Efficient, nonparametric removal of noise and recovery of probability distributions from time series using nonlinear-correlation functions: Photon and photon-counting noise.

A preceding paper [M. Dhar, J. A.

Efficient, nonparametric removal of noise and recovery of probability distributions from time series using nonlinear-correlation functions: Additive noise.

Single-molecule and related experiments yield time series of an observable as it fluctuates due to thermal motion. In such data, it can be difficult to distinguish fluctuating signal from fluctuating noise. We present a method of separating signal from noise using nonlinear-correlation functions.

Tinea Gladiatorum Detection With a Dermatophyte Test Strip.

Objective: Determine sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), and concordance of diafactory hs-TP (DTS) to detect tinea gladiatorum using direct potassium hydroxide (KOH) microscopy as the reference standard.

Design: Prospective, comparative study.

Setting: Seventeen Minnesota high schools during the winter wrestling season.

Nonlinear measurements of kinetics and generalized dynamical modes. II. Application to a simulation of solvation dynamics in an ionic liquid.

Solvation dynamics in ionic liquids show features that are often associated with supercooled liquids, including "stretched" nonexponential relaxation. To better understand the mechanism behind the stretching, the nonlinear mode-correlation methods proposed in Paper I [S. R.

Nonlinear measurements of kinetics and generalized dynamical modes. I. Extracting the one-dimensional Green's function from a time series.

Often, a single correlation function is used to measure the kinetics of a complex system. In contrast, a large set of k-vector modes and their correlation functions are commonly defined for motion in free space. This set can be transformed to the van Hove correlation function, which is the Green's function for molecular diffusion.

Jump-precursor state emerges below the crossover temperature in supercooled o-terphenyl.

In a supercooled liquid, the crossover temperature T_{c} separates a high-temperature region of diffusive dynamics from a low-temperature region of activated dynamics. A molecular-dynamics simulation of all-atom, flexible o-terphenyl [Eastwood et al., J.

Micelle Heterogeneity from the 2D Kinetics of Solute Rotation.

The chemical and physical properties of microstructured materials vary with position. The photophysics of solute molecules can measure these local properties, but they often show multiple rates (rate dispersion), which complicates the interpretation. In the case of micelles, rate dispersion in a solute's anisotropy decay has been assigned to either local anisotropy or heterogeneity in the local viscosity.

Nonparametric analysis of nonexponential and multidimensional kinetics. I. Quantifying rate dispersion, rate heterogeneity, and exchange dynamics.

The quantification of nonexponential (dispersed) kinetics has relied on empirical functions, which yield parameters that are neither unique nor easily related to the underlying mechanism. Multidimensional kinetics provide more information on dispersed processes, but a good approach to their analysis is even less clear than for standard, one-dimensional kinetics. This paper is the first in a series that analyzes kinetic data in one or many dimensions with a scheme that is nonparametric: it quantifies nonexponential decays without relying on a specific functional form.

Measuring a hidden coordinate: Rate-exchange kinetics from 3D correlation functions.

Nonexponential kinetics imply the existence of at least one slow variable other than the observable, that is, the system has a "hidden" coordinate. We develop a simple, but general, model that allows multidimensional correlation functions to be calculated for these systems. Homogeneous and heterogeneous mechanisms are both included, and slow exchange of the rates is allowed.

Rate and Amplitude Heterogeneity in the Solvation Response of an Ionic Liquid.

In contrast with conventional liquids, ionic liquids have solvation dynamics with more rate dispersion and with average times that do not agree with dielectric measurements. A kinetic analog of multidimensional spectroscopy is introduced and used to look for heterogeneity in simulations of coumarin 153 in [Im12][BF4]. Strong heterogeneity is found in the diffusive solvation rate.

Two-Dimensional Anisotropy Measurements Showing Local Heterogeneity in a Polymer Melt.

In polymers, the rotation of a small solute is nonexponential. Either heterogeneity in the local friction or local anisotropy-a homogeneous process-may be responsible. A new, two-dimensional anisotropy experiment is demonstrated on this problem.

When is a single molecule heterogeneous? A multidimensional answer and its application to dynamics near the glass transition.

Even for apparently simple condensed-phase processes, bulk measurements of relaxation often yield nonexponential decays; the rate appears to be dispersed over a range of values. Taking averages over individual molecules is an intuitive way to determine whether heterogeneity is responsible for such rate dispersion. However, this method is in fundamental conflict with ergodic behavior and often yields ambiguous results.

Multiple population-period transient spectroscopy (MUPPETS) of CdSe/ZnS nanoparticles. II. Effects of high fluence and solvent heating.

