dataesr/scientific-paragraphs-categorization huggingface dataset:
Moreover, the parallel Mach 142 number is higher at the X-points. Regarding now, the ion and electron temperatures, 143 they are globally lower for D = 0. 6, meaning that for this value of density diffusion, the 144 plasma in the core has a higher density but lower temperatures. The whole process can be thus summarised as: The mesh refinement is performed using the open-source software Mmg  [5, 6]. It uses a map of elemental size in which the desired element size on each vertex must be precised. This current elemental size can be defined on each vertex of an existing mesh  [16]  using the elemental areas {|Ω k |} as follows: h j = ∑ i∈S j |Ω i | hi ∑ i∈S j |Ω i | (19) in which S j denotes the set of element indices having node j as a vertex. At the iteration n of the refinement process, a basic and straightforward formula provides a guess of the desired mesh size at the next iteration, on the element j where oscillations are detected, using the expression: h (n+1) target,j = (h (n) j ) α ( 20 ) where α (α > 1) is a control parameter to tune in order to perform the refinement.
Conclusions In this Letter, we have presented a new method for modeling interacting SNe within the time-dependent non-LTE radiative transfer code CMFGEN. The method is designed to cover conditions in which the CSM is optically thin in electron scattering, so as to complement the alternate configurations with optically thick CSM handled with HERACLES and the nonmonotonic solver in CMFGEN  (Dessart et al. 2015). The preliminary simulations presented here were focused on a Type II SN ejecta, modified to exhibit a dense shell at high velocity to mimic the swept-up mass from the interaction with CSM, and influenced by various shock powers. Although it depends on the level of clumping in the dense shell and the efficiency of thermalization therein, the bulk of the interaction power tends to emerge in the UV, making this spectral range essential in this context and emphasizing the need for future observations of transients in the UV  (Kulkarni et al.
Acknowledgements. We acknowledge fruitful discussion with  J. Anderson  and  P. Pessi. This work was supported by the  "Programme National de Physique Stellaire" of CNRS/INSU  co-funded by  CEA  and  CNES. D. J. H. thanks  NASA  for partial support through the astrophysical theory grant  80NSSC20K0524. This work was granted access to the HPC resources of CINES under the 2020 allocation A0090410554 made by  GENCI, France. This research has made use of  NASA's Astrophysics Data System Bibliographic Services.
7 million ganglion cells although the number of photoreceptors is on the order of 126 million cells. A reduced code constructed from the difference between photoreceptors in the retina (e. g. , a differential code) is sent to the brain with the same amount of information, which requires far less channel capacity  (11, 12). Hence, efficient coding for pattern separation and pattern completion is hypothesized to occur widely in the brain to manipulate natural input. The same hypothesis is expected for memory access, storage, and retrieval in areas such as the hippocampus and the prefrontal cortex  (6, 13). The question is, therefore, how the brain can encode, transmit and store one coherent signal efficiently from unreliable neurons. How can neurons communicate as much information as is theoretically possible? These two questions are tightly linked to the binding problem as well: how can neural areas specialize in different modalities, with partial access to information on an external event, coherently share their views to produce a unified representation of the world? As a novel paradigm, we propose a mechanism that exploits a neural code with a limited resolution to code and decode higher resolution sequences.
D R A F T a high repertoire cardinality (number of quantization levels). In our neural network, the neural code takes the form of a relative code to represent the relative order of items within the sequence; e. g. , the following relative ordinal code [#5, #3, #2, #4, #1, #6] corresponds to the sequence of index  [18, 13, 8, 14, 5, 19] ; see Fig. 1. Despite the coarseness of these neural codes, our results show that this mechanism can achieve errorfree reconstruction by having sparse and distributed neural representations of the original sequence. Neural cells sensitive to serial order in sequences have been found extensively in the prefrontal cortex  (14) (15) (16) (17) (18)  and the hippocampus during spatial exploration and memory tasks  (19, 20). Studies identify them either as conjunctive cells or as disjunctive cells, whether researchers are looking at their binding feature to respond nonlinearly to various signals in a mixed form  (21) (22) (23)  or at their factorizing feature to respond only to relational or structural information  (20, (24) (25) (26).
Random permutations, in effect, decorrelate redundant information in incoming signals: henceforth, few neurons become necessary to discriminate the original signal. By avoiding redundancy, we guarantee the code efficiency with maximum information compression, following the maximum entropy principle  (8). In our neural network, although any individual neuron is unreliable in reconstructing an original signal due to the coarse quantization performed by the relative order codes (pattern separation), taken at the population level, they can share their views and exploit their distributivity and sparsity to find a consensus through crosstalk (pattern completion). Such an error-correction process can be performed iteratively by selecting at each time step the solutions that best satisfy the constraints during reconstruction.
