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We find that simple neural networks with ReLU activation generate polytopes as an approximation of a unit sphere in various dimensions. The species of polytopes are regulated by the network architecture, such as the number of units and layers. For a variety of activation functions, generalization of polytopes is obtained, which we call neural polytopes. They are a smooth analogue of polytopes, exhibiting geometric duality. This finding initiates research of generative discrete geometry to approximate surfaces by machine learning., Comment: 5 pages, 9 figures. v2: References added. Accepted at the 1st Workshop on the Synergy of Scientific and Machine Learning Modeling at International Conference on Machine Learning (ICML), Honolulu, Hawaii, USA. 2023

We propose a method to calculate wave functions and energies not only of the ground state but also of low-lying excited states using a deep neural network and the unsupervised machine learning technique. For systems composed of identical particles, a simple method to perform symmetrization for bosonic systems and antisymmetrization for fermionic systems is also proposed.

We propose a method to calculate wave functions and energies not only of the ground state but also of low-lying excited states using a deep neural network and the unsupervised machine learning technique. For systems composed of identical particles, a simple method to perform symmetrization for bosonic systems and antisymmetrization for fermionic systems is also proposed., Comment: 23 pages, 18 figures, 8 tables; Typo of Eq. (25) corrected

We find that simple neural networks with ReLU activation generate polytopes as an approximation of a unit sphere in various dimensions. The species of polytopes are regulated by the network architecture, such as the number of units and layers. For a variety of activation functions, generalization of polytopes is obtained, which we call neural polytopes. They are a smooth analogue of polytopes, exhibiting geometric duality. This finding initiates research of generative discrete geometry to approximate surfaces by machine learning., Comment: 5 pages, 9 figures. v2: References added. Accepted at the 1st Workshop on the Synergy of Scientific and Machine Learning Modeling at International Conference on Machine Learning (ICML), Honolulu, Hawaii, USA. 2023

Background: Skeletal muscle fiber type distribution has implications for human health, muscle function, and performance. This knowledge has been gathered using labor-intensive and costly methodology that limited these studies. Here, we present a method based on muscle tissue RNA sequencing data (totRNAseq) to estimate the distribution of skeletal muscle fiber types from frozen human samples, allowing for a larger number of individuals to be tested. Methods: By using single-nuclei RNA sequencing (snRNAseq) data as a reference, cluster expression signatures were produced by averaging gene expression of cluster gene markers and then applying these to totRNAseq data and inferring muscle fiber nuclei type via linear matrix decomposition. This estimate was then compared with fiber type distribution measured by ATPase staining or myosin heavy chain protein isoform distribution of 62 muscle samples in two independent cohorts (n = 39 and 22). Results: The correlation between the sequencing-based method and the other two were r(ATpas) = 0.44 [0.13-0.67], [95% CI], and r(myosin) = 0.83 [0.61-0.93], with p = 5.70 x 10(-3) and 2.00 x 10(-6), respectively. The deconvolution inference of fiber type composition was accurate even for very low totRNAseq sequencing depths, i.e., down to an average of similar to 10,000 paired-end reads. Conclusions: This new method (https://github.com/OlaHanssonLab/PredictFiberType) consequently allows for measurement of fiber type distribution of a larger number of samples using totRNAseq in a cost and labor-efficient way. It is now feasible to study the association between fiber type distribution and e.g. health outcomes in large well-powered studies.

