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We define a model of Galton Watson processes in dynamical environments where the environment evolves according to a dynamical system (X, T). Three behaviours are possible: uniformly subcritical, critical, and uniformly supercritical. We study the extinction probability q in the uniformly supercritical case. In particular, we investigate the regularity of this application as a function of the environment x. In the critical case, we study the set of bad environments N (where the probability of extinction is one), which is T -invariant. We give its Hausdorff dimension in some cases.

Branching architecture characterizes numerous systems, ranging from synthetic (hyper)branched polymers and biomolecules such as lignin, amylopectin, and nucleic acids to tracheal and neuronal networks. Its ubiquity reflects the many favourable properties that arise because of it. For instance, branched macromolecules are spatially compact and have a high surface functionality, which impacts their phase characteristics and self-assembly behaviour, among others. The relationship between branching and physical properties has been studied by mapping macromolecules to mathematical trees whose architecture can be characterized using topological indices. These indices, however, do not allow for a comparison of macromolecules that map to trees of different size, be it due to different mapping procedures or differences in their molecular weight. To alleviate this, we introduce a novel normalization of topological indices using estimates of their probability density functions. We determine two optimal normalized topological indices and construct a phase space that enables a robust discrimination between different architectures of branched macromolecules. We demonstrate the necessity of such a phase space on two practical applications, one being ribonucleic acid (RNA) molecules with various branching topologies and the other different methods of coarse-graining branched macromolecules. Our approach can be applied to any type of branched molecules and extended as needed to other topological indices, making it useful across a wide range of fields where branched molecules play an important role, including polymer physics, green chemistry, bioengineering, biotechnology, and medicine., Comment: 13 pages, 4 figures; 16 pages and 13 figures of supporting information

In the field of materials science and manufacturing, a vast amount of heterogeneous data exists, encompassing measurement and simulation data, machine data, publications, and more. This data serves as the bedrock of valuable knowledge that can be leveraged for various engineering applications. However, efficiently storing and handling such diverse data remain significantly challenging, often due to the lack of standardization and integration across different organizational units. Addressing these issues is crucial for fully utilizing the potential of data-driven approaches in these fields. In this paper, we present a novel technology stack named Dataspace Management System (DSMS) for powering dataspace solutions. The core of DSMS lies on its distinctive knowledge management approach tuned to meet the specific demands of the materials science and manufacturing domain, all while adhering to the FAIR principles. This includes data integration, linkage, exploration, visualization, processing, and enrichment, in order to support engineers in decision-making and in solving design and optimization problems. We provide an architectural overview and describe the core components of DSMS. Additionally, we demonstrate the applicability of DSMS to typical data processing tasks in materials science through use cases from two research projects, namely StahlDigital and KupferDigital, both part of the German MaterialDigital initiative.

Network systems can exhibit memory effects in which the interactions between different pairs of nodes adapt in time, leading to the emergence of preferred connections, patterns, and sub-networks. To a first approximation, this memory can be modelled through a ``plastic'' Hebbian or homophily mechanism, in which edges get reinforced proportionally to the amount of information flowing through them. However, recent studies on glia-neuron networks have highlighted how memory can evolve due to more complex dynamics, including multi-level network structures and ``meta-plastic'' effects that modulate reinforcement. Inspired by those systems, here we develop a simple and general model for the dynamics of an adaptive network with an additional meta-plastic mechanism that varies the rate of Hebbian strengthening of its edge connections. Specifically, we consider a biased random walk on a cyclic feed-forward network. The random walk chooses its steps according to the weights of the network edges. The weights evolve through a Hebbian mechanism modulated by a meta-plastic reinforcement, biasing the walker to prefer edges that have been already explored. We study the dynamical emergence (memorization) of preferred paths and their retrieval and identify three regimes: one dominated by the Hebbian term, one in which the meta-reinforcement drives memory formation, and a balanced one. We show that, in the latter two regimes, meta-reinforcement allows for the retrieval of a previously stored path even after weights have been reset to zero to erase Hebbian memory., Comment: 13 pages, 7 figures plus supplementary

