Understanding singularities in Cartan's and NSF geometric structures

In this work we establish a relationship between Cartan's geometric approach to third order ODEs and the 3-dim Null Surface Formulation (NSF). We then generalize both constructions to allow for caustics and singularities that necessarily arise in these formalisms.Comment: 22 pages, 2 figure

Mixing Flows on Moduli Spaces of Flat Bundles over Surfaces

We extend Teichmueller dynamics to a flow on the total space of a flat bundle of deformation spaces of representations of the fundamental group of a fixed surface S in a Lie group G. The resulting dynamical system is a continuous version of the action of the mapping class group of S on the deformation space. We observe how ergodic properties of this action relate to this flow. When G is compact, this flow is strongly mixing over each component of the derormation space and of each stratum of the Teichmueller unit sphere bundle over the Riemann moduli space. We prove ergodicity for the analogous lift of the Weil-Petersson geodesic local. flow.Comment: 18 pages, no figures, presented at the Oxford conference honoring Nigel Hitchin's 70th birthday (9 September 2016) and to appear in the companion volume published by Oxford University Pres

Clinical review: Biomarkers of acute kidney injury: where are we now?

The recognition that acute kidney injury (AKI) is a significant independent risk factor for morbidity and mortality has resulted in a substantial number of publications over the past 5 years or more. In no small part these have, to a degree, highlighted the inadequacy of conventional markers of renal insufficiency in the acute setting. Much effort has been invested in the identification of early, specific AKI markers in order to aid early diagnosis of AKI and hopefully improve outcome. The search for a 'biomarker' of AKI has seen early promise replaced by a degree of pessimism due to the lack of a clear candidate molecule and variability of results. We outline the major studies described to date as well as discuss potential reasons for the discrepancies observed and suggest that evolution of the field may result in success with ultimately an improvement in patient outcomes

Estimating factor models for multivariate volatilities : an innovation expansion method

We introduce an innovation expansion method for estimation of factor models for conditional variance (volatility) of a multivariate time series. We estimate the factor loading space and the number of factors by a stepwise optimization algorithm on expanding the "white noise space". Simulation and a real data example are given for illustration

Noise Bubbles

We introduce noisy information into a standard present value stock price model. Agents receive a noisy signal about the structural shock driving future dividend variations. The resulting equilibrium stock price includes a transitory component —the “noise bubble”— which can be responsible for boom and bust episodes unrelated to economic fundamentals. We propose a non-standard VAR procedure to estimate the structural shock and the “noise” shock, their impulse response functions and the bubble component of stock prices. We apply such procedure to US data and find that noise explains a large fraction of stock price volatility. In particular the dot-com bubble is entirely explained by noise. On the contrary the stock price boom peaking in 2007 is not a bubble, whereas the following stock market crisis is largely due to negative noise shocks

Halogen bonding enhances nonlinear optical response in poled supramolecular polymers

We demonstrate that halogen bonding strongly enhances the nonlinear optical response of poled supramolecular polymer systems. We compare three nonlinear optical chromophores with similar electronic structures but different bond-donating units, and show that both the type and the strength of the noncovalent interaction between the chromophores and the polymer matrix play their own distinctive roles in the optical nonlinearity of the systems

Sufficient Information in Structural VARs

We derive necessary and sufficient conditions under which a set of variables is informationally sufficient, i.e. contains enough information to estimate the structural shocks with a VAR model. Based on such conditions, we provide a procedure to test for informational sufficiency. If sufficiency is rejected, we propose a strategy to amend the VAR. Our method can be applied to FAVAR models and can be used to determine how many factors to include in such models. We apply our procedure to a VAR including TFP, unemployment and per-capita hours worked. We find that the three variables are not informationally sufficient. When adding missing information, the effects of technology shocks change dramatically