Background: Skeletal muscle fiber type distribution has implications for human health, muscle function, and performance. This knowledge has been gathered using labor-intensive and costly methodology that limited these studies. Here, we present a method based on muscle tissue RNA sequencing data (totRNAseq) to estimate the distribution of skeletal muscle fiber types from frozen human samples, allowing for a larger number of individuals to be tested. Methods: By using single-nuclei RNA sequencing (snRNAseq) data as a reference, cluster expression signatures were produced by averaging gene expression of cluster gene markers and then applying these to totRNAseq data and inferring muscle fiber nuclei type via linear matrix decomposition. This estimate was then compared with fiber type distribution measured by ATPase staining or myosin heavy chain protein isoform distribution of 62 muscle samples in two independent cohorts (n = 39 and 22). Results: The correlation between the sequencing-based method and the other two were r(ATpas) = 0.44 [0.13-0.67], [95% CI], and r(myosin) = 0.83 [0.61-0.93], with p = 5.70 x 10(-3) and 2.00 x 10(-6), respectively. The deconvolution inference of fiber type composition was accurate even for very low totRNAseq sequencing depths, i.e., down to an average of similar to 10,000 paired-end reads. Conclusions: This new method (https://github.com/OlaHanssonLab/PredictFiberType) consequently allows for measurement of fiber type distribution of a larger number of samples using totRNAseq in a cost and labor-efficient way. It is now feasible to study the association between fiber type distribution and e.g. health outcomes in large well-powered studies.

Background: Skeletal muscle fiber type distribution has implications for human health, muscle function, and performance. This knowledge has been gathered using labor-intensive and costly methodology that limited these studies. Here, we present a method based on muscle tissue RNA sequencing data (totRNAseq) to estimate the distribution of skeletal muscle fiber types from frozen human samples, allowing for a larger number of individuals to be tested. Methods: By using single-nuclei RNA sequencing (snRNAseq) data as a reference, cluster expression signatures were produced by averaging gene expression of cluster gene markers and then applying these to totRNAseq data and inferring muscle fiber nuclei type via linear matrix decomposition. This estimate was then compared with fiber type distribution measured by ATPase staining or myosin heavy chain protein isoform distribution of 62 muscle samples in two independent cohorts (n = 39 and 22). Results: The correlation between the sequencing-based method and the other two were r(ATpas) = 0.44 [0.13-0.67], [95% CI], and r(myosin) = 0.83 [0.61-0.93], with p = 5.70 x 10(-3) and 2.00 x 10(-6), respectively. The deconvolution inference of fiber type composition was accurate even for very low totRNAseq sequencing depths, i.e., down to an average of similar to 10,000 paired-end reads. Conclusions: This new method (https://github.com/OlaHanssonLab/PredictFiberType) consequently allows for measurement of fiber type distribution of a larger number of samples using totRNAseq in a cost and labor-efficient way. It is now feasible to study the association between fiber type distribution and e.g. health outcomes in large well-powered studies.

Background: Skeletal muscle fiber type distribution has implications for human health, muscle function, and performance. This knowledge has been gathered using labor-intensive and costly methodology that limited these studies. Here, we present a method based on muscle tissue RNA sequencing data (totRNAseq) to estimate the distribution of skeletal muscle fiber types from frozen human samples, allowing for a larger number of individuals to be tested. Methods: By using single-nuclei RNA sequencing (snRNAseq) data as a reference, cluster expression signatures were produced by averaging gene expression of cluster gene markers and then applying these to totRNAseq data and inferring muscle fiber nuclei type via linear matrix decomposition. This estimate was then compared with fiber type distribution measured by ATPase staining or myosin heavy chain protein isoform distribution of 62 muscle samples in two independent cohorts (n = 39 and 22). Results: The correlation between the sequencing-based method and the other two were r(ATpas) = 0.44 [0.13-0.67], [95% CI], and r(myosin) = 0.83 [0.61-0.93], with p = 5.70 x 10(-3) and 2.00 x 10(-6), respectively. The deconvolution inference of fiber type composition was accurate even for very low totRNAseq sequencing depths, i.e., down to an average of similar to 10,000 paired-end reads. Conclusions: This new method (https://github.com/OlaHanssonLab/PredictFiberType) consequently allows for measurement of fiber type distribution of a larger number of samples using totRNAseq in a cost and labor-efficient way. It is now feasible to study the association between fiber type distribution and e.g. health outcomes in large well-powered studies.