However, iterative combinations of their belief votes allows us to find a consensus and to correct errors near perfectly. Shannon showed that communication channel capacity can be attained for asymptotically long messages using a random channel code, which maps each message to a codeword that realizes of independent identically distributed symbol random variables  (38). However, such a code is impractical in terms of complexity. It was the advent of turbo codes that first demonstrated the existence of structured codes operating close to capacity with reasonable decoding complexity  (39). Turbo codes encode a message twice using a simple code, once in original positional order and once in randomly shuffled order. These two "views" on the message allow for an elaborate iterative decoding algorithm that corrects many more errors than the simple codes alone.
D R A F T Fig. 1. Schematic presentation of the neural population based on randomly permuted ordinal codes. The process has three stages: the encoding of the original sequence, its decoding and a global belief vote. In the first phase, the neurons encode the relative order (the ranks) of the items in the spatiotemporal sequence X using multiple randomly shuffled orderings of the item alphabet. The result is that each neuron sees a randomly permuted ordinal code, e. g. , P (Y /X). The items' values are no longer present in the ordinal codes, which perform a drastic quantization of information. During the decoding phase, each neuron reconstructs the sequence in its alphabet ordering by trial and error, e. g. , Q(X/Y ). Thus, each neuron has a different local estimate of the items in the sequence.
Decoder: exploits the channel code structure to correct errors introduced by the noisy channel. Digital computing: the main difference w. r. t. analog computing is that values involved in computation are from a finite set (e. g. , binary in most digital computers). This requires the ability to correct the errors introduced by every type of physical computing and storage circuit (biological or electronic). The ordinal code with a belief voting decoder used in this work is an error correcting mechanism. Turbo coding: a telecommunications error correction scheme that encodes the original input sequence and an interleaved (position-permuted) copy of it. The decoder iteratively estimates the original sequence, aided by the previous estimate of the interleaved sequence, and vice versa. This alternating decoding iteration allows many more errors to be corrected than with a single code, provided that the interleaver ensures that the two estimates for a symbol are almost independent.
Although sparse, the encoding is not relative; therefore, there is no reduction in the number of synaptic weights. We will develop more in the Discussion section on how the brain might carry out this function and the biological plausibility of it. We can use the example presented in Fig. 3 a ) and b) to explain the difference between the two types of coding, respectively STDP/ROC and ordinal encoding. For instance, in a time series of 6 items ordered as follows seq :  [18, 13, 8, 14, 5, 19]  in Fig. 3 a ), the ordinal code corresponding to this sequence is order : [#5, #3, #2, #4, #1, #6] in Fig. 3 b ). If R is defined as the cardinality of the input space, and L is the number of items within the sequence, then it is necessary to have L or R synaptic links to encode the sequence, depending on the code used and the desired precision level (see Fig.
3 c ). For instance, the STDP learning mechanism requires R synaptic links to encode the indices and their location in the temporal sequence; the values of the synaptic weights encode the temporal delay or the index order  (40, 45, 46). In comparison, an ordinal code requires only a vector of L weights, in which the amplitude level encodes the relative order. This relative code can be seen as a harsh analog-to-digital conversion in which the exact item values in the sequence are removed. However, in the case where R ≫ L, it can represent a computational advantage to represent only the ordinal structure within the data  (47, 48) , see Fig. 3.
d). Ordinal codes implementation. The ordinal coding strategy consists of discretizing the items in the sequence based on their rank in a given alphabet. The ordering function rank(An, S, i), n ∈ [N ], i ∈ [L] , specifies as output the rank under order An of the item si located at position i within the sequence S = [S1, S2,. , SL]. The ordered alphabet An = [π (n) 1 , π (n) 2 ,. , π (n) R ] is a permutation of the original repertoire, and N is the number of output neurons, equal to the number of representations of the same sequence in different permuted orders. We implement the rank function rank(An, S, i) = 1/r as the inverse of the rank r for a particular index i, which can be obtained easily with the argsort() function in the C, MATLAB, or python languages. The equations of the neurons Y sensitive to ordinal information in a sequence are as follows.
In b), the minimum number of neurons needed is N limit to reconstruct the sequence without error with respect to the input resolution (resp. R). The graph shows a linear progression of the number of neurons required to code a sequence while the cardinality R augments exponentially; the values are averaged over ten simulations. averaged over ten simulations shows the counterintuitive result that a logarithmic relationship can be achieved between the number of neurons necessary to encode a sequence and its resolution, which can grow exponentially. This shows the surprising result that an extremely small number of neurons is required to disentangle a signal or sequence of very high resolution, and this is achieved with quantized neurons with limited learning capabilities, which make large reconstruction errors.
