Estimating stochastic volatility diffusion using conditional moments of integrated volatility

We exploit the distributional information contained in high-frequency intraday data in constructing a simple conditional moment estimator for stochastic volatility diffusions. The estimator is based on the analytical solutions of the first two conditional moments for the latent integrated volatility, the realization of which is effectively approximated by the sum of the squared high-frequency increments of the process. Our simulation evidence indicates that the resulting GMM estimator is highly reliable and accurate. Our empirical implementation based on high-frequency five-minute foreign exchange returns suggests the presence of multiple latent stochastic volatility factors and possible jumps. © 2002 Elsevier Science B.V. All rights reserved.

A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

Uncovering compounds by synergy of cluster expansion and high-throughput methods.

Predicting from first-principles calculations whether mixed metallic elements phase-separate or form ordered structures is a major challenge of current materials research. It can be partially addressed in cases where experiments suggest the underlying lattice is conserved, using cluster expansion (CE) and a variety of exhaustive evaluation or genetic search algorithms. Evolutionary algorithms have been recently introduced to search for stable off-lattice structures at fixed mixture compositions. The general off-lattice problem is still unsolved. We present an integrated approach of CE and high-throughput ab initio calculations (HT) applicable to the full range of compositions in binary systems where the constituent elements or the intermediate ordered structures have different lattice types. The HT method replaces the search algorithms by direct calculation of a moderate number of naturally occurring prototypes representing all crystal systems and guides CE calculations of derivative structures. This synergy achieves the precision of the CE and the guiding strengths of the HT. Its application to poorly characterized binary Hf systems, believed to be phase-separating, defines three classes of alloys where CE and HT complement each other to uncover new ordered structures.

Ras controls melanocyte expansion during zebrafish fin stripe regeneration.

Regenerative medicine for complex tissues like limbs will require the provision or activation of precursors for different cell types, in the correct number, and with the appropriate instructions. These strategies can be guided by what is learned from spectacular events of natural limb or fin regeneration in urodele amphibians and teleost fish. Following zebrafish fin amputation, melanocyte stripes faithfully regenerate in tandem with complex fin structures. Distinct populations of melanocyte precursors emerge and differentiate to pigment regenerating fins, yet the regulation of their proliferation and patterning is incompletely understood. Here, we found that transgenic increases in active Ras dose-dependently hyperpigmented regenerating zebrafish fins. Lineage tracing and marker analysis indicated that increases in active Ras stimulated the in situ amplification of undifferentiated melanocyte precursors expressing mitfa and kita. Active Ras also hyperpigmented early fin regenerates of kita mutants, which are normally devoid of primary regeneration melanocytes, suppressing defects in precursor function and survival. By contrast, this protocol had no noticeable impact on pigmentation by secondary regulatory melanocyte precursors in late-stage kita regenerates. Our results provide evidence that Ras activity levels control the repopulation and expansion of adult melanocyte precursors after tissue loss, enabling the recovery of patterned melanocyte stripes during zebrafish appendage regeneration.

Information relaxations and duality in stochastic dynamic programs

We describe a general technique for determining upper bounds on maximal values (or lower bounds on minimal costs) in stochastic dynamic programs. In this approach, we relax the nonanticipativity constraints that require decisions to depend only on the information available at the time a decision is made and impose a "penalty" that punishes violations of nonanticipativity. In applications, the hope is that this relaxed version of the problem will be simpler to solve than the original dynamic program. The upper bounds provided by this dual approach complement lower bounds on values that may be found by simulating with heuristic policies. We describe the theory underlying this dual approach and establish weak duality, strong duality, and complementary slackness results that are analogous to the duality results of linear programming. We also study properties of good penalties. Finally, we demonstrate the use of this dual approach in an adaptive inventory control problem with an unknown and changing demand distribution and in valuing options with stochastic volatilities and interest rates. These are complex problems of significant practical interest that are quite difficult to solve to optimality. In these examples, our dual approach requires relatively little additional computation and leads to tight bounds on the optimal values. © 2010 INFORMS.

Stochastic E2F activation and reconciliation of phenomenological cell-cycle models.

The transition of the mammalian cell from quiescence to proliferation is a highly variable process. Over the last four decades, two lines of apparently contradictory, phenomenological models have been proposed to account for such temporal variability. These include various forms of the transition probability (TP) model and the growth control (GC) model, which lack mechanistic details. The GC model was further proposed as an alternative explanation for the concept of the restriction point, which we recently demonstrated as being controlled by a bistable Rb-E2F switch. Here, through a combination of modeling and experiments, we show that these different lines of models in essence reflect different aspects of stochastic dynamics in cell cycle entry. In particular, we show that the variable activation of E2F can be described by stochastic activation of the bistable Rb-E2F switch, which in turn may account for the temporal variability in cell cycle entry. Moreover, we show that temporal dynamics of E2F activation can be recast into the frameworks of both the TP model and the GC model via parameter mapping. This mapping suggests that the two lines of phenomenological models can be reconciled through the stochastic dynamics of the Rb-E2F switch. It also suggests a potential utility of the TP or GC models in defining concise, quantitative phenotypes of cell physiology. This may have implications in classifying cell types or states.

