Straight Theta Research Articles

Variations of the asset prices.

The empirical established non-Gaussian behavior of asset price fluctuations is studied using an analytical approach. The analysis is based on a nonlinear Fokker-Planck equation with a self-organized feedback-coupling term, devised as a fundamental model for price dynamics. The evidence, and the analytical form of the memory term, are discussed in the context of statistical physics. It will be suggested that the memory term in leading order offers a power law dependence with an exponent straight theta. The stationary solution of the probability density leads asymptotically to a truncated Lévy distribution, the characteristic exponent beta of which is related to the exponent straight theta by beta=3/theta-1. The empirical data can be reproduced by theta approximately 5/4.

Chern-Simons theories on the noncommutative plane.

We investigate U(N) Chern-Simons theories on the noncommutative plane. We show that for the theories to be consistent quantum mechanically, the coefficient of the Chern-Simons term should be quantized kappa = n/2pi with an integer n. This is a surprise for the U(1) gauge theory. When uniform background charge density rho(e) is present, the quantization rule changes to kappa+rho(e)straight theta = n/2pi with the noncommutative parameter straight theta. With the exact expression for the angular momentum, we argue in the U(1) theory that charged particles in the symmetric phase carry fractional spin 1/2n and vortices in the broken phase carry half-integer or integer spin -n/2.

On determination of sample size in hierarchical binomial models.

We consider a two- and a three-stage hierarchical design containing the effects of k clusters with n units per cluster. In the two-stage model, the conditional distribution of the discrete response Y(i) is assumed to be independent binomial with mean n(straight theta)i (I=1,....k). The success probabilities, straight theta(i)'s, are assumed exchangeable across the k clusters, each arising from a beta distribution. In the three-stage model, the parameters in the beta distribution are assumed to have independent gamma distributions. The size of each cluster, n, is determined for functions of straight theta(i). Lengths of central posterior intervals are computed for various functions of the straight theta(i)'s using Markov chain Monte Carlo and Monte Carlo simulations. Several prior distributions are characterized and tables are provided for n with given k. Methods for sample size calculations under the two- and three-stage models are illustrated and compared for the design of a multi-institutional study to evaluate the appropriateness of discharge planning rates for a cohort of patients with congestive heart failure.

Germline mutations of the gene encoding bone morphogenetic protein receptor 1A in juvenile polyposis.

Juvenile polyposis (JP; OMIM 174900) is an autosomal dominant gastrointestinal hamartomatous polyposis syndrome in which patients are at risk for developing gastrointestinal cancers. Previous studies have demonstrated a locus for JP mapping to 18q21.1 (ref. 3) and germline mutations in the homolog of the gene for mothers against decapentaplegic, Drosophila, (MADH4, also known as SMAD4) in several JP families. However, mutations in MADH4 are only present in a subset of JP cases, and although mutations in the gene for phosphatase and tensin homolog (PTEN) have been described in a few families, undefined genetic heterogeneity remains. Using a genome-wide screen in four JP kindreds without germline mutations in MADH4 or PTEN, we identified linkage with markers from chromosome 10q22-23 (maximum lod score of 4.74, straight theta=0.00). We found no recombinants using markers developed from the vicinity of the gene for bone morphogenetic protein receptor 1A (BMPR1A), a serine-threonine kinase type I receptor involved in bone morphogenetic protein (BMP) signaling. Genomic sequencing of BMPR1A in each of these JP kindreds disclosed germline nonsense mutations in all affected kindred members but not in normal control individuals. These findings indicate involvement of an additional gene in the transforming growth factor-beta (TGF-beta) superfamily in the genesis of JP, and document an unanticipated function for BMP in colonic epithelial growth control.

Passive Scalar Intermittency in Low Temperature Helium Flows

We report new measurements of mixing of passive temperature field in a turbulent flow. The use of low temperature helium gas allows us to span a range of microscale Reynolds number, R(lambda), from 100 to 650. The exponents xi(n) of the temperature structure functions </straight theta(x+r)-straight theta(x)/(n)> approximately r(xi(n)) are shown to saturate to xi(infinity) approximately 1.45+/-0.1 for the highest orders, n approximately 10. This saturation is a signature of statistics dominated by frontlike structures, the cliffs. Statistics of the cliffs' characteristics are performed, particularly their widths are shown to scale as the Kolmogorov length scale.

Extremal statistics in the energetics of domain walls.

