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BackgroundMachine learning and artificial intelligence have shown promising results in many areas and are driven by the increasing amount of available data. However, these data are often distributed across different institutions and cannot be easily shared owing to strict privacy regulations. Federated learning (FL) allows the training of distributed machine learning models without sharing sensitive data. In addition, the implementation is time-consuming and requires advanced programming skills and complex technical infrastructures. ObjectiveVarious tools and frameworks have been developed to simplify the development of FL algorithms and provide the necessary technical infrastructure. Although there are many high-quality frameworks, most focus only on a single application case or method. To our knowledge, there are no generic frameworks, meaning that the existing solutions are restricted to a particular type of algorithm or application field. Furthermore, most of these frameworks provide an application programming interface that needs programming knowledge. There is no collection of ready-to-use FL algorithms that are extendable and allow users (eg, researchers) without programming knowledge to apply FL. A central FL platform for both FL algorithm developers and users does not exist. This study aimed to address this gap and make FL available to everyone by developing FeatureCloud, an all-in-one platform for FL in biomedicine and beyond. MethodsThe FeatureCloud platform consists of 3 main components: a global frontend, a global backend, and a local controller. Our platform uses a Docker to separate the local acting components of the platform from the sensitive data systems. We evaluated our platform using 4 different algorithms on 5 data sets for both accuracy and runtime. ResultsFeatureCloud removes the complexity of distributed systems for developers and end users by providing a comprehensive platform for executing multi-institutional FL analyses and implementing FL algorithms. Through its integrated artificial intelligence store, federated algorithms can easily be published and reused by the community. To secure sensitive raw data, FeatureCloud supports privacy-enhancing technologies to secure the shared local models and assures high standards in data privacy to comply with the strict General Data Protection Regulation. Our evaluation shows that applications developed in FeatureCloud can produce highly similar results compared with centralized approaches and scale well for an increasing number of participating sites. ConclusionsFeatureCloud provides a ready-to-use platform that integrates the development and execution of FL algorithms while reducing the complexity to a minimum and removing the hurdles of federated infrastructure. Thus, we believe that it has the potential to greatly increase the accessibility of privacy-preserving and distributed data analyses in biomedicine and beyond.

We show that certain known or new inequalities for the logarithm of circular hyperbolic functions imply bounds for exp(±x2) proved in [1].

Upper bounds for σ(n) are provided in terms of other arithmetic functions as ϕ(n), d(n), ψ(n), P(n), etc. Comparision of older results are given, too.

We obtain an arithmetic proof and a refinement of the inequality ϕ (nk) + σk(n) < 2nk, where n ≧ 2 and k ≧ 2. An application to another inequality is also provided.

The southeastern part of Transylvania has a specific location in the Carpathian Basin. Being situated on the western fringe of the Eastern Carpathians, influences from west (inner Transylvania and the Great Hungarian Plain) and east (Moldavia and the northern Pontic area) can be traced through human history. The mountains were never an impenetrable border, and their porosity has made it possible for external cultural influences to expand. As a result southeastern Transylvania can be seen as a "contact zone" between East and West, where the above-mentioned influences have sometimes been weaker, but have never ceased: the continuous contacts and links were always present between the two sides of the Carpathians, something that has been confirmed by the numerous archaeological discoveries. While in recent years more and more [14]C data have been reported from central and western Transylvania, this number has been negligible from the study area. In the last three years we have managed to measure 33 samples from 23 key-sites belonging to the Bronze Age, covering the whole period. The results have brought us closer to answering the questions that have preoccupied specialists dealing with the Bronze Age for decades. Many of the dates are the first ones for some of the cultures present in the study area (for example, for the Jigodin and Gáva Cultures), offering new, independent dating. The new results confirm many of the earlier suppositions regarding the Bronze Age chronology of the area, but have also raised some problems, which will need to be clarified in the future. [ABSTRACT FROM AUTHOR]