Exercise [2.1.5] Let > 0 and pick K = K( ) finite such that if k ≥ K then r(k) ≤ . Applying the Cauchy-Schwarz inequality for Xi −EXi and Xj −EXj we have that Cov(Xi, Xj) ≤ [Var(Xi)Var(Xj)] ≤ r(0) <∞ for all i, j. Thus, breaking the double sum in Var(Sn) = ∑n i,j=1 Cov(Xi, Xj) into {(i, j) : |i − j| < K} and {(i, j) : |i− j| ≥ K} gives the bound Var(Sn) ≤ 2Knr(0) + n . Dividing by n we see that...

Value-at-risk (VaR) has become the standard criterion for assessing risk in the financial industry. Given the widespread usage of VaR, it becomes increasingly important to study the effects of VaR-based risk management on the prices of stocks and options. We solve a continuous-time asset pricing model, based on Lucas (1978) and Basak and Shapiro (2001), to investigate these effects. We find tha...

The importance of a gene's natural chromatin environment for its normal expression is poignantly illustrated when a change in chromosome position results in variable gene repression, such as is observed in position effect variegation (PEV) when the Drosophila melanogaster white (omega) gene is juxtaposed with heterochromatin. The Enhancer of variegation 3-9 [E(var)3-9] gene was one of over a hu...

Our aim is to introduce and study a new partial integrodifferential equation (PIDE) associated with the dynamics of some physical granular structure with arbitrary component sizes, like a sandpile or sea dyke. Our PIDE is closely related to the nonlocal evolution problem introduced in [F. Andreu et al., Calc. Var. Partial Differential Equations, 35 (2009), pp. 279–316] by studying the limit, as...

A dynamic factor VAR model, estimated by MCMC simulation, is employed to assess the relative severity of post-war U.S. recessions. Joint modeling and estimation of all model unknowns yields rank estimates that fully account for parameter uncertainty. A convenient by-product of the simulation approach is a probability distribution of possible recession ranks that (i) accommodates uncertainty abo...

The primary objective of the proposed research is to develop a weak constraint, 4-dimensional variational (4D-Var) data assimilation capability for the Regional Ocean Modeling System (ROMS) with application to the California Current System (CCS). The CCS is of considerable socio-economic and strategic significance to the United States, and ROMS CCS is transitioning towards a real-time forecasti...

Cowden syndrome (CS), a Mendelian autosomal-dominant disorder, predisposes to breast, thyroid and other cancers. Germline mutations in phosphatase and tensin homolog (PTEN) have been recently reported in 23% of a large series of classic CS. Here, we validated our small (n = 10) pilot study in a large patient series that germline variations in succinate dehydrogenase genes (SDHx) occur in 8% (49...

Exercise [2.1.5] Let > 0 and pick K = K( ) finite such that if k ≥ K then r(k) ≤ . Applying the Cauchy-Schwarz inequality for Xi −EXi and Xj −EXj we have that Cov(Xi, Xj) ≤ [Var(Xi)Var(Xj)] ≤ r(0) <∞ for all i, j. Thus, breaking the double sum in Var(Sn) = ∑n i,j=1 Cov(Xi, Xj) into {(i, j) : |i − j| < K} and {(i, j) : |i− j| ≥ K} gives the bound Var(Sn) ≤ 2Knr(0) + n . Dividing by n we see that...

It is difficult to find an existing single model which is able to simultaneously model exceedances over thresholds in multivariate financial time series. A new modeling approach, which is a combination of max-stable processes, GARCH processes, and Markov processes, is proposed. Combining Markov processes and max-stable processes defines a new statistical model which has the flexibility of model...

Streptococcus faecium var. casseliflavus is a gram-positive, spherical cell. The cells occur chiefly as pairs within chains and elongate to ogive-shaped cells during growth. Growth is good on 5% bile salts-agar and in broth at 10 C, and in broth adjusted to pH 9.6 or containing 6.5% NaCl, but many strains fail to grow at 45 C. Litmus is reduced rapidly prior to formation of an acid curd. Few st...