what time did you wake up today (eyes open, ready to get up)?' The accelerometer was configured to collect data at 85. 70 Hz with a ±8 g dynamic range. A more complete description of the accelerometer protocol can be found in our earlier publication  2. In the second and third study, polysomnography (Embletta ® , Denver) was performed using a standard pro- cedure, including video recording, a sleep electroencephalogram (leads C4-A1 and C3-A2), bilateral eye movements, submental EMG, and bilateral anterior tibialis EMG to record leg movements during sleep.
Respiratory movements were detected with chest and abdominal bands measuring inductance, airflow was detected with nasal cannulae measuring pressure, and oxygen saturation of arterial blood was measured. Airflow limitation and changes in respiratory movement were used to detect increased upper-airway resistance. All respiratory events and sleep stages were scored according to standard criteria so that EEG determined total sleep time could be measured  9. Participants in the second study (PSG in sleep clinic) were asked to wear the same brand of accelerometer as in the first study (GENEActiv, Activinsights Ltd, Kimbolton, UK) on both wrists throughout the one-night polysomnography assessment. Here, the accelerometer was also configured to record at 85. 70 Hz. Accelerometer data were collected on both wrist to assess the role of sensor location on classification performance, unfortunately no information on handedness was recorded.
Accelerometer data preparation. A previously published method was used to minimize sensor calibration error  13  and to detect and impute accelerometer non-wear periods  2, 14. Arm angle was estimated as follows: π =        +        ⋅ - angle tan a a a 180/ , z z x y 1 2 2 where a x , a y , and a z are the median values of the three orthogonally positioned raw acceleration sensors in gravitational (g) units (1 g = 1000 mg) derived based on a rolling five second time window. Here, the z-axis corresponds to the axis positioned perpendicular to the skin surface (dorsal-ventral direction when the wrist is in the anatomical position). Next, estimated arm angles were averaged per 5 second epoch and used as input for our algorithms for detecting sleep period time (SPT-window) and sleep episodes.
Heuristic algorithm to detect the SPT-window. There are several challenges in the development of an algorithm to detect the SPT-window: absence of hard data labels to train a classifier under daily life conditions (not in a clinic), consideration of daily life behaviour, e. g. how to handle sleep scattered across the full 24-hour day and ensure that the algorithm is not over fitted to a specific population or accelerometer brand. Thus an algorithm was developed by visually inspecting twenty random accelerometer multi-day recordings from different studies and accelerometer brands (ten from the Whitehall II Study as reported in this paper and ten from UK Biobank study 1 ) while iteratively enhancing the algorithm to best detect the visible data segment of no movement without using or looking at sleep diary data.
These differences presumably reflect the degree of sedentary lifestyle and amount of sleep in a day. Using a percentile as part of the threshold calculation allows the threshold to account for between-individual differences in z-angle distribution. The factor 15 in step 6 of the algorithm was derived iteratively using visual inspection of the classification. The 30-minute time period is motivated by the assumption that people are typically not in bed for less than 30 minutes for their nocturnal time in bed, as opposed to daytime napping, and the 60-minute time period is motivated by the assumption that sleep separated by awake periods greater than 60 minutes ought to be treated as two distinct sleep episodes to avoid adding early evening naps or afternoon naps to the SPT-window. A sensitivity analysis on HDCZA parameter settings and their influence on algorithm performance across the datasets can be found in Supplementary information (page 81).
Statistical analysis. Comparison with sleep diary. The SPT-window derived from both the HDCZA and L5 ± 6 were compared separately with sleep diary records with a multi-level regression to account for the variation in availability of night time data and to include both night and person level predictors. For SPT-window duration (difference between sleep onset and waking time), sleep onset and waking time, the difference between diary and accelerometer-based detection was used as the dependent variable, while population demographics (sex, age, BMI), season (winter or summer) and weekend versus weekday were used as predictors. Here, we used function lme from R package nlme. Further, correlation coefficients with diary values and mean absolute error (MAE) for sleep onset, waking time, and SPT-window duration were calculated.
