Combinatorics of tropical Hurwitz cycles

We study properties of the tropical double Hurwitz loci defined by Bertram, Cavalieri and Markwig. We show that all such loci are connected in codimension one. If we mark preimages of simple ramification points, then for a generic choice of such points the resulting cycles are weakly irreducible, i.e. an integer multiple of an irreducible cycle. We study how Hurwitz cycles can be written as divisors of rational functions and show that they are numerically equivalent to a tropical version of a representation as a sum of boundary divisors. The results and counterexamples in this paper were obtained with the help of a-tint, an extension for polymake for tropical intersection theory.Comment: 29 pages, 16 figures. Minor revisions, to appear in Journal of Algebraic Combinatoric

Russula vinosoflavescens sp. nov., from deciduous forests of Northern Alsace, France

Based on morphological, molecular, and ecological data, a new species of Russula sect. Russula, found on several occasions under deciduous trees in Northern Alsace is described and illustrated as: Russula vinosoflavescens, belonging to R. subsect. Sardoninae

Moduli spaces of rational weighted stable curves and tropical geometry

We study moduli spaces of rational weighted stable tropical curves, and their connections with the classical Hassett spaces. Given a vector w of weights, the moduli space of tropical w-stable curves can be given the structure of a balanced fan if and only if w has only heavy and light entries. In this case, we can express the moduli space as the Bergman fan of a graphic matroid. Furthermore, we realize the tropical moduli space as a geometric tropicalization, and as a Berkovich skeleton, of the classical moduli space. This builds on previous work of Tevelev, Gibney--Maclagan, and Abramovich--Caporaso--Payne. Finally, we construct the moduli spaces of heavy/light weighted tropical curves as fiber products of unweighted spaces, and explore parallels with the algebraic world.Comment: 26 pages, 8 TikZ figures. v3: Minor changes and corrections. Final version to appear in Forum of Mathematics, Sigm

Rationality as the Therapy of Self-Liberation in Spinoza's Ethics

A given statement may be plausible, well founded or true. An individual action may be judged courageous, useful or good. Human beings are judged as well, for statements or actions that invite such evaluations, though the terms used may be different: a person may be described as truthful and virtuous, clever and happy. Epistemology and ethics - the theories that justify theoretical and practical judgements - may address not only the criteria used to assess states of belief, assertions, knowledge and the like, actions, omissions and feelings, but also the people that give rise to them. Nowadays, the issue of when and how a human being becomes clever, truthful, good or happy is less a matter of philosophy and more a question for religion, psychology and pedagogy. This has not always been the case. There has been a perceptible shift in moral philosophy: in antiquity, inquiries as to when a life is to be classified as good or happy were prevalent; in the modern era, the focus is primarily on when an individual action is to be regarded as right or good, wrong or ba

More on the as-predicative: Granularity issues in the description of construction networks

Abstract Usage-based construction grammar needs to determine which schematizations are really supported by usage: Previous research on argumentstructure constructions with object-related complements has assumed overarching constructions with a formally underspecified component (Gries et al. 2005, 2010; Gonzalvez-Garcia 2009). These schematize over a number of formally different subconstructions. It has been shown, however, that paying attention to the formally different realisations of a constructional component may bring out the functional differential between subconstructions which are closely related within a construction network (Hampe 2011a). Based on the data used by Gries and colleagues (2010), this paper presents a fine-grained collostruction analysis of the as-predicative as a network of tightly related subconstructions and checks whether there is a functional difference between the subconstructions with nominal and adjectival as-complements. It is shown that the extended uses of the construction sketched out by Gries et al. (2005) are licensed by the subconstruction with nominal as-complement, rather than present a property of the overarching, most general pattern. Beyond this, the present paper locates the as-predicative within the network of all argument-structure constructions with phrasal object-related complements. In this context, it also discusses under which conditions the occurrence of a specific verb as a collexeme of more than one argument-structure construction can be seen as a verb-specific constructeme uniting several allostructions (Capelle 2006)