Lower Bounds for Heights in Relative Galois Extensions

The goal of this paper is to obtain lower bounds on the height of an algebraic number in a relative setting, extending previous work of Amoroso and Masser. Specifically, in our first theorem we obtain an effective bound for the height of an algebraic number $\alpha$ when the base field $\mathbb{K}$ is a number field and $\mathbb{K}(\alpha)/\mathbb{K}$ is Galois. Our second result establishes an explicit height bound for any non-zero element $\alpha$ which is not a root of unity in a Galois extension $\mathbb{F}/\mathbb{K}$, depending on the degree of $\mathbb{K}/\mathbb{Q}$ and the number of conjugates of $\alpha$ which are multiplicatively independent over $\mathbb{K}$. As a consequence, we obtain a height bound for such $\alpha$ that is independent of the multiplicative independence condition

Cellular automata on regular rooted trees

We study cellular automata on regular rooted trees. This includes the characterization of sofic tree shifts in terms of unrestricted Rabin automata and the decidability of the surjectivity problem for cellular automata between sofic tree shifts

Autonomy in Weapons Systems. The Military Application of Artificial Intelligence as a Litmus Test for Germany’s New Foreign and Security Policy

The future international security landscape will be critically impacted by the military use of artificial intelligence (AI) and robotics. With the advent of autonomous weapon systems (AWS) and a currently unfolding transformation of warfare, we have reached a turning point and are facing a number of grave new legal, ethical and political concerns. In light of this, the Task Force on Disruptive Technologies and 21st Century Warfare, deployed by the Heinrich Böll Foundation, argues that meaningful human control over weapon systems and the use of force must be retained. In their report, the task force authors offer recommendations to the German government and the German armed forces to that effect

Complex network modelling of origin–destination commuting flows for the COVID-19 epidemic spread analysis in Italian Lombardy Region

Currently the whole world is affected by the COVID-19 disease. Italy was the first country to be seriously affected in Europe, where the first COVID-19 outbreak was localized in the Lombardy region. The further spreading of the cases led to the lockdown of the most affected regions in northern Italy and then the entire country. In this work we investigated an epidemic spread scenario in the Lombardy region by using the origin–destination matrix with information about the commuting flows among 1450 urban areas within the region. We performed a large-scale simulation-based modeling of the epidemic spread over the networks related to three main motivations, i.e., work, study and occasional transfers to quantify the potential contribution of each category of travellers to the spread of the epidemic process. Our findings outline that the three networks are characterised by different weight dynamic growth rates and that the network “work” has a critical role in the diffusion phenomenon showing the greatest contribution to the epidemic spread

Extensive evaluation of morphological statistical harmonization for brain age prediction

Characterizing both neurodevelopmental and aging brain structural trajectories is important for understanding normal biological processes and atypical patterns that are related to pathological phenomena. Initiatives to share open access morphological data contributed significantly to the advance in brain structure characterization. Indeed, such initiatives allow large brain morphology multi-site datasets to be shared, which increases the statistical sensitivity of the outcomes. However, using neuroimaging data from multi-site studies requires harmonizing data across the site to avoid bias. In this work we evaluated three different harmonization techniques on the Autism Brain Imaging Data Exchange (ABIDE) dataset for age prediction analysis in two groups of subjects (i.e., controls and autism spectrum disorder). We extracted the morphological features from T1-weighted images of a mixed cohort of 654 subjects acquired from 17 sites to predict the biological age of the subjects using three machine learning regression models. A machine learning framework was developed to quantify the effects of the different harmonization strategies on the final performance of the models and on the set of morphological features that are relevant to the age prediction problem in both the presence and absence of pathology. The results show that, even if two harmonization strategies exhibit similar accuracy of predictive models, a greater mismatch occurs between the sets of most age-related predictive regions for the Autism Spectrum Disorder (ASD) subjects. Thus, we propose to use a stability index to extract meaningful features for a robust clinical validation of the outcomes of multiple harmonization strategies

Variety Village District Economic Analysis: Retail Market Expansion, Economic Impact, and Fiscal Impact

This study outlines the economic and fiscal impacts of the redevelopment of the Variety Village District, comprised of the Variety Theatre Complex, a new public parking lot, and 40,000 square feet of new retail along Lorain Avenue. In addition, as shown in the full report, a portion of the location decision for at least three local industries which are moving to, or expanding their enterprise in, the immediate Westown neighborhood, can be attributed to the catalytic effect of the Variety Village District redevelopment

An equity-oriented rethink of global rankings with complex networks mapping development

Nowadays, world rankings are promoted and used by international agencies, governments and corporations to evaluate country performances in a specific domain, often providing a guideline for decision makers. Although rankings allow a direct and quantitative comparison of countries, sometimes they provide a rather oversimplified representation, in which relevant aspects related to socio-economic development are either not properly considered or still analyzed in silos. In an increasingly data-driven society, a new generation of cutting-edge technologies is breaking data silos, enabling new use of public indicators to generate value for multiple stakeholders. We propose a complex network framework based on publicly available indicators to extract important insight underlying global rankings, thus adding value and significance to knowledge provided by these rankings. This approach enables the unsupervised identification of communities of countries, establishing a more targeted, fair and meaningful criterion to detect similarities. Hence, the performance of states in global rankings can be assessed based on their development level. We believe that these evaluations can be crucial in the interpretation of global rankings, making comparison between countries more significant and useful for citizens and governments and creating ecosystems for new opportunities for development