Stationary processes whose filtrations are standard

We study the standard property of the natural filtration associated to a 0--1 valued stationary process. In our main result we show that if the process has summable memory decay, then the associated filtration is standard. We prove it by coupling techniques. For a process whose associated filtration is standard, we construct a product type filtration extending it, based upon the usual couplings and the Vershik's criterion for standardness.Comment: Published at http://dx.doi.org/10.1214/009117906000000151 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

COORDINATION CHEMISTRY OF BIS(BENZYL)PHOSPHINATE

The work presented in this dissertation deals with the coordination chemistry of the bis(benzyl)phosphinate ligand with vanadium, tungsten and cobalt. The long term goal of this project was to produce and physically characterize high oxidation state transition metal oxide phosphinate compounds with potential catalytic applications. The reaction of bis(benzyl)phosphinic acid with VO(acac)2 in the presence of water or pyridine leads to the synthesis of trimeric vanadium(IV) clusters (V3(µ3-O)O2)(µ2-O2P(CH2C6H5)2)6(H2O) and (V3(µ3-O)O2)(µ2-O2P(CH2C6H5)2)6(py). In contrast, when diphenylphosphinic acid or 2-hydroxyisophosphindoline-2-oxide were reacted with VO(acac)2, insoluble polymeric compounds were produced. The trimeric clusters were characterized using FTIR, elemental analysis, single crystal diffraction, room temperature magnetic susceptibility, thermogravimetric analysis and differential scanning calorimetry. The variable-temperature, solid-state magnetic susceptibility was measured on (V3(µ3-O)O2)(µ2-O2P(CH2C6H5)2)6(py). The polymeric compounds were characterized using FTIR, powder diffraction and elemental analysis. Two different cubane clusters made of tungsten(V) and vanadium(V) were stabilized using bis(benzyl)phosphinate. The oxidation of (V3(µ3-O)O2)(µ2-O2P(CH2C6H5)2)6(H2O) with tBuOOH led to the formation of V4(µ3-O)4(µ2-O2P(Bn)2)4(O4). W4(µ3-O)4(µ2-O2P(Bn)2)4(O4) was produced by heating W(CO)6 in a 1:1 mixture of EtOH/THF at 120 ˚C. Both compounds were characterized using single crystal diffraction, FTIR, 31P-NMR, 1H-NMR and elemental analysis. W4(µ3-O)4(µ2-O2P(Bn)2)4(O4) was also characterized using UV-vis. Cobalt(II) reacted with bis(benzyl)phosphinate to produce three different dinuclear complexes. [(py)3Co(µ2-O2P(Bn)2)3Co(py)][ClO4], (py)3Co(µ2-O2P(Bn)2)3Co(Cl) and (py)(µ2-NO3)Co(µ2-O2P(Bn)2)3Co(py) were all characterized using single crystal diffraction, elemental analysis and FTIR. Room temperature magnetic susceptibility measurements were performed on [(py)3Co(µ2-O2P(Bn)2)3Co(py)][ClO4] and (py)3Co(µ2-O2P(Bn)2)3Co(Cl). The variable-temperature, solid-state magnetic susceptibility was also measured on [(py)3Co(µ2-O2P(Bn)2)3Co(py)][ClO4]

Influence of external magnetic fields on growth of alloy nanoclusters

Kinetic Monte Carlo simulations are performed to study the influence of external magnetic fields on the growth of magnetic fcc binary alloy nanoclusters with perpendicular magnetic anisotropy. The underlying kinetic model is designed to describe essential structural and magnetic properties of CoPt_3-type clusters grown on a weakly interacting substrate through molecular beam epitaxy. The results suggest that perpendicular magnetic anisotropy can be enhanced when the field is applied during growth. For equilibrium bulk systems a significant shift of the onset temperature for L1_2 ordering is found, in agreement with predictions from Landau theory. Stronger field induced effects can be expected for magnetic fcc-alloys undergoing L1_0 ordering.Comment: 10 pages, 3 figure

Hopping Transport in the Presence of Site Energy Disorder: Temperature and Concentration Scaling of Conductivity Spectra

