Modification of the pattern informatics method for forecasting large earthquake events using complex eigenvectors

Recent studies have shown that real-valued principal component analysis can be applied to earthquake fault systems for forecasting and prediction. In addition, theoretical analysis indicates that earthquake stresses may obey a wave-like equation, having solutions with inverse frequencies for a given fault similar to those that characterize the time intervals between the largest events on the fault. It is therefore desirable to apply complex principal component analysis to develop earthquake forecast algorithms. In this paper we modify the Pattern Informatics method of earthquake forecasting to take advantage of the wave-like properties of seismic stresses and utilize the Hilbert transform to create complex eigenvectors out of measured time series. We show that Pattern Informatics analyses using complex eigenvectors create short-term forecast hot-spot maps that differ from hot-spot maps created using only real-valued data and suggest methods of analyzing the differences and calculating the information gain.Comment: 13 pages, 1 figure. Submitted to Tectonophysics on 30 August 200

Gutenberg Richter and Characteristic Earthquake Behavior in Simple Mean-Field Models of Heterogeneous Faults

The statistics of earthquakes in a heterogeneous fault zone is studied analytically and numerically in the mean field version of a model for a segmented fault system in a three-dimensional elastic solid. The studies focus on the interplay between the roles of disorder, dynamical effects, and driving mechanisms. A two-parameter phase diagram is found, spanned by the amplitude of dynamical weakening (or ``overshoot'') effects (epsilon) and the normal distance (L) of the driving forces from the fault. In general, small epsilon and small L are found to produce Gutenberg-Richter type power law statistics with an exponential cutoff, while large epsilon and large L lead to a distribution of small events combined with characteristic system-size events. In a certain parameter regime the behavior is bistable, with transitions back and forth from one phase to the other on time scales determined by the fault size and other model parameters. The implications for realistic earthquake statistics are discussed.Comment: 21 pages, RevTex, 6 figures (ps, eps

Heat kernel regularization of the effective action for stochastic reaction-diffusion equations

The presence of fluctuations and non-linear interactions can lead to scale dependence in the parameters appearing in stochastic differential equations. Stochastic dynamics can be formulated in terms of functional integrals. In this paper we apply the heat kernel method to study the short distance renormalizability of a stochastic (polynomial) reaction-diffusion equation with real additive noise. We calculate the one-loop {\emph{effective action}} and its ultraviolet scale dependent divergences. We show that for white noise a polynomial reaction-diffusion equation is one-loop {\emph{finite}} in $d=0$ and $d=1$, and is one-loop renormalizable in $d=2$ and $d=3$ space dimensions. We obtain the one-loop renormalization group equations and find they run with scale only in $d=2$.Comment: 21 pages, uses ReV-TeX 3.

Identification and Functional Characterization of G6PC2 Coding Variants Influencing Glycemic Traits Define an Effector Transcript at the G6PC2-ABCB11 Locus

Genome wide association studies (GWAS) for fasting glucose (FG) and insulin (FI) have identified common variant signals which explain 4.8% and 1.2% of trait variance, respectively. It is hypothesized that low-frequency and rare variants could contribute substantially to unexplained genetic variance. To test this, we analyzed exome-array data from up to 33,231 non-diabetic individuals of European ancestry. We found exome-wide significant (P<5×10-7) evidence for two loci not previously highlighted by common variant GWAS: GLP1R (p.Ala316Thr, minor allele frequency (MAF)=1.5%) influencing FG levels, and URB2 (p.Glu594Val, MAF = 0.1%) influencing FI levels. Coding variant associations can highlight potential effector genes at (non-coding) GWAS signals. At the G6PC2/ABCB11 locus, we identified multiple coding variants in G6PC2 (p.Val219Leu, p.His177Tyr, and p.Tyr207Ser) influencing FG levels, conditionally independent of each other and the non-coding GWAS signal. In vitro assays demonstrate that these associated coding alleles result in reduced protein abundance via proteasomal degradation, establishing G6PC2 as an effector gene at this locus. Reconciliation of single-variant associations and functional effects was only possible when haplotype phase was considered. In contrast to earlier reports suggesting that, paradoxically, glucose-raising alleles at this locus are protective against type 2 diabetes (T2D), the p.Val219Leu G6PC2 variant displayed a modest but directionally consistent association with T2D risk. Coding variant associations for glycemic traits in GWAS signals highlight PCSK1, RREB1, and ZHX3 as likely effector transcripts. These coding variant association signals do not have a major impact on the trait variance explained, but they do provide valuable biological insights

On the Mathematical Analysis of an Elastic-gravitational Layered Earth Model for Magmatic Intrusion: The Stationary Case

In the early eighties Rundle (1980, 1981a,b, 1982) developed the techniques needed for calculations of displacements and gravity changes due to internal sources of strain in layered linear elastic-gravitational media. The approximation of the solution for the half space was obtained by using the propagator matrix technique. The Earth model considered is elastic-gravitational, composed of several homogeneous layers overlying a bottom half space. Two dislocation sources can be considered, representing magma intrusions and faults. In recent decades theoretical and computational extensions of that model have been developed by Rundle and co-workers (e.g., Fernandez and Rundle, 1994a,b; Fernandez et al., 1997, 2005a; Tiampo et al., 2004; Charco et al., 2006, 2007a,b). The source can be located at any depth in the media. In this work we prove that the perturbed equations representing the elastic-gravitational deformation problem, with the natural boundary and transmission conditions, leads to a well-posed problem even for varied domains and general data. We present constructive proof of the existence and we show the uniqueness and the continuous dependence with respect to the data of weak solutions of the coupled elastic-gravitational field equations