The polymerase chain reaction (PCR) is widely used for applications which require a high level of specificity and reliability, such as genetic testing, clinical diagnostics, blood screening, forensics and biodefense. Great improvements to PCR performance have been achieved by the use of Hot Start activation strategies that aim to prevent DNA polymerase extension until more stringent, higher tem...

General elliptic equations with spatially discontinuous diffusion coefficients may be used as a simplified model for subsurface flow in heterogeneous or fractured porous media. In such model, data sparsity and measurement errors are often taken into account by randomization of the coefficient equation which reveals necessity construction flexible, random fields. Subordinated Gaussian fields fun...

We consider propagating, spatially localized waves in a class of equations that contain variational and nonvariational terms. The dynamics of the waves is analyzed through a collective coordinate approach. Motivated by the variational approximation, we show that there is a natural choice of projection onto collective variables for reducing the governing (nonlinear) partial differential equation...

We investigate stochastic quantization as a method to go from a classical PDE (with stochastic time λ) to a corresponding quantum theory in the limit λ→∞. We test the method for a linear PDE satisfied by the free scalar field. We begin by giving some background about the importance of establishing the property of reflection positivity for the limit λ → ∞. We then prove that the measure determin...

This article initiates the study of nonlinear elliptic partial difference equations (PdE) on graphs. We seek solutions u : V → R to the semilinear elliptic difference equation −Lu + f(u) = 0 on a graph G = (V,E), where L is the (negative) Laplacian on the graph G. We extend techniques used to prove existence theorems and derive numerical algorithms for the partial differential equation (PDE) ∆u...

In this paper, a hybrid inpainting method is proposed for the simultaneous reconstruction of geometry and texture in missing regions of a color image. Using inpainting methods based on partial differential equation (PDE) to fill in large image regions usually fails if these regions contain textures. On the other hand, texture synthesis algorithms sometimes fail due to complex structure and text...

For many path-dependent options, such as Asian options, lookbacks, Parisian options, using partial differentiation equation (PDE) approach to price these exotic options can be straightforward and flexible. In addition, modified versions of the standard exotic path-dependent options can be easily accommodated in the same pricing algorithms. For example, American early exercise features, barriers...

We improve upon a method introduced in (Bertalmio et. al. JCP 2001) for solving evolution PDEs on codimension-one surfaces in RN . As in the original method, by representing the surface as a level set of a smooth function, we use only finite differences on a Cartesian mesh to solve an Eulerian representation of the surface PDE in a neighborhood of the surface. We modify the original method by c...

Several recently developed multisymplectic schemes for Hamiltonian PDEs have been shown to preserve associated local conservation laws and constraints very well in long time numerical simulations. Backward error analysis for PDEs, or the method of modified equations, is a useful technique for studying the qualitative behavior of a discretization and provides insight into the preservation proper...

The single-step one-shot method has proven to be very efficient for PDEconstrained optimization where the partial differential equation (PDE) is solved by an iterative fixed point solver. In this approach, the simulation and optimization tasks are performed simultaneously in a single iteration. If the PDE is unsteady, finding an appropriate fixed point iteration is nontrivial. In this paper, we...