Fair Cake Division Under Monotone Likelihood Ratios

This work develops algorithmic results for the classic cake-cutting problem in which a divisible, heterogeneous resource (modeled as a cake) needs to be partitioned among agents with distinct preferences. We focus on a standard formulation of cake cutting wherein each agent must receive a contiguous piece of the cake. Although multiple hardness results exist in this setup for finding fair/efficient cake divisions, we show that, if the value densities of the agents satisfy the monotone likelihood ratio property (MLRP), then strong algorithmic results hold for various notions of fairness and economic efficiency. Addressing cake-cutting instances with MLRP, first we develop an algorithm that finds cake divisions (with connected pieces) that are envy free, up to an arbitrary precision. The time complexity of our algorithm is polynomial in the number of agents and the bit complexity of an underlying Lipschitz constant. We obtain similar positive results for maximizing social, egalitarian, and Nash social welfare. Many distribution families bear MLRP. In particular, this property holds if all the value densities belong to any one of the following families: Gaussian (with the same variance), linear, Poisson, and exponential distributions, linear translations of any log-concave function. Hence, through MLRP, the current work obtains novel cake-cutting algorithms for multiple distribution families.

THE PROBLEM OF THE CORRELATION BETWEEN SPIRIT AND REALITY IN T. MANN’S NOVEL “TRISTAN”

Short stories are an integral part of T. Mann’s creative heritage, which are distinguished by ideological, thematic and artistic richness, they give an idea of the evolution of the creative method and style of the writer. And although nowadays there is already a number of scientific investigations devoted to the review analysis of T. Mann’s creative path, there is a need to study the problem of culture “end of time” (in T. Mann’s terminology) in the novelistic work of the writer who went to political and social activities through art. The purpose of the article is to reveal the nuances of the relationship between spirit and reality in T. Mann’s short story “Tristan”.The article proves that within the cross-cutting problem of the relationship between art and life, which never ceased to bother the German writer, also the novel “Tristan” clearly distinguishes the related ones: art and beauty, art and morality, aesthetics and life, beauty and death, decadence and a disease of the spirit, the artist and reality, which allowed to clarify both the ideological concepts of creative individuality and the essence of its art. At the same time, the divergence between the views of the hero of the novel and T. Mann’s personal attitude to reality and art is shown. Enough attention is paid to identifying the role of the comic and the means of its formation in the novel. “Tristan” is interpreted in the context of the development of T. Mann’s work and the European literary process at the turn of the XIX - early XX centuries.The article identifies the place of the short story “Tristan” in the work of the German master of the word and outlines the ways of its further analysis.

Exploring Integration Trajectories for a European Health Union

COVID-19 emerged as a cross-cutting problem across governance sectors and levels, urging the creation of a European Health Union. There are already a number of integrated European governance strategies – such as the European Energy Union (2015) and the European Green Deal (2019) – adopted for overcoming problems of governance fragmentation and inadequacy of fragmented policy responses to cross-cutting policy challenges. Past studies focused on the interaction between crisis and policy change and investigated the activation of different mechanisms to enhance integration. This article contributes to the debate over the creation of a European Health Union by unpacking the acknowledged dimensions of policy integration – policy frame, subsystem involvement, policy goals and policy instruments – in order to assess their manifestations in the new EU4Health policy and to establish what contextual conditions triggered the activation of the integration-enabling mechanisms that led to a more integrated European Health Union. In so doing, it offers an analytical illustration and discusses implications for decision-making.