We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.

Decisions about how the population of the United States should be divided into legislative districts have powerful and not fully understood effects on the outcomes of elections. The problem of understanding what we might mean by «fair districting» intertwines mathematical, political, and legal reasoning; but only in recent years has the academic mathematical community gotten directly involved in the process. I’ll report on recent progress in this area, how newly developed mathematical tools have affected real political decisions, and what remains to be done. This survey represents the content of a lecture presented by the author in the Current Events Bulletin session of the Joint Mathematics Meetings in January 2020.

Human beings are talkative. What advantage did their ancestors find in communicating so much? Numerous authors consider this advantage to be «obvious» and «enormous». If so, the problem of the evolutionary emergence of language amounts to explaining why none of the other primate species evolved anything even remotely similar to language. What I propose here is to reverse the picture. On closer examination, language resembles a losing strategy. Competing for providing other individuals with information, sometimes striving to be heard, makes apparently no sense within a Darwinian framework. At face value, language as we can observe it should never have existed or should have been counter-selected. In other words, the selection pressure that led to language is still missing. The solution I propose consists in regarding language as a social signaling device that developed in a context of generalized insecurity that is unique to our species.

We present a survey on multilingual neural machine translation (MNMT), which has gained a lot of traction in the recent years. MNMT has been useful in improving translation quality as a result of translation knowledge transfer (transfer learning). MNMT is more promising and interesting than its statistical machine translation counterpart because end-to-end modeling and distributed representations open new avenues for research on machine translation. Many approaches have been proposed in order to exploit multilingual parallel corpora for improving translation quality. However, the lack of a comprehensive survey makes it difficult to determine which approaches are promising and hence deserve further exploration. In this paper, we present an in-depth survey of existing literature on MNMT.

Many real systems are strongly characterized by collective cooperative phenomena whose existence and properties still need a satisfactory explanation. Coherently with their collective nature, they call for new and more accurate descriptions going beyond pairwise models, such as graphs, in which all the interactions are considered as involving only two individuals at a time. Hypergraphs respond to this need, providing a mathematical representation of a system allowing from pairs to larger groups. In this work, through the use of different hypergraphs, we study how group interactions influence the evolution of cooperation in a structured population, by analyzing the evolutionary dynamics of the public goods game. Here we show that, likewise network reciprocity, group interactions also promote cooperation.

Complex systems thinking is applied to a wide variety of domains, from neuroscience to computer science and economics. The wide variety of implementations has resulted in two key challenges: the progenation of many domain-specific strategies that are seldom revisited or questioned, and the siloing of ideas within a domain due to inconsistency of complex systems language. In this work we offer basic, domain-agnostic language in order to advance towards a more cohesive vocabulary. We use this language to evaluate each step of the complex systems analysis pipeline, beginning with the system and data collected, then moving through different mathematical formalisms for encoding the observed data (i.e. graphs, simplicial complexes, and hypergraphs), and relevant computational methods for each formalism.

The reliable estimation of forecast uncertainties is crucial for risk-sensitive optimal decision making. In this paper, we propose implicit generative ensemble post-processing, a novel framework for multivariate probabilistic electricity price forecasting. We use a likelihood-free implicit generative model based on an ensemble of point forecasting models to generate multivariate electricity price scenarios with a coherent dependency structure as a representation of the joint predictive distribution. Our ensemble post-processing method outperforms well-established model combination benchmarks. This is demonstrated on a data set from the German day-ahead market. As our method works on top of an ensemble of domain-specific expert models, it can readily be deployed to other forecasting tasks.

Organizations across all sectors are increasingly undergoing deep transformation and restructuring towards data-driven operations. The central role of data highlights the need for reliable and clean data. Unreliable, erroneous, and incomplete data lead to critical bottlenecks in processing pipelines and, ultimately, service failures, which are disastrous for the competitive performance of the organization. Given its central importance, those organizations which recognize and react to the need for reliable data will have the advantage in the coming decade. We argue that the technologies for reliable data are driven by distinct concerns and expertise which complement those of the data scientist and the data engineer. Those organizations which identify the central importance of meaningful, explainable, reproducible, and maintainable data will be at the forefront of the democratization of reliable data.

In this work we provide a review of basic ideas and novel developments about Conformal Prediction — an innovative distribution-free, non-parametric forecasting method, based on minimal assumptions — that is able to yield in a very straightforward way predictions sets that are valid in a statistical sense also in in the finite sample case. The in-depth discussion provided in the paper covers the theoretical underpinnings of Conformal Prediction, and then proceeds to list the more advanced developments and adaptations of the original idea.

During the Cold War, the US and Soviet Union’s arms race expanded to space exploration. This indeed accelerated space technology development and exploration of space. But the US slowed down the process following the collapse of the Soviet Union.
Any country’s attempt to militarize space will result in changes in the international strategic balance. Other major countries will not stand by and watch. In modern warfare, information is key to victory, and space is one of the most important places to gather and transfer information. Why? Because technologies like satellite navigation, ground observation and information transmission have become integrated parts of combat systems of major military powers. This includes nuclear-armed intercontinental ballistic missiles and new hypersonic weapons that can also fly in outer space.
No major military power will accpet this facing the threat that their navigation systems could fail, communications may become jammed, command systems would go blind and deaf, and nuclear deterrence could run amok.