Statistical Mechanics of 2+1 Gravity From Riemann Zeta Function and Alexander Polynomial:Exact Results

In the recent publication (Journal of Geometry and Physics,33(2000)23-102) we demonstrated that dynamics of 2+1 gravity can be described in terms of train tracks. Train tracks were introduced by Thurston in connection with description of dynamics of surface automorphisms. In this work we provide an example of utilization of general formalism developed earlier. The complete exact solution of the model problem describing equilibrium dynamics of train tracks on the punctured torus is obtained. Being guided by similarities between the dynamics of 2d liquid crystals and 2+1 gravity the partition function for gravity is mapped into that for the Farey spin chain. The Farey spin chain partition function, fortunately, is known exactly and has been thoroughly investigated recently. Accordingly, the transition between the pseudo-Anosov and the periodic dynamic regime (in Thurston's terminology) in the case of gravity is being reinterpreted in terms of phase transitions in the Farey spin chain whose partition function is just a ratio of two Riemann zeta functions. The mapping into the spin chain is facilitated by recognition of a special role of the Alexander polynomial for knots/links in study of dynamics of self homeomorphisms of surfaces. At the end of paper, using some facts from the theory of arithmetic hyperbolic 3-manifolds (initiated by Bianchi in 1892), we develop systematic extension of the obtained results to noncompact Riemannian surfaces of higher genus. Some of the obtained results are also useful for 3+1 gravity. In particular, using the theorem of Margulis, we provide new reasons for the black hole existence in the Universe: black holes make our Universe arithmetic. That is the discrete Lie groups of motion are arithmetic.Comment: 69 pages,11 figures. Journal of Geometry and Physics (in press

A Usability Study of E-book Platforms

While e-books offer great potential for academic libraries, research has shown that usability issues can prevent readers from reading e-books or from using certain ebook functions. This study presents the results of usability testing on the platforms of three of the largest aggregators of academic e-books: ebrary, MyiLibrary, and Ebook Library. In addition to learning about the usability of these specific platforms, this research provides greater insight into the usability issues that students encounter while reading e-books and a deeper understanding of how e-books can meet the academic needs of students. Five undergraduate and five graduate students participated in testing, completing a series of tasks in each platform. Testing revealed several usability issues. Students want flexible navigational options, including the ability to scroll. Additionally, students enjoy certain e-book features, such as annotation and highlighting tools, but they were not sure that they would use these tools

Multi-temperature state-dependent equivalent circuit discharge model for lithium-sulfur batteries

Lithium-sulfur (Li-S) batteries are described extensively in the literature, but existing computational models aimed at scientific understanding are too complex for use in applications such as battery management. Computationally simple models are vital for exploitation. This paper proposes a non-linear state-of-charge dependent Li-S equivalent circuit network (ECN) model for a Li-S cell under discharge. Li-S batteries are fundamentally different to Li-ion batteries, and require chemistry-specific models. A new Li-S model is obtained using a ‘behavioural’ interpretation of the ECN model; as Li-S exhibits a ‘steep’ open-circuit voltage (OCV) profile at high states-of-charge, identification methods are designed to take into account OCV changes during current pulses. The prediction-error minimization technique is used. The model is parameterized from laboratory experiments using a mixed-size current pulse profile at four temperatures from 10 °C to 50 °C, giving linearized ECN parameters for a range of states-of-charge, currents and temperatures. These are used to create a nonlinear polynomial-based battery model suitable for use in a battery management system. When the model is used to predict the behaviour of a validation data set representing an automotive NEDC driving cycle, the terminal voltage predictions are judged accurate with a root mean square error of 32 mV

Transcription-Independent Heritability of Induced Histone Modifications in the Mouse Preimplantation Embryo

Enzyme-catalyzed, post-translational modifications of core histones have been implicated in the complex changes in gene expression that drive early mammalian development. However, until recently the small number of cells available from the preimplantation embryo itself has prevented quantitative analysis of histone modifications at key regulator genes. The possible involvement of histone modifications in the embryo's response to extracellular signals, or as determinants of cell fate or lineage progression, remains unclear. Here we describe the use of a recently-developed chromatin immunoprecipitation technique (CChIP) to assay histone modification levels at key regulator genes (Pou5f1, Nanog, Cdx2, Hoxb1, Hoxb9) as mouse embryos progress from 8-cell to blastocyst in culture. Only by the blastocyst stage, when the embryonic (Inner Cell Mass) and extra-embryonic (Trophoblast) lineages are compared, do we see the expected association between histone modifications previously linked to active and silent chromatin, and transcriptional state. To explore responses to an environmental signal, we exposed embryos to the histone deacetylase inhibitor, anti-epileptic and known teratogen valproic acid (VPA), during progression from 8-cell to morula stage. Such treatment increased H4 acetylation and H3 lysine 4 methylation at the promoters of Hoxb1 and Hoxb9, but not the promoters of Pou5f1, Nanog,Cdx2 or the housekeeping gene Gapdh. Despite the absence of detectable Hoxb transcription, these VPA-induced changes were heritable, following removal of the inhibitor, at least until the blastocyst stage. The selective hyperacetylation of Hoxb promoters in response to a histone deacetylase inhibitor, suggests that Hox genes have a higher turnover of histone acetates than other genes in the preimplantation embryo. To explain the heritability, through mitosis, of VPA-induced changes in histone modification at Hoxb promoters, we describe how an epigenetic feed-forward loop, based on cross-talk between H3 acetylation and H3K4 methylation, might generate a persistently increased steady-state level of histone acetylation in response to a transient signal