Feedback between US and UK Prices: a Frequency Domain Analysis

This paper decomposes the feedback between US and UK price levels by frequency over the period 1791 to 1990. By adapting Geweke's (1982) method of decomposing the feedback between time series to the case of I(1) time series generated by a bivariate error-correction model, we find that most of the feedback between the two time series occurs at very low frequencies. This result provides a reconciliation of the typical rejection of purchasing power parity (PPP) in short-run studies with the findings of paradoxically short half-lives for deviations from PPP often found in long-run studies.feedback decomposition

Set Systems Containing Many Maximal Chains

The purpose of this short problem paper is to raise an extremal question on set systems which seems to be natural and appealing. Our question is: which set systems of a given size maximise the number of $(n+1)$-element chains in the power set $\mathcal{P}(\{1,2,\dots,n\})$? We will show that for each fixed $\alpha>0$ there is a family of $\alpha 2^n$ sets containing $(\alpha+o(1))n!$ such chains, and that this is asymptotically best possible. For smaller set systems we are unable to answer the question. We conjecture that a `tower of cubes' construction is extremal. We finish by mentioning briefly a connection to an extremal problem on posets and a variant of our question for the grid graph.Comment: 5 page

Earthquake Arrival Association with Backprojection and Graph Theory

The association of seismic wave arrivals with causative earthquakes becomes progressively more challenging as arrival detection methods become more sensitive, and particularly when earthquake rates are high. For instance, seismic waves arriving across a monitoring network from several sources may overlap in time, false arrivals may be detected, and some arrivals may be of unknown phase (e.g., P- or S-waves). We propose an automated method to associate arrivals with earthquake sources and obtain source locations applicable to such situations. To do so we use a pattern detection metric based on the principle of backprojection to reveal candidate sources, followed by graph-theory-based clustering and an integer linear optimization routine to associate arrivals with the minimum number of sources necessary to explain the data. This method solves for all sources and phase assignments simultaneously, rather than in a sequential greedy procedure as is common in other association routines. We demonstrate our method on both synthetic and real data from the Integrated Plate Boundary Observatory Chile (IPOC) seismic network of northern Chile. For the synthetic tests we report results for cases with varying complexity, including rates of 500 earthquakes/day and 500 false arrivals/station/day, for which we measure true positive detection accuracy of > 95%. For the real data we develop a new catalog between January 1, 2010 - December 31, 2017 containing 817,548 earthquakes, with detection rates on average 279 earthquakes/day, and a magnitude-of-completion of ~M1.8. A subset of detections are identified as sources related to quarry and industrial site activity, and we also detect thousands of foreshocks and aftershocks of the April 1, 2014 Mw 8.2 Iquique earthquake. During the highest rates of aftershock activity, > 600 earthquakes/day are detected in the vicinity of the Iquique earthquake rupture zone

Dynamic induced softening in frictional granular material investigated by DEM simulation

A granular system composed of frictional glass beads is simulated using the Discrete Element Method. The inter-grain forces are based on the Hertz contact law in the normal direction with frictional tangential force. The damping due to collision is also accounted for. Systems are loaded at various stresses and their quasi-static elastic moduli are characterized. Each system is subjected to an extensive dynamic testing protocol by measuring the resonant response to a broad range of AC drive amplitudes and frequencies via a set of diagnostic strains. The system, linear at small AC drive amplitudes has resonance frequencies that shift downward (i.e., modulus softening) with increased AC drive amplitude. Detailed testing shows that the slipping contact ratio does not contribute significantly to this dynamic modulus softening, but the coordination number is strongly correlated to this reduction. This suggests that the softening arises from the extended structural change via break and remake of contacts during the rearrangement of bead positions driven by the AC amplitude.Comment: acoustics, nonlinearity, granular medi

Simple and inexpensive perturbative correction schemes for antisymmetric products of nonorthogonal geminals

A new multireference perturbation approach has been developed for the recently proposed AP1roG scheme, a computationally facile parametrization of an antisymmetric product of nonorthogonal geminals. This perturbation theory of second-order closely follows the biorthogonal treatment from multiconfiguration perturbation theory as introduced by Surjan et al., but makes use of the additional feature of AP1roG that the expansion coefficients within the space of closed-shell determinants are essentially correct already, which further increases the predictive power of the method. Building upon the ability of AP1roG to model static correlation, the perturbation correction accounts for dynamical electron correlation, leading to absolute energies close to full configuration interaction results. Potential surfaces for multiple bond dissociation in H2O and N-2 are predicted with high accuracy up to bond breaking. The computational cost of the method is the same as that of conventional single-reference MP2

Acoustically-induced slip in sheared granular layers: application to dynamic earthquake triggering

A fundamental mystery in earthquake physics is ``how can an earthquake be triggered by distant seismic sources?'' Here, we use discrete element method simulations of a granular layer, during stick-slip, that is subject to transient vibrational excitation to gain further insight into the physics of dynamic earthquake triggering. Using Coulomb friction law for grains interaction, we observe delayed triggering of slip in the granular gouge. We find that at a critical vibrational amplitude (strain) there is an abrupt transition from negligible time-advanced slip (clock advance) to full clock advance, {\it i.e.}, transient vibration and triggered slip are simultaneous. The critical strain is order of $10^{-6}$, similar to observations in the laboratory and in Earth. The transition is related to frictional weakening of the granular layer due to a dramatic decrease in coordination number and the weakening of the contact force network. Associated with this frictional weakening is a pronounced decrease in the elastic modulus of the layer. The study has important implications for mechanisms of triggered earthquakes and induced seismic events and points out the underlying processes in response of the fault gouge to dynamic transient stresses