Digital computation. We found the counterintuitive result that a very limited number of neurons with coarse resolution and random connections can accurately encode arbitrary signals of very high resolution, one hundred million times higher than the neurons' learning capabilities, and this ratio grows linearly. Because of the neurons' ordinal representation of the sequence, items taken in a repertoire of dimension R can be represented by a neural code with values taken in a repertoire of dimension L only, making the computation cycles of encoding and decoding very fast. Surprisingly, the principal bottleneck is at the reconstruction stage, which is dependent on the parameter σ and the number of neurons N used in the calculation of the Gaussian functions. The larger σ is, the heavier the computation but also the more precise the reconstruction, as shown in the experiments.
1 and 2. These equations can provide insights for a neural information theory and the design of novel digital neural networks, for which the neural network we propose is one of the first instances our knowledge. The ordinal codes in our neural architecture operate a discretization (quantization) of information. Additionally, the randomly permuted orders yield independent and identically distributed rank items to be coded (with maximum entropy). This max entropy holds under the model assumption that the random permutations are chosen uniformly for each sequence learned. Together, they form a joint source-channel code that allows disambiguation of sequences that map to the same rank order in the original alphabet. This is in line with the efficient coding principle of redundancy reduction and the whitening phenomenon, which is found in sparse coding  (3, 8, 11, 12, 57).
Error-correcting codes are at the heart of the revolution of modern communication theory and practice. Interestingly, the pioneering work that first came within reach of the Shannon limit to error-free communication is the turbo-codes  (37) , which exploit the three mechanisms we similarly use here: shuffling of the input signal, coarse representation (by paritycheck codes), and belief votes at the decoder. Within the brain, since the task of correctly retrieving a particular group of neurons is incommensurate (58) considering the number of neural units (10 10 cells) and the number of synaptic connections (10 14 dendrites), the brain has to find an efficient solution to overcome its complexity for processing, protecting and retrieving information (3). One outstanding and provocative question is, therefore, does the brain effectively use a digital code to process neural information? Although not a computer, does the brain incidentally exploit the same principles found in current man-made telecommunication networks? After all, if 'DNA is encoded digital information in the "Strong Sense"' according to Richard Dawkins  (59) , the brain may also exploit some kind of digital processing for memory preservation, access and learning.
However, the problem of how the organization of memory and information processing can be efficiently combined, what the brain does, still remains. To make a parallel with these neural networks and also with the von Neuman's computer architecture, we may see the neural population we introduced to realize the function of a random access memory (RAM) to retrieve quickly the addresses of neurons in a large-scale memory network. These neural addresses are represented in our neural architecture by quantized ordinal codes. Our results showed that a relatively small neural code can retrieve sequences in a very large-scale repertoire; e. g. , an external memory system.
Software Design The general concept of xifusim is that it simulates the X-IFU readout chain as a sequence of data processing blocks, starting from photon impacts. This chain is shown in Fig. 1. Similar to tessim  [5] , the TES signal is generated by solving a differential equation system in the time domain, with the effect of photons introduced via an external energy term in the TES thermal equation. The output of the TES block is a continuous current stream per simulated pixel. Deviating from tessim, which continues by digitizing the simulated current and then triggering, xifusim simulates more components of the readout chain. The first block after the TES array is the SQUID block, primarily used as an amplifier and in the case of Time-Division Multiplexing (TDM) a separate multiplexing stage.
The demultiplexed output of the DRE is then processed by the Trigger block, which cuts out sections of the data stream before and after a triggering condition is met. An important part of xifusim is that the individual blocks in Fig. 1  can each be represented by different models, which are summarized in Sect. 3. The models of each block have the same input and output data types and can be replaced independently from each other, making xifusim a modular code. This is handled in xifusim, which is written in C++, by generating individual objects from object templates. Note that while xifusim is written in standard C++, running on CPUs, some of its components, most importantly the TES array, have also been implemented in CUDA, enabling the use of GPUs  [6]. This is especially useful when running simulations on the scale of the whole TES array.
Models An important feature of xifusim is the on-the-fly selection of different models representing the readout chain blocks. The main benefit of this feature is the ability to continuously add models to the software as needed by internal studies to quickly judge the impact of changes to the readout chain. This section will briefly describe the models that have been added to xifusim thus far. For the TES block, xifusim supports two main models. The first is the same model used by tessim, consisting of the standard TES differential equations  [7]  with a linear resistance R(T, I). This model is able to produce representative TES pulses for pixels with standard lab characterizations (thermal conductances, circuit parameters and TES transition parameters and ). As opposed to the small signal model, the detector response is nonlinear in energy  [5, 6].