We study at T=0 the minimum energy of a domain wall and its gap to the first excited state, concentrating on two-dimensional random-bond Ising magnets. The average gap scales as deltaE1 approximately L(straight theta)f(N(z)), where f(y) approximately [ln y](-1/2), straight theta is the energy fluctuation exponent, L is the length scale, and N(z) is the number of energy valleys. The logarithmic scaling is due to extremal statistics, which is illustrated by mapping the problem into the Kardar-Parisi-Zhang roughening process. It follows that the susceptibility of domain walls also has a logarithmic dependence on the system size.

Hexagonal ammonium zinc phosphate, (NH4)ZnPO4, at 10 K.

The title compound, (NH(4))ZnPO(4)-HEX, is built up from a three-dimensional network of ZnO(4) and PO(4) tetrahedra [d(av)(Zn-O) = 1.9400 (7) A and d(av)(P-O) = 1.5396 (7) A], fused together via Zn-O-P links [straight theta(av) = 133.47 (4) degrees ]. An undisordered linear Zn-O-P bond occurs (all three atoms lie on a threefold axis). Extra-framework NH(4)(+) cations, which interact with the [ZnPO(4)](-) framework by hydrogen bonds, complete the crystal structure.

Measurement of Persistence in 1D Diffusion

Using a novel NMR scheme we observed persistence in 1D gas diffusion. Analytical approximations and numerical simulations have indicated that for an initially random array of spins undergoing diffusion, the probability p(t) that the average spin magnetization in a given region has not changed sign (i.e., "persists") up to time t follows a power law t(-straight theta), where straight theta depends on the dimensionality of the system. Using laser-polarized 129Xe gas, we prepared an initial "quasirandom" 1D array of spin magnetization and then monitored the ensemble's evolution due to diffusion using real-time NMR imaging. Our measurements are consistent with analytical and numerical predictions of straight theta approximately 0.12.

Spatial persistence of fluctuating interfaces.

We show that the probability, P0(l), that the height of a fluctuating (d+1)-dimensional interface in its steady state stays above its initial value up to a distance l, along any linear cut in the d-dimensional space, decays as P0(l) approximately l(theta). Here straight theta is a "spatial" persistence exponent, and takes different values, straight theta(s) or straight theta(0), depending on how the point from which l is measured is specified. These exponents are shown to map onto corresponding temporal persistence exponents for a generalized d = 1 random-walk equation. The exponent straight theta(0) is nontrivial even for Gaussian interfaces.

Neutrino unification.

Present neutrino data are consistent with neutrino masses arising from a common seed at some "neutrino unification" scale M(X). Such a simple theoretical ansatz naturally leads to quasidegenerate neutrinos that could lie in the electron-volt range with neutrino mass splittings induced by renormalization effects associated with supersymmetric thresholds. In such a scheme the leptonic analog of the Cabibbo angle straight theta(middle dot in circle) describing solar neutrino oscillations is nearly maximal. Its exact value is correlated with the smallness of straight theta(reactor). The two leading mass-eigenstate neutrinos present in nu(e) form a pseudo-Dirac neutrino, avoiding conflict with neutrinoless double beta decay.

Polarization measurements in high-energy deuteron photodisintegration.

We present measurements of the recoil proton polarization for the d(gamma-->,p-->)n reaction at straight theta(c.m.) = 90 degrees for photon energies up to 2.4 GeV. These are the first data in this reaction for polarization transfer with circularly polarized photons. The induced polarization p(y) vanishes above 1 GeV, contrary to meson-baryon model expectations, in which resonances lead to large polarizations. However, the polarization transfer Cx does not vanish above 1 GeV, inconsistent with hadron helicity conservation. Thus, we show that the scaling behavior observed in the d(gamma,p)n cross sections is not a result of perturbative QCD. These data should provide important tests of new nonperturbative calculations in the intermediate energy regime.

Observation of toroidal flow antiparallel to the drift direction in the hot electron mode plasmas in the compact helical system.

A toroidal flow antiparallel to the <E(r) x B(straight theta)> drift direction is observed in the hot electron mode plasmas when a large positive electric field and a sharp electron temperature gradient are sustained inside the internal transport barrier in the Compact Helical System. This toroidal flow reaches up to 5x10(4) m/s at the plasma center, and it is large enough to reverse the toroidal flow driven by a tangentially injected neutral beam. These observations clearly show the plasma favors flow in the minimum nablaB direction at the transport barrier.