Multiple population-period transient spectroscopy (MUPPETS) is a six-pulse experiment with two time dimensions that is capable of adding information about systems with complicated kinetics. The core theory for MUPPETS focuses on the χ(5) response of the chromophores. This theory was used to analyze the dynamics of excitons and biexcitons in CdSe/ZnS core-shell nanoparticles in part I of this paper [J.

Multiple population-period transient spectroscopy (MUPPETS) of CdSe/ZnS nanoparticles. I. Exciton and biexciton dynamics.

The nonradiative relaxation of both the exciton and biexciton in CdSe/ZnS core-shell nanoparticles have complicated, nonexponential kinetics. This paper presents data on this system from multiple population-period transient spectroscopy (MUPPETS), a method for two-dimensional kinetics. An initial report of a dispersed (nonexponential) biexciton decay [J.

Multiple population-period transient spectroscopy (MUPPETS) in excitonic systems.

Time-resolved experiments with more than one period of incoherent time evolution are becoming increasingly accessible. When applied to a two-level system, these experiments separate homogeneous and heterogeneous contributions to kinetic dispersion, i.e.

Rate dispersion in the biexciton decay of CdSe/ZnS nanoparticles from multiple population-period transient spectroscopy.

Measurements of biexciton decays in semiconductor nanoparticles are easily contaminated by contributions from photoproducts or higher excitons. Theoretical work has shown that multiple population-period transient spectroscopy (MUPPETS) can measure biexciton decays free from these interferences. In this communication, the biexciton decay of CdSe/ZnS core-shell nanoparticles is measured with MUPPETS.

Heterogeneity of the electron-trapping kinetics in CdSe nanoparticles.

The kinetics of electron trapping in CdSe nanoparticles are examined from 0.5 ps to 1.8 ns.

Heterogeneous reaction rates in an ionic liquid: quantitative results from two-dimensional multiple population-period transient spectroscopy.

The hypotheses that ionic liquids are structurally heterogeneous at the molecular level and, even further, that this heterogeneity can transfer to the rates of reactions run in ionic liquids is being actively debated. Here, this hypothesis is tested using multiple population-period transient spectroscopy (MUPPETS), an emerging type of multidimensional measurement that resolves the kinetics of subensembles within a heterogeneous sample. A previous MUPPETS study of the excited-state twisting and electronic relaxation of auramine indicated that an ionic-liquid solvent induces rate dispersion due to a combination of heterogeneous and homogeneous processes, but those data could not quantitatively separate these contributions [Khurmi, C.

Thermal gratings and phase in high-order, transient-grating spectroscopy.

Thermal gratings are a well known feature in one-dimensional (i.e., single excitation) transient-grating spectroscopy.

Hilbert-space treatment of incoherent, time-resolved spectroscopy. II. Pathway description of optical multiple population-period transient spectroscopy.

This paper applies the general methods developed in the previous paper (Paper I) to the case of one-photon, dipole transitions of a molecular solute. The results generalize transient-grating spectroscopy to an arbitrarily number of dimensions. Transition and detection operators are derived, and their matrix elements are calculated in the complex-valued basis set developed in Paper I.

Hilbert-space treatment of incoherent, time-resolved spectroscopy. I. Formalism, a tensorial classification of high-order orientational gratings and generalized MUPPETS "echoes".

Time-resolved spectroscopy that uses more than one incoherent excitation, and thus has multiple periods of time evolution, is becoming more common. A recent example is multiple population-period transient spectroscopy (MUPPETS), which is implemented as a high-order transient grating. In this paper, a formalism is developed to treat these types of incoherent spectroscopy in a manner that parallels the Liouville-pathway formalism used to treat multidimensional coherent spectroscopy.

Dynamics of water and ions near DNA: comparison of simulation to time-resolved stokes-shift experiments.

Time-resolved Stokes-shift experiments measure the dynamics of biomolecules and of the perturbed solvent near them on subnanosecond time scales, but molecular dynamics simulations are needed to provide a clear interpretation of the results. Here we show that simulations using standard methods quantitatively reproduce the main features of TRSS experiments in DNA and provide a molecular assignment for the dynamics. The simulations reproduce the magnitude and unusual power-law dynamics of the Stokes shift seen in recent experiments [ Andreatta, D.

Parallels between multiple population-period transient spectroscopy and multidimensional coherence spectroscopies.

We have recently shown that homogeneous and heterogeneous kinetics can be distinguished by experiments that compare the evolution of the population of a state over two time intervals [E. van Veldhoven et al., ChemPhysChem 8, 1761 (2007)].