Representation of functionals of Ito processes and their first exit times

The representation theorem is obtained for functionals of non-Markov processes and their first exit times from bounded domains. These functionals are represented via solutions of backward parabolic Ito equations. As an example of applications, analogs of forward Kolmogorov equations are derived for conditional probability density functions of Ito processes being killed on the boundary. In addition, a maximum principle and a contraction property are established for SPDEs in bounded domains.Comment: 25 page

Determination of characteristic relaxation times and their significance in glassy disordered insulators

We revisit the field effect procedure used to characterise the slow dynamics of glassy Anderson insulators. It is shown that in the slowest systems the procedure fails and the "characteristic" time values extracted are not intrinsic but determined by the experimental procedure itself. In other cases (like lightly doped indium oxide) qualitative indications about the dynamics might be obtained, however the times extracted cannot be seen as characteristic relaxation times of the system in any simple manner, and more complete experiments are necessary. Implications regarding the effect of carrier concentration on the emergence of glassiness are briefly outlined.Comment: published with minor proof correction

Historians of Their Own Times

This article urges greater appreciation of the accounts written by witnesses to historical events

Limits of space-times in five dimensions and their relation to the Segre Types

A limiting diagram for the Segre classification in 5-dimensional space-times is obtained, extending a recent work on limits of the energy-momentum tensor in general relativity. Some of Geroch's results on limits of space-times in general relativity are also extended to the context of five-dimensional Kaluza-Klein space-times.Comment: Late

Melvin Twists of global AdS_5 \times S_5 and their Non-Commutative Field Theory Dual

We consider the Melvin Twist of AdS_5 \times S_5 under U(1) \times U(1) isometry of the boundary S_3 of the global AdS_5 geometry and identify its field theory dual. We also study the thermodynamics of the Melvin deformed theory.Comment: 17 pages, references adde

Remarks on evolution of space-times in 3+1 and 4+1 dimensions

A large class of vacuum space-times is constructed in dimension 4+1 from hyperboloidal initial data sets which are not small perturbations of empty space data. These space-times are future geodesically complete, smooth up to their future null infinity, and extend as vacuum space-times through their Cauchy horizon. Dimensional reduction gives non-vacuum space-times with the same properties in 3+1 dimensions.Comment: 10pp, exposition improved; final versio

Array-based iterative measurements of SmKS travel times and their constraints on outermost core structure

Vigorous convection in Earth's outer core led to the suggestion that it is chemically homogeneous. However, there is increasing seismic evidence for structural complexities close to the outer core's upper and lower boundaries. Both body waves and normal mode data have been used to estimate a P wave velocity, V_p, at the top of the outer core (the E’ layer), which is lower than that in the Preliminary Reference Earth Model. However, these low V_p models do not agree on the form of this velocity anomaly. One reason for this is the difficulty in retrieving and measuring SmKS arrival times. To address this issue, we propose a novel approach using data from seismic arrays to iteratively measure SmKS-SKKS-differential travel times. This approach extracts individual SmKS signal from mixed waveforms of the SmKS series, allowing us to reliably measure differential travel times. We successfully use this method to measure SmKS time delays from earthquakes in the Fiji‐Tonga and Vanuatu subduction zones. SmKS time delays are measured by waveform cross correlation between SmKS and SKKS, and the cross‐correlation coefficient allows us to access measurement quality. We also apply this iterative scheme to synthetic SmKS seismograms to investigate the 3‐D mantle structure's effects. The mantle structure corrections are not negligible for our data, and neglecting them could bias the V_p estimation of uppermost outer core. After mantle structure corrections, we can still see substantial time delays of S3KS, S4KS, and S5KS, supporting a low V_p at the top of Earth's outer core

A Fine Balance: Effectively Managing Growth and Contraction

[Excerpt] Times of economic hardship and prosperity both pose unique challenges to companies and their talent management practices. On one hand, while companies are experiencing contraction, employers may neglect motivating and developing their employees. Conversely, during periods of expansion, companies may set themselves on an unsustainable course that may lead to dramatic consequences when leaner times prevail. Indeed, it is easy for companies to fall into talent management traps both in times of growth and recession