On Cyclic Edge-Connectivity of Fullerenes

A graph is said to be cyclic $k$-edge-connected, if at least $k$ edges must be removed to disconnect it into two components, each containing a cycle. Such a set of $k$ edges is called a cyclic-$k$-edge cutset and it is called a trivial cyclic-$k$-edge cutset if at least one of the resulting two components induces a single $k$-cycle. It is known that fullerenes, that is, 3-connected cubic planar graphs all of whose faces are pentagons and hexagons, are cyclic 5-edge-connected. In this article it is shown that a fullerene $F$ containing a nontrivial cyclic-5-edge cutset admits two antipodal pentacaps, that is, two antipodal pentagonal faces whose neighboring faces are also pentagonal. Moreover, it is shown that $F$ has a Hamilton cycle, and as a consequence at least $15\cdot 2^{\lfloor \frac{n}{20}\rfloor}$ perfect matchings, where $n$ is the order of $F$.Comment: 11 pages, 9 figure

The rigidity of periodic body-bar frameworks on the three-dimensional fixed torus

We present necessary and sufficient conditions for the generic rigidity of body-bar frameworks on the three-dimensional fixed torus. These frameworks correspond to infinite periodic body-bar frameworks in $\mathbb{R}^3$ with a fixed periodic lattice.Comment: 31 pages, 12 figure

Stoics on the Differentiation of Character

I will show that Stoic writers were perfectly capable of distinguishing among character-types also according to secondary differentia that can be exhibited independently of one another and in greater or lesser degree. Just as one may observe variations in the sea floor without disregarding the fact that all of it is equally underwater, so Stoic theory defines traits of character which differentiate one individual from another even where all concerned have the same overall moral standing. Such secondary characteristics are identified even among the virtuous; more numerous, however, and also more philosophically interesting, are the character traits of the nonvirtuous— that is to say, of ordinary flawed individuals. For it is these that we have to deal with in ourselves and others we know. In looking at these traits of character I am especially interested in two questions. First, there is a question about how traits work as causes of emotion and of actions generally. Surviving reports make it clear that at least some traits—those called nosëmata, “sicknesses,” and arrôstëmata, “infirmities”— are defined as erroneous beliefs about the value of certain objects. It is not difficult to show that where these traits are concerned, the work of the trait in determining action and feeling is a matter of the logical operation of the corresponding proposition in the agent’s practical reasoning. For another group of traits, called “proclivities,” the evidence is less clear; I hope to show, however, that an analogous interpretation in terms of belief is plausible for these as well. This is not to deny that proclivities such as irascibility may also have a material basis, say in one’s body type or mix of constitutive humors; indeed, we should expect that every trait of character will be describable in material as well as intentionalist terms. But it is as beliefs, i.e. as corresponding to particular premises in the practical syllogism, that traits exercise their determinative capacity

The Dregs of Romulus. Stoic Philosophy in Cicero’s Pro Murena and De Oratore

The dregs of Romulus reviews the evidence for Cicero’s attitude toward Stoic philosophy in the speech pro Murena, in letters of 61-60 referring to Cato, and in de oratore. None of these texts expresses any direct opposition to the core postulate of Stoic ethics, viz., that only what is honorable is good for a human being. What we do find in this group of works is a concern that adherence to a dogmatic system of ethics (1) impedes political communication, and (2) strips away the flexibility of application that is required for moral decision-making in complex situations. Cicero’s own stance as a philosophically trained politician is defined accordingly. The dregs of Romulus examine la preuve de l’attitude de Cicéron à l’égard de la philosophie stoïcienne dans le discours pro Murena, dans des lettres de 61 à 60 se référant à Caton et au de Oratore. Aucun de ces textes n’exprime une opposi-tion directe au postulat de base de l’éthique stoïcienne, à savoir que seul ce qui est honorable est bon pour un être humain. Ce que nous trouvons dans ce groupe d’oeuvres est une préoccupation selon laquelle l’adhésion à un système dogma-tique d’éthique (1) entrave la communication politique, et (2) écarte la flexibilité d’application requise pour la prise de décision morale dans des situations com-plexes. La position de Cicéron en tant que politicien philosophiquement formé est définie en conséquence.

The role of B cells in giant cell arteritis and polymyalgia rheumatica

Giant cell arteritis (GCA) is an inflammatory vascular disease (vasculitis) affecting cranial arteries, aorta and its major branches in people older than 50 years of age. GCA frequently overlaps with polymyalgia rheumatica (PMR) which is characterized by inflammation of the shoulder- and hip girdle. Despite immunosuppressive treatment with glucocorticoids (GC), inflammation often persists in these diseases necessitating long-term treatment with considerable side effects (GC toxicity). Novel and improved treatment options are therefore highly needed. Research on the immunopathogenesis of GCA/PMR has been focussed on T cells and macrophages. The B cells have long been neglected due to the lack of specific auto-antibodies and the limited presence of B cells in temporal artery biopsies. Beside differentiating into antibody secreting cells, B cells can also contribute to autoimmune diseases via pro-inflammatory cytokine production. This thesis aimed to explore the role of B cells in the pathogenesis of GCA and PMR with a focus on cytokine production. We propose a disease model where B cells contribute to disease by fuelling inflammation. This is based on observation of infiltrating B cells which organize into tertiary lymphoid structures (TLOs) in affected arteries, especially the aorta. These B cells can produce chemokines and cytokines. After in vitro stimulation circulating B cells also produce several pro-inflammatory cytokines which are capable of polarizing macrophages towards a pro-inflammatory and tissue destructive phenotype. Our findings suggest that B cells might be an interesting target for treatment to interfere with disease chronicity in patients with GCA/PMR