Cosmological Time in (2+1) - Gravity

We consider maximal globally hyperbolic flat (2+1) spacetimes with compact space S of genus g>1. For any spacetime M of this type, the length of time that the events have been in existence is M defines a global time, called the cosmological time CT of M, which reveals deep intrinsic properties of spacetime. In particular, the past/future asymptotic states of the cosmological time recover and decouple the linear and the translational parts of the ISO(2,1)-valued holonomy of the flat spacetime. The initial singularity can be interpreted as an isometric action of the fundamental group of S on a suitable real tree. The initial singularity faithfully manifests itself as a lack of smoothness of the embedding of the CT level surfaces into the spacetime M. The cosmological time determines a real analytic curve in the Teichmuller space of Riemann surfaces of genus g, which connects an interior point (associated to the linear part of the holonomy) with a point on Thurston's natural boundary (associated to the initial singularity).Comment: Totally new version with strongly improved exposition. Clarifying examples and figures have been included. 21 pages, Latex, 9 figure

The Effect of Inkjet Ink Composition on Rheology And Jetting Behaviour

This work presents recent results on the way linear and non linear viscoelastic properties of the fluids affect the jetting mechanism. Recent progress on quantitative characterising both high frequency linear (LVE) and non-linear (NLVE) viscoelasticity of fluids allows fluids to be assessed for their jettability before using such materials in a DoD print head. In term of linear viscoelastic measurements, the Piezo Axial Vibrator (PAV) was used to probe the rheology of the fluids on a frequency range between 10Hz and 10000Hz. A filament stretching apparatus, called the “Cambridge Trimaster”, was used in combination with high speed cinematography, to characterize the fluids high speed stretching and break-up behaviour. The series of fluids investigated here consist in dilutions of mono disperse polystyrene with different molecular weight (110, 210, 306 and 488 kg/mol respectively) diluted in diethyl phthalate. The choice of polymer weights and concentrations were chosen to match both the complex viscosity and the LVE. However, non linear rheological data experiments exhibit differences in the fluid relaxation time and filament break-up mechanism. Ultra-high speed cinematography of DoD jetting events were correlated with filament break-up experiments and demonstrated that fluid rheology provides valuable information on the jetting quality of the fluids

Timescale uncertainty of abrupt events in the geologic record arising from unsteady sedimentation

Defining the time scale of abrupt events in the stratigraphic record is a primary goal of high-resolution paleoclimate analysis. A significant hurdle in this endeavor is that abrupt, i.e., millennial and submillennial, events in deep time can rarely be temporally constrained accurately owing to the typical absence of high-precision age control at the scale of the events. Instead, the duration of abrupt events is commonly estimated via the linear partitioning of time between age control points (e.g., defined using astronomical cycles or radiometric dates) that bracket the event and span longer time intervals. The flaw with this approach is that sedimentation is an unsteady process and does not proceed linearly with time. Here a numerical model, parameterized by geologic data, is used to quantify theoretical time-scale uncertainties that result from unsteady sedimentation. This work demonstrates that the duration of assumed millennial events estimated via a linear partitioning approach may be significantly in error, even in complete, astronomically calibrated and unbioturbated successions best suited to the study of abrupt paleoclimate change. The uncertainties established in this study are largely a function of the precise statistical properties of the sedimentation process, properties that are difficult to constrain empirically, particularly over short time spans. Nevertheless, this study illustrates how unsteady sedimentation sets an important limit on the attainable temporal resolution of the stratigraphic record, with consequent implications for defining accurately the rates and durations of rapid events in Earth history

Recurrence time analysis, long-term correlations, and extreme events

The recurrence times between extreme events have been the central point of statistical analyses in many different areas of science. Simultaneously, the Poincar\'e recurrence time has been extensively used to characterize nonlinear dynamical systems. We compare the main properties of these statistical methods pointing out their consequences for the recurrence analysis performed in time series. In particular, we analyze the dependence of the mean recurrence time and of the recurrence time statistics on the probability density function, on the interval whereto the recurrences are observed, and on the temporal correlations of time series. In the case of long-term correlations, we verify the validity of the stretched exponential distribution, which is uniquely defined by the exponent $\gamma$, at the same time showing that it is restricted to the class of linear long-term correlated processes. Simple transformations are able to modify the correlations of time series leading to stretched exponentials recurrence time statistics with different $\gamma$, which shows a lack of invariance under the change of observables.Comment: 9 pages, 7 figure

Translocation of polymers with folded configurations across nanopores

The transport of polymers with folded configurations across membrane pores is investigated theoretically by analyzing simple discrete stochastic models. The translocation dynamics is viewed as a sequence of two events: motion of the folded segment through the channel followed by the linear part of the polymer. The transition rates vary for the folded and linear segments because of different interactions between the polymer molecule and the pore. It is shown that the translocation time depends non-monotonously on the length of the folded segment for short polymers and weak external fields, while it becomes monotonous for long molecules and large fields. Also, there is a critical interaction between the polymers and the pore that separates two dynamic regimes. For stronger interactions the folded polymer moves slower, while for weaker interactions the linear chain translocation is the fastest. In addition, our calculations show that the folding does not change the translocation scaling properties of the polymer. These phenomena can be explained by the interplay between the translocation distances and transition rates for the folded and linear segments of the polymer. Theoretical results are applied for analysis of experimental translocations through solid-state nanopores.Comment: submitted to J. Chem. Phy

Sparsity-Promoting Bayesian Dynamic Linear Models

Sparsity-promoting priors have become increasingly popular over recent years due to an increased number of regression and classification applications involving a large number of predictors. In time series applications where observations are collected over time, it is often unrealistic to assume that the underlying sparsity pattern is fixed. We propose here an original class of flexible Bayesian linear models for dynamic sparsity modelling. The proposed class of models expands upon the existing Bayesian literature on sparse regression using generalized multivariate hyperbolic distributions. The properties of the models are explored through both analytic results and simulation studies. We demonstrate the model on a financial application where it is shown that it accurately represents the patterns seen in the analysis of stock and derivative data, and is able to detect major events by filtering an artificial portfolio of assets