Disjoint Genus-0 Surfaces in Extremal Graph Theory and Set Theory Lead To a Novel Topological Theorem

When an edge is removed, a cycle graph Cn becomes a n-1 tree graph. This observation from extremal set theory leads us to the realm of set theory, in which a topological manifold of genus-1 turns out to be of genus-0. Starting from these premises, we prove a theorem suggesting that a manifold with disjoint points must be of genus-0, while a manifold of genus-1 cannot encompass disjoint points.

Twistor spaces on foliated manifolds

The theory of twistors on foliated manifolds is developed. We construct the twistor space of the normal bundle of a foliation. It is demonstrated that the classical constructions of the twistor theory lead to foliated objects and permit to formulate and prove foliated versions of some well-known results on holomorphic mappings. Since any orbifold can be understood as the leaf space of a suitably defined Riemannian foliation we obtain orbifold versions of the classical results as a simple consequence of the results on foliated mappings.

Concentration in Seed and Biotech Markets: Extent, Causes, and Impacts

The merger of Dow and DuPont, the acquisition of Syngenta by ChemChina, and the acquisition of Monsanto by Bayer have recently reshaped the global seed and biotech industry and caused concern about growing market concentration. This review documents market concentration in seed and agricultural biotech markets and discusses its causes and impacts. The available evidence suggests that concentration in seed markets varies strongly by crop and by country, while markets for biotech traits are considerably more concentrated. Complementarities between seed, biotech, and crop protection chemicals explain much of the observed structural changes in the industry, and new complementarities may be emerging with digital agriculture. Although growing concentration might in theory lead to higher prices and less innovation, evidence on this is currently limited; this tendency is also in part offset by the remedies imposed by competition authorities.

Exponential Perturbative Expansions and Coordinate Transformations

We propose a unified approach for different exponential perturbation techniques used in the treatment of time-dependent quantum mechanical problems, namely the Magnus expansion, the Floquet–Magnus expansion for periodic systems, the quantum averaging technique, and the Lie–Deprit perturbative algorithms. Even the standard perturbation theory fits in this framework. The approach is based on carrying out an appropriate change of coordinates (or picture) in each case, and it can be formulated for any time-dependent linear system of ordinary differential equations. All of the procedures (except the standard perturbation theory) lead to approximate solutions preserving by construction unitarity when applied to the time-dependent Schrödinger equation.

Introduction

This chapter provides an overall introduction to the book. It outlines its methodological approach, explains the selection of authors, and sets out the case that will be argued. Central for the approach is the concept of Patristic philosophy meant to stem the traditional dualism of Christian thought and philosophy. Christian writers themselves are thus seen as philosophers. While Christian philosophy in this sense began in the second century, it obtains a distinctive shape at the end of the fourth century through the work of the Cappadocian fathers. The book recounts the history of this uniquely influential, classical theory. It is subsequently received but also modified and transformed. The history must represent the diversity of this development and cannot be restricted to Chalcedonian authors only. The tensions between the needs of the Christological controversy and the inherited Cappadocian theory lead to philosophical innovations that prepare much later developments.

A first time lesson study that turned into a learning study

Purpose The purpose of this paper is to present an implemented lesson study (LS) in English as a second language course for 11-year-old students in the fifth grade. The aim of the research lesson was to learn how to describe a person systematically. Design/methodology/approach Two LS cycles in two different classes were conducted and evaluated using systematic observation, case student interviews and student feedback. The data were analysed by the involved teacher team and the mentor. Findings The study shows that and how LS and variation theory promotes theory-based lesson preparation and postprocessing as well as team orientation among teachers without LS experience. Second, the lesson data show how elements of variation theory lead to a significant improvement in student learning activity. Originality/value This paper provides insights how teachers apply a first time LS and variation theory and how this effects student learning positively.

Idealism and Self-Authorship: A Note on Paul Kahn’s Making the Case

The article examines the notion of self-authorship through judicial review in Paul Kahn’s book Making the Case. It argues that, for Kahn, the primary function of the court is to bring the people to see the law as something they have themselves authored, and that we can only open up this dimension to study by looking at the universe of meaning to which the law makes reference. The article ties Kahn’s cultural analysis of law back to his earlier work on body politics in a liberal polity. It shows how law and culture intertwine in Kahn’s work, law being the same time a limit to and a product of culture. Finally, the article problematizes Kahn’s use of culture as a means to destabilize liberalism. It argues that, despite his avowed concern with liberty (which self-authorship translates into constitutional parlance), his efforts to transcend liberal theory lead him to adopt basic political conceptions that leave no room for liberty in political life.

Theoretical Analysis and Numerical Optimization of a Wearable Spring-Clutch Mechanism for Reducing Metabolic Energy Cost During Human Walking

There is a growing interest in assistive wearable devices for laden walking, with applications to civil hiking or military soldiers carrying heavy loads in outdoor rough terrains. While the solution of powered exoskeleton is known to be heavy and energy consuming, recent works presented wearable light-weight (semi-)passive elements based on elastic springs engaged by timed clutches. In this work, we theoretically study the dynamics of a five-link model of a human walker with point feet, using numerical simulations. We propose a novel mechanism of a spring and two triggered clutches, which enables locking the spring with stored energy while the device's length can change freely. For a given gait of joint angles trajectories, we numerically optimize the spring parameters and clutch timing for minimizing the metabolic energy cost. We show that a cleverly designed device can, in theory, lead to a drastic reduction in metabolic energy expenditure.

Adaptive benefits from small mutation supplies in an antibiotic resistance enzyme

Populations with large mutation supplies adapt via the “greedy” substitution of the fittest genotype available, leading to fast and repeatable short-term responses. At longer time scales, smaller mutation supplies may in theory lead to larger improvements when distant high-fitness genotypes more readily evolve from lower-fitness intermediates. Here we test for long-term adaptive benefits from small mutation supplies using in vitro evolution of an antibiotic-degrading enzyme in the presence of a novel antibiotic. Consistent with predictions, large mutant libraries cause rapid initial adaptation via the substitution of cohorts of mutations, but show later deceleration and convergence. Smaller libraries show on average smaller initial, but also more variable, improvements, with two lines yielding alleles with exceptionally high resistance levels. These two alleles share three mutations with the large-library alleles, which are known from previous work, but also have unique mutations. Replay evolution experiments and analyses of the adaptive landscape of the enzyme suggest that the benefit resulted from a combination of avoiding mutational cohorts leading to local peaks and chance. Our results demonstrate adaptive benefits from limited mutation supplies on a rugged fitness landscape, which has implications for artificial selection protocols in biotechnology and argues for a better understanding of mutation supplies in clinical settings.