Estimating the Heavy Tail Index from Scaling Properties

This paper deals with the estimation of the tail index for empirical heavy-tailed distributions, such as have been encountered in telecommunication systems. We present a method (called the scaling estimator) based on the scaling properties of sums of heavy-tailed random variables. It has the advantages of being nonparametric, of being easy to apply, of yielding a single value, and of being relatively accurate on synthetic datasets. Since the method relies on the scaling of sums, it measures a property that is often one of the most important effects of heavy-tailed behavior. Most importantly, we present evidence that the scaling estimator appears to increase in accuracy as the size of the dataset grows. It is thus particularly suited for large datasets, as are increasingly encountered in measurements of telecommunications and computing systems.     

Decomposition of self-similar stable mixed moving averages

 Let α? (1,2) and X _α be a symmetric α-stable (S α S) process with stationary increments given by the mixed moving average

New classes of self-similar symmetric stable random fields

We construct two new classes of symmetric stable self-similar random fields with stationary increments, one of the moving average type, the other of the harmonizable type. The fields are defined through an integral representation whose kernel involves a norm on ⁿ . We examine how the choice of the norm affects the finite-dimensional distributions. We also study the processes which are obtained by projecting the random fields on a one-dimensional subspace. We compare these projection processes with each other and with other well-known self-similar processes and we characterize their asymptotic dependence structure.The research was done at Boston University while the first author was on leave from the Hugo Steinhaus Center, Poland. The second author was partially supported by the ONR Grant N00014-90-J-1287 at Boston University and by a grant of the United States-Israel Binational Science Foundation.     

Convergence of integrated processes of arbitrary Hermite rank

Summary Let {X(s), –<s<} be a normalized stationary Gaussian process with a long-range correlation. The weak limit in C[0,1] of the integrated process , is investigated. Here d(x) = x ^H L(x) with <H<1 and L(x) is a slowly varying function at infinity. The function G satisfies EG(X(s))=0, EG ² (X(s))< and has arbitrary Hermite rank m1. (The Hermite rank of G is the index of the first non-zero coefficient in the expansion of G in Hermite polynomials.) It is shown thatZ _x (t) converges for all m1 to some process ¯Z _m (t) that depends essentially on m. The limiting process ¯Z _m (t) is characterized through various representations involving multiple Itô integrals. These representations are all equivalent in the finite-dimensional distributions sense. The processes ¯Z _m (t) are non-Gaussian when m2. They are self-similar, that is,¯Z _m (at) and a ^H ¯Z _m (t) have the same finite-dimensional distributions for all a>0.Research supported by the National Science Foundation grants MCS 77-03543 and ENG 78-11454.This paper contains results closely connected to those of the paper by Dobrushin and Major, Z. Wahrscheinlichkeitstheorie verw. Gebiete 50, 27–52 (1979). The investigations were done independently and at about the same time. Different methods were usedDedicated to Professor Leopold Schmetterer on occasion of his 60th Birthday     

DNA scaffold supports long-lived vibronic coherence in an indodicarbocyanine (Cy5) dimer

Vibronic coupling between pigment molecules is believed to prolong coherences in photosynthetic pigment–protein complexes. Reproducing long-lived coherences using vibronically coupled chromophores in synthetic DNA constructs presents a biomimetic route to efficient artificial light harvesting. Here, we present two-dimensional (2D) electronic spectra of one monomeric Cy5 construct and two dimeric Cy5 constructs (0 bp and 1 bp between dyes) on a DNA scaffold and perform beating frequency analysis to interpret observed coherences. Power spectra of quantum beating signals of the dimers reveal high frequency oscillations that correspond to coherences between vibronic exciton states. Beating frequency maps confirm that these oscillations, 1270 cm⁻¹ and 1545 cm⁻¹ for the 0-bp dimer and 1100 cm⁻¹ for the 1-bp dimer, are coherences between vibronic exciton states and that these coherences persist for ∼300 fs. Our observations are well described by a vibronic exciton model, which predicts the excitonic coupling strength in the dimers and the resulting molecular exciton states. The energy spacing between those states closely corresponds to the observed beat frequencies. MD simulations indicate that the dyes in our constructs lie largely internal to the DNA base stacking region, similar to the native design of biological light harvesting complexes. Observed coherences persist on the timescale of photosynthetic energy transfer yielding further parallels to observed biological coherences, establishing DNA as an attractive scaffold for synthetic light harvesting applications.

Dyes coupled to DNA display distance-dependent vibronic couplings that prolongs quantum coherences detected with 2D spectroscopy.     

