Ricci flat metrics for Calabi-Yau threefolds are not known analytically. In this work, we employ techniques from machine learning to deduce numerical flat metrics for K3, the Fermat quintic, and the Dwork quintic. This investigation employs a simple, modular neural network architecture that is capable of approximating Ricci flat Kähler metrics for Calabi-Yau manifolds of dimensions two and three. We show that measures that assess the Ricci flatness and consistency of the metric decrease after training. This improvement is corroborated by the performance of the trained network on an independent validation set. Finally, we demonstrate the consistency of the learnt metric by showing that it is invariant under the discrete symmetries it is expected to possess.

International Press of Boston - publishers of scholarly mathematical and scientific journals and books

Calabi-Yau compactifications of the E 8 × E 8 heterotic string provide a promising route to recovering the four-dimensional particle physics described by the Standard Model. While the topology of the Calabi-Yau space determines the overall matter content in the low-energy effective field theory, further details of the compactification geometry are needed to calculate the normalized physical couplings and masses of elementary particles. In this work, we present numerical computations of physical Yukawa couplings in a number of heterotic models in the standard embedding and demonstrate the existence of natural hierarchies, a coveted feature in string model building.

Marker-based Optical Motion Capture (OMC) systems and associated musculoskeletal (MSK) modelling predictions offer non-invasively obtainable insights into muscle and joint loading at an in vivo level, aiding clinical decision-making. However, an OMC system is lab-based, expensive, and requires a line of sight. Inertial Motion Capture (IMC) techniques are widely-used alternatives, which are portable, user-friendly, and relatively low-cost, although with lesser accuracy. Irrespective of the choice of motion capture technique, one typically uses an MSK model to obtain the kinematic and kinetic outputs, which is a computationally expensive tool increasingly well approximated by machine learning (ML) methods. Here, an ML approach is presented that maps experimentally recorded IMC input data to the human upper-extremity MSK model outputs computed from (‘gold standard’) OMC input data. Essentially, this proof-of-concept study aims to predict higher-quality MSK outputs from the much easier-to-obtain IMC data. We use OMC and IMC data simultaneously collected for the same subjects to train different ML architectures that predict OMC-driven MSK outputs from IMC measurements. In particular, we employed various neural network (NN) architectures, such as Feed-Forward Neural Networks (FFNNs) and Recurrent Neural Networks (RNNs) (vanilla, Long Short-Term Memory, and Gated Recurrent Unit) and a comprehensive search for the best-fit model in the hyperparameters space in both subject-exposed (SE) as well as subject-naive (SN) settings. We observed a comparable performance for both FFNN and RNN models, which have a high degree of agreement (r${}_{\mathrm{avg},\mathrm{SE},\mathrm{FFNN}}={0.90}_{\pm 0.19}$, r${}_{\mathrm{avg},\mathrm{SE},\mathrm{RNN}}={0.89}_{\pm 0.17}$, r${}_{\mathrm{avg},\mathrm{SN},\mathrm{FFNN}}={0.84}_{\pm 0.23}$, and r${}_{\mathrm{avg},\mathrm{SN},\mathrm{RNN}}={0.78}_{\pm 0.23}$) with the desired OMC-driven MSK estimates for held-out test data. The findings demonstrate that mapping IMC inputs to OMC-driven MSK outputs using ML models could be instrumental in transitioning MSK modelling from ‘lab to field’.

We propose a novel machine learning (ML)-driven methodology to estimate biomechanical variables of interest traditionally obtained from upper-extremity musculoskeletal (MSK) modeling. MSK models facilitate personalized modeling, perform “what-if” analyses, and potentially enhance clinical decision-making. In certain settings, MSK models are driven by inertial motion capture (IMC) data. IMC systems are portable, user-friendly, and relatively affordable as well as provide additional biomechanical information. However, MSK models can be computationally expensive, often require extensive data, and can be prohibitively slow in making real-time predictions. Our ML method—involving a rigorous hyperparameters search—predicts kinematic and kinetic biomechanical information associated with human upper-extremity movements solely using IMC input data, thereby bypassing MSK models. The scaled cadaver-based MSK model was based on the Dutch Shoulder Model and the spine model implemented in the AnyBody Managed Model Repository. We employ neural networks (NNs), which are trained on IMC data obtained from five nondisabled subjects in subject-exposed (SE) settings (at least a trial from all subjects is used in training) and subject-naive (SN) settings (no information from test subjects is used in training). We compare the predictions of our ML model with that of an MSK model and find an excellent agreement in SE settings (average Pearson’s ${r}={0.96}$ , $\text {normalized RMSE (NRMSE)} ={0.23}$ ) and strong correspondence in SN settings (average ${r}={0.89}$ , $\text {NRMSE} ={0.45}$ ). The linear model performed poorly for SN settings, which motivated a more complex ML model. Our findings suggest that an ML-based approach is highly viable for estimating upper-extremity biomechanical information solely from IMC data.

In this paper, we classify non-freely acting discrete symmetries of complete intersection Calabi–Yau manifolds and their quotients by freely-acting symmetries. These non-freely acting symmetries can appear as symmetries of low-energy theories resulting from string compactifications on these Calabi–Yau manifolds, particularly in the context of the heterotic string. Hence, our results are relevant for four-dimensional model building with discrete symmetries and they give an indication which symmetries of this kind can be expected from string theory. For the 1695 known quotients of complete intersection manifolds by freely-acting discrete symmetries, non-freely-acting, generic symmetries arise in 381 cases and are, therefore, a relatively common feature of these manifolds. We find that 9 different discrete groups appear, ranging in group order from 2 to 18, and that both regular symmetries and R-symmetries are possible.