Discrete structures in continuum descriptions of defective crystals

I discuss various mathematical constructions that combine together to provide a natural setting for discrete and continuum geometric models of defective crystals. In particular I provide a quite general list of `plastic strain variables', which quantifies inelastic behaviour, and exhibit rigorous connections between discrete and continuous mathematical structures associated with crystalline materials that have a correspond-ingly general constitutive specification

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

Stochastic tuning of gene expression enables cellular adaptation in the absence of pre-existing regulatory circuitry

Cells adapt to familiar changes in their environment by activating predefined regulatory programs that establish adaptive gene expression states. These hard-wired pathways, however, may be inadequate for adaptation to environments never encountered before. Here, we reveal evidence for an alternative mode of gene regulation that enables adaptation to adverse conditions without relying on external sensory information or genetically predetermined cis-regulation. Instead, individual genes achieve optimal expression levels through a stochastic search for improved fitness. By focusing on improving the overall health of the cell, the proposed stochastic tuning mechanism discovers global gene expression states that are fundamentally new and yet optimized for novel environments. We provide experimental evidence for stochastic tuning in the adaptation of Saccharomyces cerevisiae to laboratory-engineered environments that are foreign to its native gene-regulatory network. Stochastic tuning operates locally at individual gene promoters, and its efficacy is modulated by perturbations to chromatin modification machinery

Density functional theory

Density functional theory (DFT) finds increasing use in applications related to biological systems. Advancements in methodology and implementations have reached a point where predicted properties of reasonable to high quality can be obtained. Thus, DFT studies can complement experimental investigations, or even venture with some confidence into experimentally unexplored territory. In the present contribution, we provide an overview of the properties that can be calculated with DFT, such as geometries, energies, reaction mechanisms, and spectroscopic properties. A wide range of spectroscopic parameters is nowadays accessible with DFT, including quantities related to infrared and optical spectra, X-ray absorption and Mössbauer, as well as all of the magnetic properties connected with electron paramagnetic resonance spectroscopy except relaxation times. We highlight each of these fields of application with selected examples from the recent literature and comment on the capabilities and limitations of current methods