For its final block, xifusim implements several triggering models, which can be used as in a real instrument to only output data of scientific interest. The standard triggering algorithm of xifusim is the differential trigger described in  [5] , based on a low pass filtered one-sided derivative of the signal. Additionally, xifusim includes a 'noise' trigger (continuous triggering regardless of input signal, used to extract noise samples) as well as a 'perfect' trigger, which bypasses triggering on the DRE output and instead triggers whenever a photon is processed by the simulator. The latter is mostly used in studies to avoid systematics introduced by an actual triggering algorithm based on the input data stream. In application, a user can select from any sensible combination of the above models (mostly restricted by needing to use the same multiplexing scheme) whenever the program is called.
Applications One of the primary uses of xifusim is in providing input for the development of event processing software for the X-IFU. Here, both tessim  [11, 12]  and later xifusim  [13]  were used to generate synthetic data streams used to test different triggering and energy reconstruction algorithms. xifusim was also used to study the effect of cosmic ray impacts on the X-IFU energy resolution  [14]. This study used xifusim to simulate photon impacts during thermal bath temperature fluctuations due to cosmic rays impacting the detector wafer, with the wafer thermal response calculated externally. Another use of xifusim is the creation of input for the SIXTE simulation environment  [4] , specifically for the X-IFU end-to-end simulator xifupipeline. Unlike xifusim, this simulator does not directly simulate the TES array and readout chain.
Instead, it determines the detected photon energy based on a redistribution matrix file in addition to simulating energy offsets due to crosstalk. Here, crosstalk energy shifts are calculated from precomputed tables, generated either from laboratory data or xifusim simulations. An example of such a xifusim simulation is the mutual inductance crosstalk shown in Sect. 4. To determine the effect of crosstalk on a photon's measured energy, we repeat this simulation with an additional signal photon in the pixel receiving the crosstalk voltage shift. We then apply an optimal filter to the output pulse record produced by xifusim. The difference between this reconstructed energy and the energy reconstructed from a pulse record without the crosstalk signal corresponds to the crosstalk energy shift.
The granular output and parameter variation features described in Sect. 4 are also an important part of xifusim, with extensive use both during development as a testing and debugging tool as well as for studies focused on individual readout chain components. As a consequence of its modular design, it is also in principle possible to use xifusim to simulate individual readout chain blocks (such as only a TES) or even other instruments. An example would be the X-IFU 's cryogenic anticoincidence detector  [18] , which is also based on transition edge sensors-a simulator for this instrument using the xifusim code base is currently under development. Lastly, while the xifusim source code has so far only been accessible to members of the X-IFU consortium, we also plan a future open source release enabling the use of the simulator or parts of its code in other software for the general community.
Acknowledgements This research has made use of ISIS functions (ISISscripts) provided by  ECAP/ Remeis observatory  and  MIT  (http://www. sternwarte. uni-erlangen. de/isis/). We thank  John E. Davis  for the development of the SLXfig module used to prepare the figures. This work has been funded by the  Bundesministerium für Wirtschaft und Technologie  under DLR Grant Number  50 QR 1903. This work has been funded by the  Spanish Ministry MCIU  under project  RTI2018-096686-B-C21  ( MCIU/AEI/FEDER, UE ), co-funded by  FEDER  funds.
Recent advances in genome sequencing and imputation technologies provide an exciting opportunity to comprehensively study the contribution of genetic variants to complex phenotypes. However, our ability to translate genetic discoveries into mechanistic insights remains limited at this point. In this paper, we propose an efficient knockoff-based method, GhostKnockoff, for genome-wide association studies (GWAS) that leads to improved power and ability to prioritize putative causal variants relative to conventional GWAS approaches. The method requires only Z-scores from conventional GWAS and hence can be easily applied to enhance existing and future studies. The method can also be applied to meta-analysis of multiple GWAS allowing for arbitrary sample overlap. We demonstrate its performance using empirical simulations and two applications: (1) a meta-analysis for Alzheimer's disease comprising nine overlapping large-scale GWAS, whole-exome and wholegenome sequencing studies and (2) analysis of 1403 binary phenotypes from the UK Biobank data in 408,961 samples of European ancestry.
We simulated genetic data directly using whole-genome sequencing (WGS) data from the Alzheimer's Disease Sequencing Project (ADSP). The ADSP WGS data (NG00067. v5) are jointly called by the ADSP consortium following the SNP/Indel Variant Calling Pipeline and data management tool (VCPA)  19. We restricted the sampling to individuals with >80% European ancestry (estimated by SNPWeights v2. 1 using reference populations from the 1000 Genomes Consortium  20, 21  ). For each replicate, we randomly drew individuals for two overlapping studies with 2500 individuals per study and 2000 genetic variants randomly selected from a 1Mb region near the APOE region (chr19:44,909,011-45,912,650; hg38). We then restricted the simulation studies to variants with minor allele counts > 25 and to variants that are not tightly linked.