In recent years, there has been a growing interest in accelerated materials innovation in the context of the process-structure-property chain. In this regard, it is essential to take into account manufacturing processes and tailor materials design approaches to support downstream process design approaches. As a major step into this direction, we present a holistic optimization approach that covers the entire process-structure-property chain in materials engineering. Our approach specifically employs machine learning to address two critical identification problems: a materials design problem, which involves identifying near-optimal material structures that exhibit desired properties, and a process design problem that is to find an optimal processing path to manufacture these structures. Both identification problems are typically ill-posed, which presents a significant challenge for solution approaches. However, the non-unique nature of these problems offers an important advantage for processing: By having several target structures that perform similarly well, processes can be efficiently guided towards manufacturing the best reachable structure. The functionality of the approach will be demonstrated manufacturing crystallographic textures with desired properties in a metal forming process.

This paper presents a novel methodology for improving the performance of machine learning based space traffic management tasks through the use of a pre-trained orbit model. Taking inspiration from BERT-like self-supervised language models in the field of natural language processing, we introduce ORBERT, and demonstrate the ability of such a model to leverage large quantities of readily available orbit data to learn meaningful representations that can be used to aid in downstream tasks. As a proof of concept of this approach we consider the task of all vs. all conjunction screening, phrased here as a machine learning time series classification task. We show that leveraging unlabelled orbit data leads to improved performance, and that the proposed approach can be particularly beneficial for tasks where the availability of labelled data is limited., Comment: Presented at the 2021 International Association for the Advancement of Space Safety (IAASS) Conf

The crystallographic texture of metallic materials is a key microstructural feature that is responsible for the anisotropic behavior, e.g., important in forming operations. In materials science, crystallographic texture is commonly described by the orientation distribution function, which is defined as the probability density function of the orientations of the monocrystal grains conforming a polycrystalline material. For representing the orientation distribution function, there are several approaches such as using generalized spherical harmonics, orientation histograms, and pole figure images . Measuring distances between crystallographic textures is essential for any task that requires assessing texture similarities, e.g. to guide forming processes. Therefore, we introduce novel distance measures based on (i) the Earth Movers Distance that takes into account local distance information encoded in histogram-based texture representations and (ii) a distance measure based on pole figure images. For this purpose, we evaluate and compare existing distance measures for selected use-cases. The present study gives insights into advantages and drawbacks of using certain texture representations and distance measures with emphasis on applications in materials design and optimal process control.

Using anonymized mobility data from Facebook users and publicly available information on the Italian population, we model the circulation of people in Italy before and during the early phase of the SARS-CoV-2 pandemic (COVID-19). We perform a spatial and temporal clustering of the movement network at the level of fluxes across provinces on a daily basis. The resulting partition in time successfully identifies the first two lockdowns without any prior information. Similarly, the spatial clustering returns 11 to 23 clusters depending on the period ("standard" mobility vs. lockdown) using the greedy modularity communities clustering method, and 16 to 30 clusters using the critical variable selection method. Fascinatingly, the spatial clusters obtained with both methods are strongly reminiscent of the 11 regions into which emperor Augustus had divided Italy according to Pliny the Elder. This work introduces and validates a data analysis pipeline that enables us: i) to assess the reliability of data obtained from a partial and potentially biased sample of the population in performing estimates of population mobility nationwide; ii) to identify areas of a Country with well-defined mobility patterns, and iii) to distinguish different patterns from one another, resolve them in time and find their optimal spatial extent. The proposed method is generic and can be applied to other countries, with different geographical scales, and also to similar networks (e.g. biological networks). The results can thus represent a relevant step forward in the development of methods and strategies for the containment of future epidemic phenomena., Comment: 24 pages, 16 figures

