The whole and its parts : why and how to disentangle plant communities and synusiae in vegetation classification

Most plant communities consist of different structural and ecological subsets, ranging from cryptogams to different tree layers. The completeness and approach with which these subsets are sampled have implications for vegetation classification. Non‐vascular plants are often omitted or sometimes treated separately, referring to their assemblages as “synusiae” (e.g. epiphytes on bark, saxicolous species on rocks). The distinction of complete plant communities (phytocoenoses or holocoenoses) from their parts (synusiae or merocoenoses) is crucial to avoid logical problems and inconsistencies of the resulting classification systems. We here describe theoretical differences between the phytocoenosis as a whole and its parts, and outline consequences of this distinction for practise and terminology in vegetation classification. To implement a clearer separation, we call for modifications of the International Code of Phytosociological Nomenclature and the EuroVegChecklist. We believe that these steps will make vegetation classification systems better applicable and raise the recognition of the importance of non‐vascular plants in the vegetation as well as their interplay with vascular plants

The Historical Context of the Gender Gap in Mathematics

This chapter is based on the talk that I gave in August 2018 at the ICM in Rio de Janeiro at the panel on "The Gender Gap in Mathematical and Natural Sciences from a Historical Perspective". It provides some examples of the challenges and prejudices faced by women mathematicians during last two hundred and fifty years. I make no claim for completeness but hope that the examples will help to shed light on some of the problems many women mathematicians still face today

Clinical course, therapeutic responses and outcomes in relapsing MOG antibody-associated demyelination.

Abstract OBJECTIVE: We characterised the clinical course, treatment and outcomes in 59 patients with relapsing myelin oligodendrocyte glycoprotein (MOG) antibody-associated demyelination. METHODS: We evaluated clinical phenotypes, annualised relapse rates (ARR) prior and on immunotherapy and Expanded Disability Status Scale (EDSS), in 218 demyelinating episodes from 33 paediatric and 26 adult patients. RESULTS: The most common initial presentation in the cohort was optic neuritis (ON) in 54% (bilateral (BON) 32%, unilateral (UON) 22%), followed by acute disseminated encephalomyelitis (ADEM) (20%), which occurred exclusively in children. ON was the dominant phenotype (UON 35%, BON 19%) of all clinical episodes. 109/226 (48%) MRIs had no brain lesions. Patients were steroid responsive, but 70% of episodes treated with oral prednisone relapsed, particularly at doses <10\u2009mg daily or within 2 months of cessation. Immunotherapy, including maintenance prednisone (P=0.0004), intravenous immunoglobulin, rituximab and mycophenolate, all reduced median ARRs on-treatment. Treatment failure rates were lower in patients on maintenance steroids (5%) compared with non-steroidal maintenance immunotherapy (38%) (P=0.016). 58% of patients experienced residual disability (average follow-up 61 months, visual loss in 24%). Patients with ON were less likely to have sustained disability defined by a final EDSS of 652 (OR 0.15, P=0.032), while those who had any myelitis were more likely to have sustained residual deficits (OR 3.56, P=0.077). CONCLUSION: Relapsing MOG antibody-associated demyelination is strongly associated with ON across all age groups and ADEM in children. Patients are highly responsive to steroids, but vulnerable to relapse on steroid reduction and cessation

Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond

Many historians of the calculus deny significant continuity between infinitesimal calculus of the 17th century and 20th century developments such as Robinson's theory. Robinson's hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, Robinson regards Berkeley's criticisms of the infinitesimal calculus as aptly demonstrating the inconsistency of reasoning with historical infinitesimal magnitudes. We argue that Robinson, among others, overestimates the force of Berkeley's criticisms, by underestimating the mathematical and philosophical resources available to Leibniz. Leibniz's infinitesimals are fictions, not logical fictions, as Ishiguro proposed, but rather pure fictions, like imaginaries, which are not eliminable by some syncategorematic paraphrase. We argue that Leibniz's defense of infinitesimals is more firmly grounded than Berkeley's criticism thereof. We show, moreover, that Leibniz's system for differential calculus was free of logical fallacies. Our argument strengthens the conception of modern infinitesimals as a development of Leibniz's strategy of relating inassignable to assignable quantities by means of his transcendental law of homogeneity.Comment: 69 pages, 3 figure

On the relations between historical epistemology and students’ conceptual developments in mathematics

There is an ongoing discussion within the research field of mathematics education regarding the utilization of the history of mathematics within mathematics education. In this paper we consider problems that may emerge when the historical epistemology of mathematics is paralleled to students’ conceptual developments in mathematics. We problematize this attempt to link the two fields on the basis of Grattan-Guinness’ distinction between “history” and “heritage”. We argue that when parallelism claims are made, history and heritage are often mixed up, which is problematic since historical mathematical definitions must be interpreted in its proper historical context and conceptual framework. Furthermore, we argue that cultural and local ideas vary at different time periods, influencing conceptual developments in different directions regardless of whether historical or individual developments are considered, and thus it may be problematic to uncritically assume a platonic perspective. Also, we have to take into consideration that an average student of today and great mathematicians of the past are at different cognitive levels

Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc

Densification of Fresh Concrete by Microwave

Concrete mixes with different fly ash replacement levels, namely 0%, 35% and 55% at a fixed water to binder ratio (W/B) of 0.6 were heated by a tailor-made microwave oven up to 50oC immediately after casting until initial setting in order to remove excessive free water. The compressive strengths of microwave densified samples after 7 days were 3.2%, 7.7% and 29.6% higher than those of oven heated batches. It demonstrated that higher density, lower water absorption and better microstructure were achieved after microwave heating, indicating microwave heating can be a promising technique for densifying fresh concrete

Dynamic coordination in brain and mind

Our goal here is to clarify the concept of 'dynamic coordination', and to note major issues that it raises for the cognitive neurosciences. In general, coordinating interactions are those that produce coherent and relevant overall patterns of activity, while preserving the essential individual identities and functions of the activities coordinated. 'Dynamic coordination' is the coordination that is created on a moment-by-moment basis so as to deal effectively with unpredictable aspects of the current situation. We distinguish different computational goals for dynamic coordination, and outline issues that arise concerning local cortical circuits, brain systems, cognition, and evolution. Our focus here is on dynamic coordination by widely distributed processes of self-organisation, but we also discuss the role of central executive processes