Additionally, the algorithm's threshold that scales with the variance in the data was constrained to a range corresponding to the 2. 5 th and 97. 5 th percentile of the distribution of the threshold value observed in a sample of daily life accelerometer recordings, 0. 13 and 0. 50, respectively. This was done because the in-clinic PSG does not provide a full 24-hour cycle of body movement to derive this threshold. In the PSG evaluation we did not evaluate L5 ± 6, because it requires more than 12 hours of (non-simulated) data, which most PSG recordings do not offer. After sleep classification with HDCZA and before running the comparison between HDCZA and PSG, 60 minutes of simulated data were removed at the beginning and end. The following performance metrics for SPT-window detection were used: difference in onset, waking time, and duration, accuracy, c-statistic, t-test, and mean absolute error (MAE).
Performance estimates accuracy and c-statistic were derived from both the data, as well as from the data expanded with wakefulness time to simulate performance estimates in a 24 hour recording. Sleep classification within the SPT-window was evaluated as difference in duration (t-test) and as the percentage of time spent in sleep stages REM, and non-REM stages 1, 2, and 3 (N1, N2, and N3) correctly classified by the algorithm as part of SPT-window. Sleep efficiency within the SPT-window by PSG and algorithm was compared via t-test and MAE. A P-value of <0. 005 was considered significant  15. Further, method agreement was evaluated with modified Bland-Altman plots  16  with PSG criterion values on the horizontal axis. Considering the relatively small sample size in our PSG analysis, we also report the minimal detectable difference between estimated and PSG reference values given the sample size, observed standard deviation, observed correlation, a required significance level of 0.
Comparison between accelerometer results and that from polysomnography. In the PSG study in sleep clinic patients, on average 9. 4 (standard deviation 1. 6) hours of matching data from PSG and accelerometer were retrieved per participant, with no difference in recording duration between left and right wrist (P = 0. 75). Sleep onset time, waking time, SPT-window duration, and sleep duration within the SPT-window derived from the HDCZA algorithm differed all non-significantly from polysomnography and MAE ranged from 31 minutes for sleep onset to 71 minutes for SPT-window duration, see Table  4. The combined MAE from onset and waking time was 38. 9 and 36. 7 minutes for the left and right wrist, respectively. SPT-window duration was estimated for the left wrist within 2 hours for the majority of individuals (75%) but deviated by more than 2 hours in seven individuals, six of which had a sleep disorder, as shown in Fig.
The sensitivity analysis on parameter configuration as reported in Supplementary information (Page 81) demonstrates that the current configuration provides a relatively good average performance across alternative configurations that is relatively robust against changing study conditions. Improvement in algorithm performance in a specific dataset via optimization of parameter configuration can lead to overfitting, which comes with poor performance in other datasets or a subset of the data. We found one other study that compared SPT-window extracted from accelerometry (or actigraphy) unaided by sleep diary to facilitate further interpretation of our current findings. Recently, O'Donnell and colleagues also investigated possible approaches to SPT-window detection, currently available as a non-peer reviewed preprint on bioRxiv  23.
To derive sleep latency, one would need diary records of time in bed or the lights out period. Future research is warranted to investigate how sleep latency, time in bed, and the lights out period may reliably be detected from wearable accelerometer data without asking the participant to record their sleep behaviour using a diary or marker button. The analysis presented in this paper will facilitate feasible large-scale population research on sleep and physical activity. In addition to the proof of validity as provided in this paper additional support for the credibility of the algorithm was found in our separate study (non-peer reviewed preprint on bioRxiv) identifying genome wide associations with sleep parameters derived from our algorithm in UK Biobank, replicating signals previously associated with self-reported sleep duration and chronotype  [27] [28] [29] [30] [31] [32] [33] [34].
Code availability. Both SPT-window detection algorithms are implemented and available in open source R package GGIR version 1. 5-23 (https://cran. r-project. org/web/packages/GGIR/) 18 , see the software's documentation on input arguments 'loglocation' and 'def. noc. sleep' for further details on the use of L5 ± 6 and HDCZA. The R code used for our comparisons with sleep diary can be found at: https://github. com/wadpac/ whitehall-acc-spt-detection-eval. The R code used for our comparisons with polysomnography can be found at: https://github. com/wadpac/psg-ncl-acc-spt-detection-eval, with the code used for the Newcastle data in the master branch of the repository and its adaptation for the differently formatted Pennsylvanian data in the psg-penn branch.