Background: Skeletal muscle fiber type distribution has implications for human health, muscle function, and performance. This knowledge has been gathered using labor-intensive and costly methodology that limited these studies. Here, we present a method based on muscle tissue RNA sequencing data (totRNAseq) to estimate the distribution of skeletal muscle fiber types from frozen human samples, allowing for a larger number of individuals to be tested. Methods: By using single-nuclei RNA sequencing (snRNAseq) data as a reference, cluster expression signatures were produced by averaging gene expression of cluster gene markers and then applying these to totRNAseq data and inferring muscle fiber nuclei type via linear matrix decomposition. This estimate was then compared with fiber type distribution measured by ATPase staining or myosin heavy chain protein isoform distribution of 62 muscle samples in two independent cohorts (n = 39 and 22). Results: The correlation between the sequencing-based method and the other two were r(ATpas) = 0.44 [0.13-0.67], [95% CI], and r(myosin) = 0.83 [0.61-0.93], with p = 5.70 x 10(-3) and 2.00 x 10(-6), respectively. The deconvolution inference of fiber type composition was accurate even for very low totRNAseq sequencing depths, i.e., down to an average of similar to 10,000 paired-end reads. Conclusions: This new method (https://github.com/OlaHanssonLab/PredictFiberType) consequently allows for measurement of fiber type distribution of a larger number of samples using totRNAseq in a cost and labor-efficient way. It is now feasible to study the association between fiber type distribution and e.g. health outcomes in large well-powered studies.

Background: Skeletal muscle fiber type distribution has implications for human health, muscle function, and performance. This knowledge has been gathered using labor-intensive and costly methodology that limited these studies. Here, we present a method based on muscle tissue RNA sequencing data (totRNAseq) to estimate the distribution of skeletal muscle fiber types from frozen human samples, allowing for a larger number of individuals to be tested. Methods: By using single-nuclei RNA sequencing (snRNAseq) data as a reference, cluster expression signatures were produced by averaging gene expression of cluster gene markers and then applying these to totRNAseq data and inferring muscle fiber nuclei type via linear matrix decomposition. This estimate was then compared with fiber type distribution measured by ATPase staining or myosin heavy chain protein isoform distribution of 62 muscle samples in two independent cohorts (n = 39 and 22). Results: The correlation between the sequencing-based method and the other two were r(ATpas) = 0.44 [0.13-0.67], [95% CI], and r(myosin) = 0.83 [0.61-0.93], with p = 5.70 x 10(-3) and 2.00 x 10(-6), respectively. The deconvolution inference of fiber type composition was accurate even for very low totRNAseq sequencing depths, i.e., down to an average of similar to 10,000 paired-end reads. Conclusions: This new method (https://github.com/OlaHanssonLab/PredictFiberType) consequently allows for measurement of fiber type distribution of a larger number of samples using totRNAseq in a cost and labor-efficient way. It is now feasible to study the association between fiber type distribution and e.g. health outcomes in large well-powered studies.

Picorna-like plant viruses are non-enveloped RNA spherical viruses of ~30 nm. Part of the survival of these viruses depends on their capsid being stable enough to harbour the viral genome and yet malleable enough to allow its release. However, molecular mechanisms remain obscure. Here, we report a structure of a picorna-like plant virus, apple latent spherical virus, at 2.87 Å resolution by single-particle cryo-electron microscopy (cryo-EM) with a cold-field emission beam. The cryo-EM map reveals a unique structure composed of three capsid proteins Vp25, Vp20, and Vp24. Strikingly Vp25 has a long N-terminal extension, which substantially stabilises the capsid frame of Vp25 and Vp20 subunits. Cryo-EM images also resolve RNA genome leaking from a pentameric protrusion of Vp24 subunits. The structures and observations suggest that genome release occurs through occasional opening of the Vp24 subunits, possibly suppressed to a low frequency by the rigid frame of the other subunits.

We consider the optimization of the first eigenvalue of -nabla. ( $rho$nabla u) = $lambda$ u on a bounded domain $Omega$ subset mathbb{R}^{n} with a constraint on the diffusion coefficient $rho$. We reduce our optimization problem to the Hamilton-Jacobi type equation for the function determining $rho$ via the level set method. We take the viscous approximation of the Hamilton-Jacobi type equation and prove its global well-posedness. We expect that solutions of the original Hamilton-Jacobi type equation are obtained as the limit of its viscous approximation. We also expect that the proposing approach leads to the optimization analysis of general energy functionals including constraints. This article is written in Japanese.