We give a thoroughful explanation of the general properties of different, general scales, corresponding to different (all possible) mathematical functions f(x), we mention and analyse many examples. These observations and statements might help us to plan and realize any specific scale we need in the future, or to understand better any interesting or miserable properties of old scales.

Peut-on opposer ou même séparer la foi avec les acquis de l’activité scientifique? Le théorème de Gödel a souvent été utilisé pour rendre compte de cette séparation. Le caractère abusif de cette utilisation a été bien analysé ([42], [11]). Nous nous proposons d’affiner cette analyse dans le cadre de l’hypothèse du Mécanisme Digital. Nous montrons que le Mécanisme Digital aboutit à une forme de concordisme spirituel ontologique, épistémologique et éthique. En effet, dans ce cadre, la théologie, dans le sens des (néo) platoniciens de la Grèce antique, devient ou redevient une science, et même la science la plus fondamentale en ce sens qu’elle devient capable de justifier, en principe et conceptuellement, toutes les autres. Une notion naturelle de théologie des machines, incluant la physique, est définissable, par les faits mêmes de l’incomplétude de Gödel, et de la non définissabilité de la vérité (Tarski) et de la connaissance (Kaplan-Montague [15]).

Daniel H. Rothman The carbon cycle represents metabolism at a global scale. When viewed through a mathematical lens, observational data suggest that the cycle exhibits an underlying mathematical structure. This review focuses on two types of emerging results: evidence of global dynamical coupling between life and the environment, and an understanding of the ways in […]

Agriculture provides economic opportunity through innovation; helps rural America to thrive; promotes agricultural production that better nourishes Americans; and aims to preserve natural resources through healthy private working lands, conservation, improved watersheds, and restored forests. From agricultural production to food supply, agriculture supports rural and urban economies across the U.S. It accounts for 10% of U.S. jobs and is currently creating new jobs in the growing field of data-driven farming. However, U.S. global competitiveness associated with food and nutrition security is at risk because of accelerated investments by many other countries in agriculture, food, energy, and resource management. To ensure U.S. global competitiveness and long-term food security, it is imperative that we build sustainable physical and cyber infrastructures to enable self-managing and sustainable farming. Such infrastructures should enable next generation precision-farms by harnessing modern and emerging technologies such as small satellites, broadband Internet, tele-operation, augmented reality, advanced data analytics, sensors, and robotics.

Visibility algorithms are a family of geometric and ordering criteria by which a real-valued time series of N data is mapped into a graph of N nodes. This graph has been shown to often inherit in its topology non-trivial properties of the series structure, and can thus be seen as a combinatorial representation of a dynamical system. Here we explore in some detail the relation between visibility graphs and symbolic dynamics. To do that, we consider the degree sequence of horizontal visibility graphs generated by the one-parameter logistic map, for a range of values of the parameter for which the map shows chaotic behaviour. Numerically, we observe that in the chaotic region the block entropies of these sequences systematically converge to the Lyapunov exponent of the system. Via Pesin identity, this in turn suggests that these block entropies are converging to the Kolmogorov- Sinai entropy of the map, which ultimately suggests that the algorithm is implicitly and adaptively constructing phase space partitions which might have the generating property.

Determining how scientific achievements influence the subsequent process of knowledge creation is a fundamental step in order to build a unified ecosystem for studying the dynamics of innovation and competitiveness. Yet, relying separately on data about scientific production on one side, through bibliometric indicators, and about technological advancements on the other side, through patents statistics, gives only a limited insight on the key interplay between science and technology which, as a matter of fact, move forward together within the innovation space. In this paper, using citation data of both scientific papers and patents, we quantify the direct impact of the scientific outputs of nations on further advancements in science and on the introduction of new technologies.

We identify multirole logic as a new form of logic in which conjunction/disjunction is interpreted as an ultrafilter on the power set of some underlying set (of roles) and the notion of negation is generalized to endomorphisms on this underlying set. We formalize both multirole logic (MRL) and linear multirole logic (LMRL) as natural generalizations of classical logic (CL) and classical linear logic (CLL), respectively, and also present a filter-based interpretation for intuitionism in multirole logic. Among various meta-properties established for MRL and LMRL, we obtain one named multiparty cut-elimination stating that every cut involving one or more sequents (as a generalization of a (binary) cut involving exactly two sequents) can be eliminated, thus extending the celebrated result of cut-elimination by Gentzen.

The event GW150914 was the first historical detection of gravitational waves (GWs). The emergence of this ground-breaking discovery came not only from incredibly innovative experimental work, but also from a centennial of theoretical analyses. Many such analyses were performed by pioneering scientists who had wandered through a wild territory of mathematical laws. We explore such wandering and explain how it may impact the grand goal of unification in physics.

Experience curves are widely used to predict the cost benefits of increasing the scale of deployment of a technology. But how good are such forecasts? Can one predict their accuracy a priori? In this paper we answer these questions by developing a method to make distributional forecasts for experience curves. We test our method using a dataset with proxies for cost and experience for 46 products and technologies and show that it works reasonably well. The framework that we develop helps clarify why the experience curve method often gives similar results to simply assuming that costs decrease exponentially. To illustrate our method we make a distributional forecast for prices of solar photovoltaic modules.

The centrality of technological innovation in China’s economic development model, and the alignment of innovation and industrial policy have resulted in a multiplier effect of its innovation policies, leading to a steep ascent on the value chain. This rise on the value chain both results from and reinforces shifts in the global dynamics of innovation. The approach has had large-scale results in terms of financial benefit, infrastructural development, expanding consumer markets, and increasing quality and quantity of the human resources R&D pool. China’s rapid catch-up in areas such as green technology and its endeavors to appropriate core technologies in sensitive military domains such as space, have made technology an important pawn in the power play between the West and China. This vision paper examines how China has developed its innovation policy and strategically integrated it with other policies to strengthen its overall economic and political position. The paper provides an overview of the strategic policies adopted by China both in the innovation realm and in related policy fields, as well as the implications they have on European innovation abilities.