The challenges of purely mechanistic models in biology and the minimum need for a 'mechanism-plus-X' framework

Ever since the advent of molecular biology in the 1970s, mechanical models have become the dogma in the field, where a "true" understanding of any subject is equated to a mechanistic description. This has been to the detriment of the biomedical sciences, where, barring some exceptions, notable new feats of understanding have arguably not been achieved in normal and disease biology, including neurodegenerative disease and cancer pathobiology. I argue for a "mechanism-plus-X" paradigm, where mainstay elements of mechanistic models such as hierarchy and correlation are combined with nomological principles such as general operative rules and generative principles. Depending on the question at hand and the nature of the inquiry, X could range from proven physical laws to speculative biological generalizations, such as the notional principle of cellular synchrony. I argue that the "mechanism-plus-X" approach should ultimately aim to move biological inquiries out of the deadlock of oft-encountered mechanistic pitfalls and reposition biology to its former capacity of illuminating fundamental truths about the world

The old linguistic problem of 'reference' in a modern reading of Plato's Sophist

This paper is about interpreting the aim of Plato's Sophist in a linguistic framework and arguing that in its attempt at resolving the conundrum of what the true meaning and essence of the word "sophist" could be, it resembles a number of themes encountered in contemporary linguistics. I think it is important to put our findings from the Sophist in a broader Platonic context: in other words, I assume—I think not too unreasonably—that Plato pursued (or at least had in mind) a number of overall projects ('OP' for short) throughout some or most of the dialogues, while each one of the dialogues would in addition have more specific projects ('SP') as part of its individual blueprint. To be sure, the OPs, if they actually existed, might have evolved from the earlier-written to later dialogues, but their foundational premises should have remained intact. In Section A, I provide evidence for reading the Sophist on a linguistic basis. In Section B, I focus on two OPs that I think are relevant to our discussion, one having to do with language and meaning acquisition, and the second concerning the "mind" or a "thought faculty". Ultimately, in Section C, I will use the OPs to contextualise two (related) SPs in the Sophist: (i) identifying cases of intentional referrals for names versus (ii) identifying internal references when searching for word meanings without particular referable instances. At the end of this section, I will draw close parallels between this interpretation of the dialogue and a congruous project of modern 'generative' linguistics

Edge Clique Cover of Claw-free Graphs

The smallest number of cliques, covering all edges of a graph $G$, is called the (edge) clique cover number of $G$ and is denoted by $cc(G)$. It is an easy observation that for every line graph $G$ with $n$ vertices, $cc(G)\leq n$. G. Chen et al. [Discrete Math. 219 (2000), no. 1--3, 17--26; MR1761707] extended this observation to all quasi-line graphs and questioned if the same assertion holds for all claw-free graphs. In this paper, using the celebrated structure theorem of claw-free graphs due to Chudnovsky and Seymour, we give an affirmative answer to this question for all claw-free graphs with independence number at least three. In particular, we prove that if $G$ is a connected claw-free graph on $n$ vertices with $\alpha(G)\geq 3$, then $cc(G)\leq n$ and equality holds if and only if $G$ is either the graph of icosahedron, or the complement of a graph on $10$ vertices called twister or the $p^{th}$ power of the cycle $C_n$, for $1\leq p \leq \lfloor (n-1)/3\rfloor$.Comment: 74 pages, 4 figure