Regular and anomalous scaling of a randomly advected passive scalar.

Extending Kolmogorov's refined similarity hypothesis to study the inertial behavior <[T(x+r,t)-T(x,t)](2n)>~r(zeta(2n)) of a passive scalar T(x,t) advected by a rapidly changing incompressible velocity field, a random variable straight theta was introduced by Ching [Phys. Rev. Lett. 79, 3644 (1997)]. In this paper, the statistical distribution of the random variable X=straight theta/sqrt[<straight theta(2)>] is investigated analytically for the scaling in two limits, n-independent scaling zeta(2n)=zeta(2) and regular scaling zeta(2n)=nzeta(2), and numerically for the scaling of the Kraichnan conjecture zeta(2n)=1 / 2[sqrt[4ndzeta(2)+(d-zeta(2))(2)]-(d-zeta(2))]. For n-independent scaling zeta(2n)=zeta(2), the statistical distribution of X tends to an exponential distribution when zeta(2)-->0 or d-->infinity and to a Gaussian distribution when zeta(2)-->2 and d=2. For regular scaling zeta(2n)=nzeta(2), the statistical distribution of X tends to a Gaussian distribution when zeta(2)-->0 or d-->infinity. In d=2, there seems to be a phase transition for the probability density function P(X) from a convex to a concave function when the value of zeta(2) is increased and the critical point is zeta(2)=4/3 where the random variable X has a uniform distribution in [-sqrt[3],sqrt[3]]. In d=3, P(X) is a convex function for all 0<zeta(2)<2 and tends to a constant on its support [-sqrt[3],sqrt[3]] when zeta(2)-->2. For the scaling of the Kraichnan conjecture, P(X) has two peaks in d=2 for zeta(2)>1.33, but, in d=3, it has only one peak for all 0<zeta(2)<2 and changes very slowly with the value of X in the neighborhood of X=0 as zeta(2)-->2.

X-ray determination of Debye-Waller factors and Debye temperatures of h.c.p. elements Ti, Zr, Ru, Tm, Hf.

Debye-Waller factors of five h.c.p. elements (Ti, Zr, Ru, Tm, Hf) have been determined from X-ray diffraction intensities. Within the limits of experimental errors, the Debye-Waller factors associated with the two principal directions are equal. The Debye temperatures (straight theta(M)) have been evaluated. The energy of formation of vacancies (E(f)) has been estimated from a semi-empirical relation between E(f) and straight theta.

Phase-induced stability in a parametric dimer.

We report results on a model of two coupled oscillators that undergo periodic parametric modulations with a phase difference straight theta. Being to a large extent analytically solvable, the model reveals a rich straight theta dependence of the regions of parametric resonance. In particular, the intuitive notion that antiphase modulations are less prone to parametric resonance is confirmed for sufficiently large coupling and damping. Some general results concerning synchronization properties in this system are presented. We also compare our results to a recently reported mean-field model of collective parametric instability, showing that the two-oscillator model captures much of the qualitative behavior of the infinite system.

A Novel Form of “Central Pouchlike” Cataract, with Sutural Opacities, Maps to Chromosome 15q21-22

Congenital cataract is a clinically and genetically highly heterogeneous eye disorder, with autosomal dominant inheritance being most common. We investigated a large seven-generation family with 74 individuals affected by autosomal dominant congenital cataract (ADCC). The phenotype in this family can be described as "central pouchlike" cataract with sutural opacities, and it differs from the other mapped cataracts. We performed linkage analysis with microsatellite markers in this family and excluded the known candidate genes. A genomewide search revealed linkage to markers on chromosome 15, with a maximum two-point LOD score of 5.98 at straight theta=0 with marker D15S117. Multipoint analysis also gave a maximum LOD score of 5.98 at D15S117. Multipoint and haplotype analysis narrowed the cataract locus to a 10-cM region between markers D15S209 and D15S1036, closely linked to marker D15S117 in q21-q22 region of chromosome 15. This is the first report of a gene for a clinically new type of ADCC at 15q21-22 locus.

Operator Lévy motion and multiscaling anomalous diffusion.