Coherent parity check (CPC) codes The signature feature of CPC codes is the ability to implement QEC routines with any sequence of parity checks. This is possible due to a fail-safe code structure that ensures syndrome measurements cannot decohere the register. This freedom in the choice of parity checks gives the CPC framework multiple advantages over traditional QEC techniques. First, it is possible to directly translate the parity checking sequences from classical codes into a CPC code, which allows the derivation of dense QEC codes that encode multiple data qubits per logical block. Second, the CPC framework does not require quantum data to be initially redundantly encoded. Third, the space of possible CPC codes can be searched numerically, meaning code discovery can be automated. In this section, we outline the tools of the CPC framework, starting with the fundamental CPC gadget.
Traditional quantum error correction Before beginning our presentation of the CPC framework, we briefly outline the key concepts and shortcomings of conventional stabilizer QEC codes. This will provide a point-of-reference with which to compare CPC codes. The circuit in figure  1  shows the basic structure of a traditional stabilizer code. A register of data qubits, |ψ D , is entangled with a number of blank redundancy qubits, |0 R , via an encoding operation to create a logical qubit |ψ L. At this stage, the data previously stored solely in |ψ D is distributed across the combined Hilbert space of data and redundancy qubits  [22]. Once the quantum information has been encoded as a logical qubit, errors can be detected by making parity measurements. In practice, this is achieved via the construction shown to the right of the circuit in figure  1.
The fundamental CPC gadget The fundamental CPC gadget, shown in figure  2 , is the building block upon which all CPC codes are based  [3]. The basic premise behind the CPC gadget is that the parity of the quantum register is never explicitly measured. Instead, parity information is stored coherently as quantum data and compared over time. This is made possible by the gadget's symmetric encode-error-decode structure. The CPC gadget takes a multi-qubit register |ψ D and a parity qubit p, prepared in the state |0 p , as its input. The action of the encode stage of the gadget, labelled U enc in figure  2 , is to apply the parity operator P to the register and record the outcome in parity qubit p. Rather than measuring the syndrome immediately, the parity qubit is kept coherent during a wait stage in which the register is potentially subject to an error E.
A quantum error detection protocol can therefore be constructed from the CPC gadget by selecting a parity check that anticommutes with the error to be identified. In the following subsections, we will show that CPC gadgets can be combined to create full QEC codes which can detect and localise multiple error types simultaneously. The CPC gadget can be thought of as an extended measurement of the ±1 1 D operator on the data register, where the sign depends upon the commutation relation between P and E. As the ±1 states, there is no need for CPC codes to encode quantum information as logical qubits. Furthermore, it is clear from the output of the CPC gadget in equation (  5 ), that the quantum data register is completely disentangled from the parity qubit prior to syndrome measurement. As a result, the only requirement on the parity checks is that they are Pauli group operators P ∈ G.
The canonical form of CPC codes The  [[4,2,2] ] quantum error detection code illustrates the basic principles behind the operation of a CPC code. The encoder is constructed by combining a bit-flip CPC gadget with a phase-flip CPC gadget. Under this canonical ordering, errors on the parity qubits are identifiable via the addition of the cross-check operators. A compact way of representing CPC codes is in terms of adjacency matrices which describe the connectivity between the register and parity qubits. For example, the adjacency matrices for the  [[4,2,2] ] code are m b = [p1] [p2] [A] 1 0 [B] 1 0 , m p = [p1] [p2] [A] 0 1 [B] 0 1 , m c = [p1] [p2] [p1] 0 1 [p2] 0 0 , (11) where m b represents the bit-checks, m p the phase-checks and m c the cross-checks. For the bit-flip and phase-flip adjacency matrices, m b and m p , the rows refer to the data qubits and the columns the parity qubits.
Looking at the bit-flip matrix, we can see that both register qubits connect to parity qubit p 1 via CNOT gates in accordance with the circuit in figure  8. Likewise, matrix m P tells us that both register qubits are connected to parity qubit p 2 via conjugate-propagator gates. Finally, from matrix m c , we see that there is a single cross-check between parity qubits p 1 and p 2. The cross-checks result in a matrix that is always symmetric. We follow  [3]  in representing this as an upper triangular matrix, so that the number of non-zero entries corresponds to the number of two-qubit gates. We are now in a position to extend the CPC framework to enable the description of more general codes. The canonical form of an  [[n,k,d] ] CPC code is shown in figure  9. Such codes have k data qubits, |ψ D = |ψ D 1 ψ D 2.