Public Procurement refers to governments' purchasing activities of goods, services, and construction of public works. In the European Union (EU), it is an essential sector, corresponding to 15% of the GDP. EU public procurement generates large amounts of data, because award notices related to contracts exceeding a predefined threshold must be published on the TED (EU's official journal). Under the framework of the DeCoMaP project, which aims at leveraging such data in order to predict fraud in public procurement, we constitute the FOPPA (French Open Public Procurement Award notices) database. It contains the description of 1,380,965 lots obtained from the TED, covering the 2010--2020 period for France. We detect a number of substantial issues in these data, and propose a set of automated and semi-automated methods to solve them and produce a usable database. It can be leveraged to study public procurement in an academic setting, but also to facilitate the monitoring of public policies, and to improve the quality of the data offered to buyers and suppliers.

In a seminal paper, Bacry and L\'evy-Leblond classified kinematical algebras, a class of Lie algebras encoding the symmetries of spacetime. Homogeneous spacetimes (infinitesimally, Klein pairs) associated to these possible kinematics can be partitioned into four families -- riemannian, lorentzian, galilean and carrollian -- based on the type of invariant metric structure they admit. In this work, we classify possible ambient kinematics -- defined as extensions of kinematical algebras by a scalar ideal -- as well as their associated Klein pairs. Kinematical Klein pairs arising as quotient space along the extra scalar ideal are said to admit a lift into the corresponding ambient Klein pair. While all non-galilean Klein pairs admit a unique -- trivial and torsion-free -- higher-dimensional lift, galilean Klein pairs are constructively shown to admit lifts into two distinct families of ambient Klein pairs. The first family includes the bargmann algebra as well as its curved/torsional avatars while the second family is novel and generically allows lifts into torsional ambient spaces. We further comment on the relation between these two families and the maximally symmetric family of leibnizian Klein pairs., Comment: 48 pages, 14 tables, 1 figure; Matches published version

Operating Si quantum dot (QD) arrays requires homogeneous and ultra-dense structures with aggressive gate pitch. Such a density is necessary to separately control the QDs chemical potential (i.e. charge occupation of each QD) from the exchange interaction (i.e. tunnel barriers between each QD). We present here a novel Si quantum device integration that halves the effective gate pitch and provides full controllability in 1D FDSOI QD arrays. The major advantages of this architecture are explored through numerical simulations. Functionality of the fabricated structure is validated via 300K statistical electrical characterization, while tunnel-coupling control is demonstrated at cryogenic temperature.

Analyzing and modeling the constitutive behavior of materials is a core area in materials sciences and a prerequisite for conducting numerical simulations in which the material behavior plays a central role. Constitutive models have been developed since the beginning of the 19th century and are still under constant development. Besides physics-motivated and phenomenological models, during the last decades, the field of constitutive modeling was enriched by the development of machine learning-based constitutive models, especially by using neural networks. The latter is the focus of the present review, which aims to give an overview of neural networks-based constitutive models from a methodical perspective. The review summarizes and compares numerous conceptually different neural networks-based approaches for constitutive modeling including neural networks used as universal function approximators, advanced neural network models and neural network approaches with integrated physical knowledge. The upcoming of these methods is in-turn closely related to advances in the area of computer sciences, what further adds a chronological aspect to this review. We conclude this review paper with important challenges in the field of learning constitutive relations that need to be tackled in the near future.

We present in this reference paper an instrumental project dedicated to the monitoring of solar activity during solar cycle 25. It concerns the survey of fast evolving chromospheric events implied in Space Weather, such as flares, coronal mass ejections, filament instabilities and Moreton waves. Coronal waves are produced by large flares around the solar maximum and propagate with chromospheric counterparts; they are rare, faint, difficult to observe, and for that reason, challenging. They require systematic observations with automatic, fast and multi-channel optical instruments. MeteoSpace is a high cadence telescope assembly specially designed for that purpose. The large amount of data will be freely available to the solar community. We describe in details the optical design, the qualification tests and capabilities of the telescopes, and show how waves can be detected. MeteoSpace will be installed at Calern observatory (C{\^o}te d'Azur, 1270 m) and will be in full operation in 2023.