The long-term limit motions of individual heavy-tailed (power-law) particle jumps that characterize anomalous diffusion may have different scaling rates in different directions. Operator stable motions [Y(t):t> or =0] are limits of d-dimensional random jumps that are scale-invariant according to c(H)Y(t)=Y(ct), where H is a dxd matrix. The eigenvalues of the matrix have real parts 1/alpha(j), with each positive alpha(j)< or =2. In each of the j principle directions, the random motion has a different Fickian or super-Fickian diffusion (dispersion) rate proportional to t(1/alpha(j)). These motions have a governing equation with a spatial dispersion operator that is a mixture of fractional derivatives of different order in different directions. Subsets of the generalized fractional operator include (i) a fractional Laplacian with a single order alpha and a general directional mixing measure m(straight theta); and (ii) a fractional Laplacian with uniform mixing measure (the Riesz potential). The motivation for the generalized dispersion is the observation that tracers in natural aquifers scale at different (super-Fickian) rates in the directions parallel and perpendicular to mean flow.

Glass transition of a particle in a random potential, front selection in nonlinear renormalization group, and entropic phenomena in Liouville and sinh-Gordon models.

We study via renormalization group (RG), numerics, exact bounds, and qualitative arguments the equilibrium Gibbs measure of a particle in a d-dimensional Gaussian random potential with translationally invariant logarithmic spatial correlations. We show that for any d>/=1 it exhibits a transition at T=T(c)>0. The low-temperature glass phase has a nontrivial structure, being dominated by a few distant states (with replica symmetry breaking phenomenology). In finite dimension this transition exists only in this "marginal glass" case (energy fluctuation exponent straight theta=0) and disappears if correlations grow faster (single ground-state dominance straight theta>0) or slower (high-temperature phase). The associated extremal statistics problem for correlated energy landscapes exhibits universal features which we describe using a nonlinear Kolmogorov (KPP) RG equation. These include the tails of the distribution of the minimal energy (or free energy) and the finite-size corrections, which are universal. The glass transition is closely related to Derrida's random energy models. In d=2, the connection between this problem and Liouville and sinh-Gordon models is discussed. The glass transition of the particle exhibits interesting similarities with the weak- to strong-coupling transition in Liouville (c=1 barrier) and with a transition that we conjecture for the sinh-Gordon model, with correspondence in some exact results and RG analysis. Glassy freezing of the particle is associated with the generation under RG of new local operators and of nonsmooth configurations in Liouville. Applications to Dirac fermions in random magnetic fields at criticality reveal a peculiar "quasilocalized" regime (corresponding to the glass phase for the particle), where eigenfunctions are concentrated over a finite number of distant regions, and allow us to recover the multifractal spectrum in the delocalized regime.

Linkage analysis in Spanish families with nonspecific X-linked mental retardation: Significant linkage at Xq13-q21.

Mental retardation (MR) is a genetically heterogeneous, clinically variable condition. Many cases of MR are linked to the X chromosome. The aim of this study was to identify candidate loci for nonspecific MR in Spanish samples. We selected seven families with nonspecific MR and a pattern of inheritance compatible with an X-linked disorder and a group of 26 sib pairs of mentally retarded individuals. We performed linkage analysis with a panel of 15 markers evenly distributed along the X chromosome. The study showed linkage to marker DXS8076, located in Xq21.1, by the lod score method (z = 2.11 at straight theta = 0.155) and the nonparametric extended relative pair analysis method (chi(2) = 5.32; P < 0.03). Genetic heterogeneity was found, with an estimated 75% of the families linked at recombination fraction straight theta = 0.10 to the DXS8076 locus (chi(2) = 9.51; P < 0.009). Xq13-q21 is one of the critical regions for X-linked MR previously reported, and our study supports the idea that this region may contain a locus for MR in Spanish patients.

Dynamics of inelastic collapse.

We consider a particle randomly accelerated by Gaussian white noise on the half-line x>0. The collisions of the particle with the wall at x=0 are inelastic. The velocities just before and after reflection are related by v(f)=-rv(i), where r is the coefficient of restitution. Cornell, Swift, and Bray have shown that for r<r(c)=e(-pi/sqrt[3])=0.163, there is inelastic collapse, i.e., boundary collisions localize the particle at x=0. The probability that the particle is not yet absorbed at the boundary after a time t decays, for long times, as t(-straight theta(r)). The exponent straight theta(r) is calculated exactly. We also consider the case of "partial-survival" boundary conditions, i.e., elastic reflection with probability p and absorption with probability 1-p, and derive the analogous persistence exponent straight phi(p). The exact exponents satisfy the Swift-Bray conjecture straight theta(r)=straight phi(r(2straight theta(r))).