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AbstractProponents of ontic conceptions of explanation require all explanations to be backed by causal, constitutive, or similar relations. Among their justifications is that only ontic conceptions can do justice to the 'directionality' of explanation, i.e., the requirement that if X explains Y, then not-Y does not explain not-X. Using topological explanations as an illustration, we argue that non-ontic conceptions of explanation have ample resources for securing the directionality of explanations. The different ways in which neuroscientists rely on multiplexes involving both functional and anatomical connectivity in their topological explanations vividly illustrate why ontic considerations are frequently (if not always) irrelevant to explanatory directionality. Therefore, directionality poses no problem to non-ontic conceptions of explanation.

Spatially embedded networks have attracted increasing attention in the past decade. In this context, network characteristics have been introduced which explicitly take spatial information into account. Among others, edge directionality properties have recently gained particular interest. In this work, we investigate the applicability of mean edge direction, anisotropy, and local mean angle as geometric characteristics in complex spherical networks. By studying these measures, both analytically and numerically, we demonstrate the existence of a systematic bias in spatial networks where individual nodes represent different shares on a spherical surface, and we describe a strategy for correcting for this effect. Moreover, we illustrate the application of the mentioned edge directionality properties to different examples of real-world spatial networks in spherical geometry (with or without the geometric correction depending on each specific case), including functional climate networks, transportation, and trade networks. In climate networks, our approach highlights relevant patterns, such as large-scale circulation cells, the El Niño–Southern Oscillation, and the Atlantic Niño. In an air transportation network, we are able to characterize distinct air transportation zones, while we confirm the important role of the European Union for the global economy by identifying convergent edge directionality patterns in the world trade network.

The aim of this article is to improve knowledge about how directionality is implemented in transformative innovation policy and mission-oriented innovation policy. Academic literature conceptualizes attention to societal challenges as the directionality of innovation systems. Directionality requires an opening-up to include actors from the demand side of innovation processes. But this opening-up raises questions about who determines the direction of transformative change. In Sweden, transformative innovation policy has taken the form of strategic innovation programmes. A case study of one programme, Internet of Things Sweden, provides the opportunity to examine how directionality is implemented. The analysis shows how a focus on demand articulation made it possible to avoid making decisions about the direction of change. Innovation projects that mimicked public procurement limited the potential for radical transformative change. However, policy layering was an enabling factor at the urban level, where regional innovation actors facilitated the participation of urban infrastructure companies. ; Funding: Vinnova; Swedish Innovation Agency

Abstract
Literature on mission-specific innovation systems (MIS) highlights the crucial role of directionality when achieving sustainability transitions, while diversity literature emphasizes the need to keep diverse directions open. Like directionality, diversity is created by innovation system actors to tackle the complex and uncertain nature of transitions. While these two literature strands are presented largely independent of one another, both are deemed necessary to achieve sociotechnical transitions. We thus aim to uncover how diversity and directionality unfold in parallel in a MIS. We conduct a qualitative single-case study of the Wageningen alternative protein ecosystem to provide insights into the types of sociotechnological trajectories actors pursue and how different selection environments shape the development of each solution. We observe a mission exhibiting a clear direction toward (meat) substitutes. Underlying this mission, diversity is visible. We propose that the interplay between diversity and directionality in a MIS can be best understood by distinguishing two different sociotechnical "levels" in which they play out: the levels of transition paths ("first-order" directionality) and search directions ("second-order" directionality). We therefore call for a more nuanced understanding of the role of diversity and directionality in transitions.

We propose an approach based on a local Hilbert transform to design non-Hermitian potentials generating arbitrary vector fields of directionality, p→(r→), with desired shapes and topologies. We derive a local Hilbert transform to systematically build such potentials by modifying background potentials (being either regular or random, extended or localized). We explore particular directionality fields, for instance in the form of a focus to create sinks for probe fields (which could help to increase absorption at the sink), or to generate vortices in the probe fields. Physically, the proposed directionality fields provide a flexible mechanism for dynamical shaping and precise control over probe fields leading to novel effects in wave dynamics. ; NATO SPS Research Grant[985048] ; Ministerio de Ciencia e Innovación ; Türkiye Bilimler Akademisi ; Spanish Ministerio de Ciencia e Innovacion[FIS2015-65998-C2-1-P] ; European Union FEDER[FIS2015-65998-C2-1-P] ; Erasmus Mundus Doctorate Program Europhotonics[159224-1-2009-1-FR-ERA MUNDUS-EMJD]