In the context of natural disasters, human responses inevitably intertwine with natural factors. The COVID-19 pandemic, as a significant stress factor, has brought to light profound variations among different countries in terms of their adaptive dynamics in addressing the spread of infection outbreaks across different regions. This emphasizes the crucial role of cultural characteristics in natural disaster analysis. The theoretical understanding of large-scale epidemics primarily relies on mean-field kinetic models. However, conventional SIR-like models failed to fully explain the observed phenomena at the onset of the COVID-19 outbreak. These phenomena included the unexpected cessation of exponential growth, the reaching of plateaus, and the occurrence of multi-wave dynamics. In situations where an outbreak of a highly virulent and unfamiliar infection arises, it becomes crucial to respond swiftly at a non-medical level to mitigate the negative socio-economic impact. Here we present a theoretical examination of the first wave of the epidemic based on a simple SIRSS model (SIR with Social Stress). We conduct an analysis of the socio-cultural features of na\"ive population behaviors across various countries worldwide. The unique characteristics of each country/territory are encapsulated in only a few constants within our model, derived from the fitted COVID-19 statistics. These constants also reflect the societal response dynamics to the external stress factor, underscoring the importance of studying the mutual behavior of humanity and natural factors during global social disasters. Based on these distinctive characteristics of specific regions, local authorities can optimize their strategies to effectively combat epidemics until vaccines are developed.

Domain adaptation is a popular paradigm in modern machine learning which aims at tackling the problem of divergence (or shift) between the labeled training and validation datasets (source domain) and a potentially large unlabeled dataset (target domain). The task is to embed both datasets red into a common space in which the source dataset is informative for training while the divergence between source and target is minimized. The most popular domain adaptation solutions are based on training neural networks that combine classification and adversarial learning modules, frequently making them both data-hungry and difficult to train. We present a method called Domain Adaptation Principal Component Analysis (DAPCA) that identifies a linear reduced data representation useful for solving the domain adaptation task. DAPCA algorithm introduces positive and negative weights between pairs of data points, and generalizes the supervised extension of principal component analysis. DAPCA is an iterative algorithm that solves a simple quadratic optimization problem at each iteration. The convergence of the algorithm is guaranteed, and the number of iterations is small in practice. We validate the suggested algorithm on previously proposed benchmarks for solving the domain adaptation task. We also show the benefit of using DAPCA in analyzing the single-cell omics datasets in biomedical applications. Overall, DAPCA can serve as a practical preprocessing step in many machine learning applications leading to reduced dataset representations, taking into account possible divergence between source and target domains.

Dealing with uncertainty in applications of machine learning to real-life data critically depends on the knowledge of intrinsic dimensionality (ID). A number of methods have been suggested for the purpose of estimating ID, but no standard package to easily apply them one by one or all at once has been implemented in Python. This technical note introduces \texttt{scikit-dimension}, an open-source Python package for intrinsic dimension estimation. \texttt{scikit-dimension} package provides a uniform implementation of most of the known ID estimators based on scikit-learn application programming interface to evaluate global and local intrinsic dimension, as well as generators of synthetic toy and benchmark datasets widespread in the literature. The package is developed with tools assessing the code quality, coverage, unit testing and continuous integration. We briefly describe the package and demonstrate its use in a large-scale (more than 500 datasets) benchmarking of methods for ID estimation in real-life and synthetic data. The source code is available from https://github.com/j-bac/scikit-dimension , the documentation is available from https://scikit-dimension.readthedocs.io .

The state of each component is determined by a Boolean function of the state of (a subset of) the components of the network. This paper addresses the synthesis of these Boolean functions from constraints on their domain and emerging dynamical properties of the resulting network. The dynamical properties relate to the existence and absence of trajectories between partially observed configurations, and to the stable behaviours (fixpoints and cyclic attractors). The synthesis is expressed as a Boolean satisfiability problem relying on Answer-Set Programming with a parametrized complexity, and leads to a complete non-redundant characterization of the set of solutions. Considered constraints are particularly suited to address the synthesis of models of cellular differentiation processes, as illustrated on a case study. The scalability of the approach is demonstrated on random networks with scale-free structures up to 100 to 1,000 nodes depending on the type of constraints.

Moreover, it is frequently assumed that the nature of this variety is a manifold, and that the data point cloud represents an i.i.d. In practice, the ID of the manifold is assumed to be not only much smaller than the number of variables defining the data space but also to be small in absolute number. Thus, any practically useful nonlinear data manifold should not have more than three or four intrinsic degrees of freedom. Theoretically, the manifold concept does not have to be universal in the case of real-life datasets. Abstract--Modern large-scale datasets are frequently said to be high-dimensional. However, their data point clouds frequently possess structures, significantly decreasing their intrinsic dimensionality (ID)due to the presence of clusters, points being located close to low-dimensional varieties or fine-grained lumping. We test a recently introduced dimensionality estimator, based on analysing the separability properties of data points, on several benchmarks and real biological datasets.

We present ElPiGraph, a method for approximating data distributions having non-trivial topological features such as the existence of excluded regions or branching structures. Unlike many existing methods, ElPiGraph is not based on the construction of a k-nearest neighbour graph, a procedure that can perform poorly in the case of multidimensional and noisy data. Instead, ElPiGraph constructs elastic principal graphs in a more robust way by minimizing elastic energy, applying graph grammars and explicitly controlling topological complexity. Using trimmed approximation error function makes ElPiGraph extremely robust to the presence of background noise without decreasing computational performance and allows it to deal with complex cases of manifold learning (for example, ElPiGraph can learn disconnected intersecting manifolds). Thanks to the quasi-quadratic nature of the elastic function, ElPiGraph performs almost as fast as a simple k-means clustering and, therefore, is much more scalable than alternative methods, and can work on large datasets containing millions of high dimensional points on a personal computer. The excellent performance of the method opens the possibility to apply resampling and to approximate complex data structures via principal graph ensembles which can be used to construct consensus principal graphs. ElPiGraph is currently implemented in five programming languages and accompanied by a graphical user interface, which makes it a versatile tool to deal with complex data in various fields from molecular biology, where it can be used to infer pseudo-time trajectories from single-cell RNASeq, to astronomy, where it can be used to approximate complex structures in the distribution of galaxies.