Generic ordering of structural transitions in quasi-one-dimensional Wigner crystals

We investigate the dependence of the structural phase transitions in an infinite quasi-one-dimensional system of repulsively interacting particles on the profile of the confining channel. Three different functional expressions for the confinement potential related to real experimental systems are used that can be tuned continuously from a parabolic to a hard-wall potential in order to find a thorough understanding of the ordering of the chain-like structure transitions. We resolve the longstanding issue why the most theories predicted a 1-2-4-3-4 sequence of chain configurations with increasing density, while some experiments found the 1-2-3-4 sequence.Comment: 7 pages, 5 figure

ALMA observations of TiO2_2 around VY Canis Majoris

Titanium dioxide, TiO$_2$, is a refractory species that could play a crucial role in the dust-condensation sequence around oxygen-rich evolved stars. To date, gas phase TiO$_2$ has been detected only in the complex environment of the red supergiant VY CMa. We aim to constrain the distribution and excitation of TiO$_2$ around VY CMa in order to clarify its role in dust formation. We analyse spectra and channel maps for TiO$_2$ extracted from ALMA science verification data. We detect 15 transitions of TiO$_2$, and spatially resolve the emission for the first time. The maps demonstrate a highly clumpy, anisotropic outflow in which the TiO$_2$ emission likely traces gas exposed to the stellar radiation field. A roughly east-west oriented, accelerating bipolar-like structure is found, of which the blue component runs into and breaks up around a solid continuum component. A distinct tail to the south-west is seen for some transitions, consistent with features seen in the optical and near-infrared. We find that a significant fraction of TiO$_2$ remains in the gas phase outside the dust-formation zone and suggest that this species might play only a minor role in the dust-condensation process around extreme oxygen-rich evolved stars like VY CMa.Comment: Accepted for publication in Astronomy & Astrophysics, 25 pages, 20 figure

Metabolic constraints on the evolution of genetic codes: Did multiple 'preaerobic' ecosystem transitions entrain richer dialects via Serial Endosymbiosis?

A mathematical model based on Tlusty's topological deconstruction suggests that multiple punctuated ecosystem shifts in available metabolic free energy, broadly akin to the 'aerobic' transition, enabled a punctuated sequence of increasingly complex genetic codes and protein translators under mechanisms similar to the Serial Endosymbiosis effecting the Eukaryotic transition. These evolved until the ancestor to the present narrow spectrum of nearly maximally robust codes became locked-in by path dependence

`The frozen accident' as an evolutionary adaptation: A rate distortion theory perspective on the dynamics and symmetries of genetic coding mechanisms

We survey some interpretations and related issues concerning the frozen hypothesis due to F. Crick and how it can be explained in terms of several natural mechanisms involving error correction codes, spin glasses, symmetry breaking and the characteristic robustness of genetic networks. The approach to most of these questions involves using elements of Shannon's rate distortion theory incorporating a semantic system which is meaningful for the relevant alphabets and vocabulary implemented in transmission of the genetic code. We apply the fundamental homology between information source uncertainty with the free energy density of a thermodynamical system with respect to transcriptional regulators and the communication channels of sequence/structure in proteins. This leads to the suggestion that the frozen accident may have been a type of evolutionary adaptation

Statistical mechanical analysis of a hierarchical random code ensemble in signal processing

We study a random code ensemble with a hierarchical structure, which is closely related to the generalized random energy model with discrete energy values. Based on this correspondence, we analyze the hierarchical random code ensemble by using the replica method in two situations: lossy data compression and channel coding. For both the situations, the exponents of large deviation analysis characterizing the performance of the ensemble, the distortion rate of lossy data compression and the error exponent of channel coding in Gallager's formalism, are accessible by a generating function of the generalized random energy model. We discuss that the transitions of those exponents observed in the preceding work can be interpreted as phase transitions with respect to the replica number. We also show that the replica symmetry breaking plays an essential role in these transitions.Comment: 24 pages, 4 figure

A Rate Distortion approach to protein symmetry

A spontaneous symmetry breaking argument is applied to the problem of protein form, via a Rate Distortion analysis of the relation between genome coding and the final condensation of the protein 'molten globule'. The Rate Distortion Function, under coding constraints, serves as a temperature analog, so that low values act to drive proteins to simple symmetries. The Rate Distortion Function itself is significantly constrained by the availability of metabolic free energy. This work extends Tlusty's (2007) elegant exploration of the evolution of the genetic code, suggesting that rate distortion considerations may play a critical role across a broad spectrum of molecular expressions of evolutionary process

Roman roads: The hierarchical endosymbiosis of cognitive modules

Serial endosymbiosis theory provides a unifying paradigm for examining the interaction of cognitive modules at vastly different scales of biological, social, and cultural organization. A trivial but not unimportant model associates a dual information source with a broad class of cognitive processes, and punctuated phenomena akin to phase transitions in physical systems, and associated coevolutionary processes, emerge as consequences of the homology between information source uncertainty and free energy density. The dynamics, including patterns of punctuation similar to ecosystem resilience transitions, are large dominated by the availability of 'Roman roads' constituting channels for the transmission of information between modules