We construct all possible complete intersection Calabi-Yau five-folds in a product of four or less complex projective spaces, with up to four constraints. We obtain $27068$ spaces, which are not related by permutations of rows and columns of the configuration matrix, and determine the Euler number for all of them. Excluding the $3909$ product manifolds among those, we calculate the cohomological data for $12433$ cases, i.e. $53.7 \%$ of the non-product spaces, obtaining $2375$ different Hodge diamonds. The dataset containing all the above information is available at https://www.dropbox.com/scl/fo/z7ii5idt6qxu36e0b8azq/h?rlkey=0qfhx3tykytduobpld510gsfy&dl=0 . The distributions of the invariants are presented, and a comparison with the lower-dimensional analogues is discussed. Supervised machine learning is performed on the cohomological data, via classifier and regressor (both fully connected and convolutional) neural networks. We find that $h^{1,1}$ can be learnt very efficiently, with very high $R^2$ score and an accuracy of $96\%$, i.e. $96 \%$ of the predictions exactly match the correct values. For $h^{1,4},h^{2,3}, \eta$, we also find very high $R^2$ scores, but the accuracy is lower, due to the large ranges of possible values.

In recent years, deep learning has become a relevant research theme in physics and mathematics. It is a very efficient method for data processing, and elaboration and exploration of patterns [1]. Though the basic building blocks are not new [2], the increase in computational capabilities and the creation of larger databases lead new deep learning techniques to thrive. Specifically, the understanding of the geometrical structures [3, 4] and the representation learning [5] are of particular interest from a mathematical and theoretical physics points of view [6-9]. We are interested in applications of data science and deep learning techniques for algebraic topology, and especially Hodge numbers, of complete intersection Calabi-Yau (CICY) manifolds [10-12].

Traditional aerial vehicles have limitations in their capabilities due to actuator constraints, such as motor saturation. The hardware components and their arrangement are designed to satisfy specific requirements and are difficult to modify during operation. To address this problem, we introduce a versatile modular multi-rotor vehicle that can change its capabilities by reconfiguration. Our modular robot consists of homogeneous cuboid modules, propelled by quadrotors with tilted rotors. Depending on the number of modules and their configuration, the robot can expand its actuation capabilities. In this paper, we build a mathematical model for the actuation capability of a modular multi-rotor vehicle and develop methods to determine if a vehicle is capable of satisfying a task requirement. Based on this result, we find the optimal configurations for a given task. Our approach is validated in realistic 3D simulations, showing that our modular system can adapt to tasks with varying requirements.

Running complex sets of machine learning experiments is challenging and time-consuming due to the lack of a unified framework. This leaves researchers forced to spend time implementing necessary features such as parallelization, caching, and checkpointing themselves instead of focussing on their project. To simplify the process, in this paper, we introduce Memento, a Python package that is designed to aid researchers and data scientists in the efficient management and execution of computationally intensive experiments. Memento has the capacity to streamline any experimental pipeline by providing a straightforward configuration matrix and the ability to concurrently run experiments across multiple threads.

Generalized Complete Intersection Calabi-Yau Manifold (gCICY) is a new construction of Calabi-Yau manifolds established recently. However, the generation of new gCICYs using standard algebraic method is very laborious. Due to this complexity, the number of gCICYs and their classification still remain unknown. In this paper, we try to make some progress in this direction using neural network. The results showed that our trained models can have a high precision on the existing type $(1,1)$ and type $(2,1)$ gCICYs in the literature. Moreover, They can achieve a $97\%$ precision in predicting new gCICY which is generated differently from those used for training and testing. This shows that machine learning could be an effective method to classify and generate new gCICY.

The dataset is considerably larger and richer than the one for CICY threefolds and Topological quantities of manifolds, such as Betti or it consists of about 900000 topological types of manifolds. Hodge numbers, are often non-trivially related to the However, so far, this new dataset has not been data describing the underlying manifold and tend to used for machine learning and the purpose of this letter be difficult to work out. Explicit formulae are usually is to fill this gap. More specifically, we will explore, not known and calculations rely on complicated and frequently within the context of supervised learning, if and to what computationally intense algorithms (see, for example, extent Hodge numbers of CICY fourfolds can be learned the volume [1] and references therein for applications by neural networks.

The latest techniques from Neural Networks and Support Vector Machines (SVM) are used to investigate geometric properties of Complete Intersection Calabi-Yau (CICY) threefolds, a class of manifolds that facilitate string model building. An advanced neural network classifier and SVM are employed to (1) learn Hodge numbers and report a remarkable improvement over previous efforts, (2) query for favourability, and (3) predict discrete symmetries, a highly imbalanced problem to which the Synthetic Minority Oversampling Technique (SMOTE) is applied to boost performance. In each case study, we employ a genetic algorithm to optimise the hyperparameters of the neural network. We demonstrate that our approach provides quick diagnostic tools capable of shortlisting quasi-realistic string models based on compactification over smooth CICYs and further supports the paradigm that classes of problems in algebraic geometry can be machine learned.