Recent measurements on ion conducting glasses have revealed that conductivity spectra for various temperatures and ionic concentrations can be superimposed onto a common master curve by an appropriate rescaling of the conductivity and frequency. In order to understand the origin of the observed scaling behavior, we investigate by Monte Carlo simulations the diffusion of particles in a lattice with site energy disorder for a wide range of both temperatures and concentrations. While the model can account for the changes in ionic activation energies upon changing the concentration, it in general yields conductivity spectra that exhibit no scaling behavior. However, for typical concentrations and sufficiently low temperatures, a fairly good data collapse is obtained analogous to that found in experiment.Comment: 6 pages, 4 figure

Long non-coding RNA in health and disease

Long non-coding RNAs (lncRNAs) interact with the nuclear architecture and are involved in fundamental biological mechanisms, such as imprinting, histone-code regulation, gene activation, gene repression, lineage determination, and cell proliferation, all by regulating gene expression. Understanding the lncRNA regulation of transcriptional or post-transcriptional gene regulation expands our knowledge of disease. Several associations between altered lncRNA function and gene expression have been linked to clinical disease phenotypes. Early advances have been made in developing lncRNAs as biomarkers. Several mouse models reveal that human lncRNAs have very diverse functions. Their involvement in gene and genome regulation as well as disease underscores the importance of lncRNA-mediated regulatory networks. Because of their tissue-specific expression potential, their function as activators or repressors, and their selective targeting of genes, lncRNAs are of potential therapeutic interest. We review the regulatory mechanisms of lncRNAs, their major functional principles, and discuss their role in Mendelian disorders, cancer, cardiovascular disease, and neurological disorders

Spontaneous structure formation in a network of chaotic units with variable connection strengths

As a model of temporally evolving networks, we consider a globally coupled logistic map with variable connection weights. The model exhibits self-organization of network structure, reflected by the collective behavior of units. Structural order emerges even without any inter-unit synchronization of dynamics. Within this structure, units spontaneously separate into two groups whose distinguishing feature is that the first group possesses many outwardly-directed connections to the second group, while the second group possesses only few outwardly-directed connections to the first. The relevance of the results to structure formation in neural networks is briefly discussed.Comment: 4 pages, 3 figures, REVTe

Scaling behavior in economics: II. Modeling of company growth

In the preceding paper we presented empirical results describing the growth of publicly-traded United States manufacturing firms within the years 1974--1993. Our results suggest that the data can be described by a scaling approach. Here, we propose models that may lead to some insight into these phenomena. First, we study a model in which the growth rate of a company is affected by a tendency to retain an ``optimal'' size. That model leads to an exponential distribution of the logarithm of the growth rate in agreement with the empirical results. Then, we study a hierarchical tree-like model of a company that enables us to relate the two parameters of the model to the exponent $\beta$, which describes the dependence of the standard deviation of the distribution of growth rates on size. We find that $\beta = -\ln \Pi / \ln z$, where $z$ defines the mean branching ratio of the hierarchical tree and $\Pi$ is the probability that the lower levels follow the policy of higher levels in the hierarchy. We also study the distribution of growth rates of this hierarchical model. We find that the distribution is consistent with the exponential form found empirically.Comment: 19 pages LateX, RevTeX 3, 6 figures, to appear J. Phys. I France (April 1997

Scaling behavior in economics: I. Empirical results for company growth

We address the question of the growth of firm size. To this end, we analyze the Compustat data base comprising all publicly-traded United States manufacturing firms within the years 1974-1993. We find that the distribution of firm sizes remains stable for the 20 years we study, i.e., the mean value and standard deviation remain approximately constant. We study the distribution of sizes of the ``new'' companies in each year and find it to be well approximated by a log-normal. We find (i) the distribution of the logarithm of the growth rates, for a fixed growth period of one year, and for companies with approximately the same size $S$ displays an exponential form, and (ii) the fluctuations in the growth rates -- measured by the width of this distribution $\sigma_1$ -- scale as a power law with $S$, $\sigma_1\sim S^{-\beta}$. We find that the exponent $\beta$ takes the same value, within the error bars, for several measures of the size of a company. In particular, we obtain: $\beta=0.20\pm0.03$ for sales, $\beta=0.18\pm0.03$ for number of employees, $\beta=0.18\pm0.03$ for assets, $\beta=0.18\pm0.03$ for cost of goods sold, and $\beta=0.20\pm0.03$ for property, plant, & equipment.Comment: 16 pages LateX, RevTeX 3, 10 figures, to appear J. Phys. I France (April 1997