High-speed simultaneous ion-exclusion/cation-exchange chromatography of anions and cations on a weakly acidic cation-exchange resin column

The simultaneous ion-exclusion/cation-exchange separation column packed with a polymethacrylate-based weakly acidic cation-exchange resin of 3 microm particle size was used to achieve the simultaneous high-speed separation of anions and cations (Cl(-), NO3(-), SO4(2-), Na(+), K(+), NH4(+), Ca(2+) and Mg(2+)) commonly found in environmental samples. The high-speed simultaneous separation is based on a combination of the ion-exclusion mechanism for the anions and the cation-exchange mechanism for cations. The complete separation of the anions and cations was achieved in 5 min by elution with 15 mM tartaric acid-2.5 mM 18-crown-6 at a flow-rate of 1.5 ml/min. Detection limits at S/N=3 ranged from 0.36 to 0.68 microM for anions and 0.63-0.99 microM for cations. This method has been applied to the simultaneous determination of anions and cations in several environmental waters with satisfactory results.     

Molecular dynamics simulations of osmosis and reverse osmosis in solutions

Computer simulation studies using the method of molecular dynamics have been carried out to investigate osmosis and reverse osmosis in solutions separated by semi-permeable membranes. The method has been used to study the dynamic approach to equilibrium in such systems from their initial nonequilibrium state. In addition density profiles of both the solute and solvent molecules have been investigated, especially near the walls for adsorption effects. Finally the diffusion coefficients and osmotic pressure have also been measured.Our results show both osmosis and reverse osmosis, as well as a smooth transition between the two when either the solution concentration is changed, or the density (pressure) difference between the solvent and solution compartments is varied. We believe this new method can be used to improve our understanding of these two important phenomena at the molecular level.     

Materials analysis using confocal Raman microscopy

The recent development of Raman microscopes with high optical throughput and very sensitive CCD cameras has led to Raman spectroscopy again competing effectively with FTIR methods for materials analysis. Modern Raman instruments, designed to operate confocally without serious alignment or energy trade-off problems, allow depth profiling of optically transparent polymers and polymer matrices to be routinely obtained with a spatial resolution of 1–2 μm. The use of such an instrument is illustrated by describing recent work on polymeric material problems including, 1 The distribution and redistribution of small molecules in polymeric matrices. 2 The monitoring of adhesion primer diffusion at a polymer/silica interface. 3 The determination of the extent of interdiffusion and interaction at a polymer/polymer interface. 4 A comparison of confocal and micotoming approaches to polymer laminate analysis. The range of possible applications is increasing rapidly. It is clear that Raman microscopy will become a very important tool for future materials analysis, both in the polymer area and many other areas.     

Fluorescence Analysis of Acridine Orange Adsorbate at the Water/N-Heptane Interface, Bulk and Interface

The amphiphilic nature of 3, 6-bisdimethylaminoacridine (trivial name, acridine orange) can be used to characterize (polar/nonpolar) interfaces. This paper studies the properties of acridine orange and its dodecyl derivative at a solvent interface by internal reflection and tension determinations. In the case of absorbance measurements of crystallized acridine orange, the potenz value of the conventional acid dissociation constant pK _a was found to be 9.6. A clear isosbestic point could be obtained after purification at a unique pH for different concentrations. In contrast, in the absorbance measurements of acridine orange dodecyl, no isosbestic point was observed; this was attributed to the free long dodecyl chain. The overlap in the absorbance spectrum and the normalized fluorescence spectrum was found in many solvents around 500 nm. Neutral species were more likely to transfer into organic phase upon shaking. For fluorescence measurements both steady-state and time-resolved spectra were investigated. Results showed that at the interface a bathochromic shift happened to the maxima. This means that chromophore species aggregated at the interface as the dimer or trimer or the macro oligomer. Fluorescence polarization in bulk was calculated and found to be ca. 0.4. For interfacial measurements a dynamic volume method was applied to obtain the interfacial tension. An extrapolated Gibbs plot was obtained. Increasing bulk concentration increased the concentration at the interface to a finite value representing saturation.     

Electron transfer networks

In this paper, we study electron transfer networks. These are generalisations of electron transport chains, and consist of a set of substrates which can exist in reduced and oxidised forms. The reduced forms can transfer electrons to the oxidised forms, and there are some electron inflow and outflow processes. We show that under mild assumptions, such systems can have only very simple behaviour, with a single globally stable equilibrium. To prove this we show that the Jacobian of the system has negative logarithmic norm in an appropriate norm. From this result, uniqueness and global stability of any equilibrium follows. The results extend, with only minor modifications, to binary interconversion networks, where the only allowed reactions are interconversions between substrates, and inflow/outflow processes.