Numerical CPC code discovery We have now outlined the canonical structure of CPC codes, and shown how they can be represented in terms of three adjacency matrices. The CPC framework removes the need to start out by redundantly encoding quantum data, and allows QEC protocols to be implemented with any parity check. As such, the CPC framework essentially reduces the task of deriving QEC codes to a classical decoding problem. A new [[n, k, d =?]] CPC circuit can be generated simply by selecting a random instance of the adjacency matrices for an n-qubit code with k data qubits. The symmetric encode-error-decode structure of the CPC code will ensure that the random sequence of parity checks this set of adjacency matrices represents does not decohere the register. The only task necessary to verify whether the circuit represents a working CPC code is to measure the code distance d.
This can be done by testing the circuits with all of the errors in the chosen error model. If each error produces a unique syndrome, then the code distance is d ≥ 3, and the circuit represents a working CPC code. In this paper we only consider quantum memories. As a result, the codes under consideration are Clifford circuits. The code distance can therefore be efficiently verified for small-distance codes using a stabilizer simulator such as  [25, 26]. Alternatively, we have developed an algorithm specifically for calculating the syndromes of CPC codes, which is based on error propagation rules outlined in sections 2. 3 and 2. 4. This algorithm is described in appendix C, and can be implemented in less than 200 lines of Python code.
Experimental data reconstruction methods The IBM Quantum Information Software Kit (QISKIT)  [33]  was used to prepare the  [[4, 2, 2] ] experiment for quantum state tomography on the output qubits Q 0 and Q 3. QISKIT quantum tomography tools were used to create a set of nine circuits from the original  [[4, 2, 2] ] circuit (depicted in figure  12c ), each of which was designed to measure the output qubits Q 0 and Q 3 in a different measurement basis from the list {XX, XY, XZ, Y X, Y Y, Y Z, ZX, ZY, ZZ}. These quantum tomography circuits were then run multiple times to create a distribution of results that could be used reconstruct an approximation to the density matrix of the output state. The QISKIT method used for state reconstruction from the experimental data was the fast maximum likelihood method for quantum tomography, a description of which can be found in  [34].
Experimental results The  [[4, 2, 2] ] CPC quantum memory circuit, depicted in figure  12c , was run on the IBMQX4 device between the 25 th and 27 th November 2017. A summary of the experimental results for state purity, fidelity and yield can be found in table 2. Error bars were calculated as one standard deviation of a single run value consisting of 8192 experimental executions of the quantum tomography circuit set. The standard error of the mean over all 154 runs was too small to be visible on our plots. Calibration data for the device on each of the three days of the experiment can be found in appendix D. Ba sis st at es Purity, P (ρ) Fidelity, F (ρ) Yield Before post-selection, ρdd 0. 52 ± 0. 02 0. 62 ± 0. 03 100% After post-selection, ρps 0. 74 ± 0. 03 0. 75 ± 0. 04 (54 ± 2)% no. runs: 154 batches of 8192 shots Table  2 : Quality metrics for the reconstructed density matrices before and after post-selection.
The results in this section demonstrate that the CPC framework provides constructive tools for discovery of optimal [  [7, 3, 3] ] codes that saturate the quantum Hamming bound. Furthermore, the search was performed using a simple brute-force technique that requires only a basic knowledge of the CPC code structure to implement. The Python script used to perform the code search is approximately 200 lines long, and required approximately 4 days to run on a CPU clocked at 3. 2GHz with 8Gb of RAM.
Stage 2: Hardware optimisation The second stage of the CPC design process involves selecting codes to meet the demands of the chosen quantum hardware and its qubit layout. Figure  19a  shows the   [7, 3, 3] ] CPC codes binned by two-qubit gate count after compilation onto a nearest-neighbour architecture. The total gate count is defined as the number of CPC gates + SWAP gates in the encode stage of the circuit. [7, 3, 3] ] codes following the SWAP gate compilation. The two-qubit gate count is defined as the number of CPC gates + SWAP gates. The depth reduction is the percentage decrease in gate-count of the smallest circuit relative to the median. idealised model ion trap under consideration, labelled with 3 data qubits and 4 parity qubits as required by the [  [7, 3, 3] ] code. Under the restriction of nearest-neighbour connectivity, interactions between spatially separated qubits can still be realised by performing SWAP operations.