Expansion of the alpha 2-adrenergic receptor family: cloning and characterization of a human alpha 2-adrenergic receptor subtype, the gene for which is located on chromosome 2.

Pharmacologic, biochemical, and genetic analyses have demonstrated the existence of multiple alpha 2-adrenergic receptor (alpha 2AR) subtypes. We have cloned a human alpha 2AR by using the polymerase chain reaction with oligonucleotide primers homologous to conserved regions of the previously cloned alpha 2ARs, the genes for which are located on human chromosomes 4 (C4) and 10 (C10). The deduced amino acid sequence encodes a protein of 450 amino acids whose putative topology is similar to that of the family of guanine nucleotide-binding protein-coupled receptors, but whose structure most closely resembles that of the alpha 2ARs. Competition curve analysis of the binding properties of the receptor expressed in COS-7 cells with a variety of adrenergic ligands demonstrates a unique alpha 2AR pharmacology. Hybridization with somatic cell hybrids shows that the gene for this receptor is located on chromosome 2. Northern blot analysis of various rat tissues shows expression in liver and kidney. The unique pharmacology and tissue localization of this receptor suggest that this is an alpha 2AR subtype not previously identified by classical pharmacological or ligand binding approaches.

Stochastic switching in infinite dimensions with applications to random parabolic PDE

© 2015 Society for Industrial and Applied Mathematics.We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution. Applying these general results to the heat equation with randomly switching boundary conditions, we find explicit formulae for various statistics of the solution and obtain almost sure results about its regularity and structure. These results are of particular interest for biological applications as well as for their significant departure from behavior seen in PDEs forced by disparate Gaussian noise. Our general results also have applications to other types of stochastic hybrid systems, such as ODEs with randomly switching right-hand sides.

A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs

We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. It is shown that if Hörmander's bracket condition holds at every point of this Hilbert space, then a lower bound on the Malliavin covariance operatorμt can be obtained. Informally, this bound can be read as "Fix any finite-dimensional projection on a subspace of sufficiently regular functions. Then the eigenfunctions of μt with small eigenvalues have only a very small component in the image of Π." We also show how to use a priori bounds on the solutions to the equation to obtain good control on the dependency of the bounds on the Malliavin matrix on the initial condition. These bounds are sufficient in many cases to obtain the asymptotic strong Feller property introduced in [HM06]. One of the main novel technical tools is an almost sure bound from below on the size of "Wiener polynomials," where the coefficients are possibly non-adapted stochastic processes satisfying a Lips chitz condition. By exploiting the polynomial structure of the equations, this result can be used to replace Norris' lemma, which is unavailable in the present context. We conclude by showing that the two-dimensional stochastic Navier-Stokes equations and a large class of reaction-diffusion equations fit the framework of our theory.

Identification of dopamine receptors across the extant avian family tree and analysis with other clades uncovers a polyploid expansion among vertebrates.

Dopamine is an important central nervous system transmitter that functions through two classes of receptors (D1 and D2) to influence a diverse range of biological processes in vertebrates. With roles in regulating neural activity, behavior, and gene expression, there has been great interest in understanding the function and evolution dopamine and its receptors. In this study, we use a combination of sequence analyses, microsynteny analyses, and phylogenetic relationships to identify and characterize both the D1 (DRD1A, DRD1B, DRD1C, and DRD1E) and D2 (DRD2, DRD3, and DRD4) dopamine receptor gene families in 43 recently sequenced bird genomes representing the major ordinal lineages across the avian family tree. We show that the common ancestor of all birds possessed at least seven D1 and D2 receptors, followed by subsequent independent losses in some lineages of modern birds. Through comparisons with other vertebrate and invertebrate species we show that two of the D1 receptors, DRD1A and DRD1B, and two of the D2 receptors, DRD2 and DRD3, originated from a whole genome duplication event early in the vertebrate lineage, providing the first conclusive evidence of the origin of these highly conserved receptors. Our findings provide insight into the evolutionary development of an important modulatory component of the central nervous system in vertebrates, and will help further unravel the complex evolutionary and functional relationships among dopamine receptors.

Modeling non-harmonic behavior of materials from experimental inelastic neutron scattering and thermal expansion measurements

Based on thermodynamic principles, we derive expressions quantifying the non-harmonic vibrational behavior of materials, which are rigorous yet easily evaluated from experimentally available data for the thermal expansion coefficient and the phonon density of states. These experimentally- derived quantities are valuable to benchmark first-principles theoretical predictions of harmonic and non-harmonic thermal behaviors using perturbation theory, ab initio molecular-dynamics, or Monte-Carlo simulations. We illustrate this analysis by computing the harmonic, dilational, and anharmonic contributions to the entropy, internal energy, and free energy of elemental aluminum and the ordered compound FeSi over a wide range of temperature. Results agree well with previous data in the literature and provide an efficient approach to estimate anharmonic effects in materials.