Soluble complexes in aqueous mixtures of low charge density comb polyelectrolyte and oppositely charged surfactant probed by scattering and NMR

A low charge density polyelectrolyte with a high graft density of 45 units long poly(ethylene oxide) side-chains has been synthesized. In this comb polymer, denoted PEO(45)MEMA:METAC-2, 2 mol% of the repeating methacrylate units in the polymer backbone carry a permanent positive charge and the remaining 98 mol% a 45 unit long PEO side-chain. Here we describe the solution conformation of this polymer and its association with an anionic surfactant, sodium dodecylsulfate, SDS. It will be shown that the polymer can be viewed as a stiff rod with a cross-section radius of gyration of 29 A. The cross section of the rod contracts with increasing temperature due to decreased solvency of the PEO side-chains. The anionic surfactant associates to a significant degree with PEO(45)MEMA:METAC-2 to form soluble complexes at all stoichiometries. A cooperative association is observed as the free SDS concentration approaches 7 mM. At saturation the number of SDS molecules associated with the polymer amounts to 10 for each PEO side-chain. Two distinct populations of associated surfactants are observed, one is suggested to be molecularly distributed over the comb polymer and the other constitutes small micellar-like structures at the periphery of the aggregate. These conclusions are reached based on results from small-angle neutron scattering, static light scattering, NMR, and surface tension measurements.     

Consistent estimation of the intensity function of a cyclic Poisson process

We construct and investigate a consistent kernel-type nonparametric estimator of the intensity function of a cyclic Poisson process when the period is unknown. We do not assume any particular parametric form for the intensity function, nor do we even assume that it is continuous. Moreover, we consider the situation when only a single realization of the Poisson process is available, and only in a bounded window. We prove, in particular, that the proposed estimator is consistent when the size of the window indefinitely expands. We also obtain complete convergence of the estimator.     

Statistical properties of a kernel-type estimator of the intensity function of a cyclic Poisson process

We consider a kernel-type nonparametric estimator of the intensity function of a cyclic Poisson process when the period is unknown. We assume that only a single realization of the Poisson process is observed in a bounded window which expands in time. We compute the asymptotic bias, variance, and the mean-squared error of the estimator when the window indefinitely expands.     

Estimating the distortion parameter of the proportional-hazard premium for heavy-tailed losses

The distortion parameter reflects the amount of loading in insurance premiums. A specific value of a given premium determines a value of the distortion parameter, which depends on the underlying loss distribution. Estimating the parameter, therefore, becomes a statistical inferential problem, which has been initiated by Jones and Zitikis [Jones, B.L., Zitikis, R., 2007. Risk measures, distortion parameters, and their empirical estimation. Insurance: Mathematics and Economics, 41, 279–297] in the case of the distortion premium and tackled within the framework of the central limit theorem. Heavy-tailed losses do not fall into this framework as they rely on the extreme-value theory. In this paper, we concentrate on a special but important distortion premium, called the proportional-hazard premium, and propose an estimator for its distortion parameter in the case of heavy-tailed losses. We derive an asymptotic distribution of the estimator, construct a practically implementable confidence interval for the distortion parameter, and illustrate the performance of the interval in a simulation study.     

On the Vervaat and Vervaat-Error Processes

It has been known since the pioneering works of Wim Vervaat in the early 70"s that the appropriately normalized Vervaat process asymptotically behaves like one half times the squared empirical process. In this paper we present a survey of the results concerning various distances between the Vervaat process and one half times the squared empirical process. In particular, the pointwise, L_p-, and sup-distances between these two processes are given full consideration.     

A Robust Heuristic Estimator for the Period of a Poisson Intensity Function

While there are a number of methods for estimating the intensity of a cyclic point process, these assume prior estimation of the period itself. The standard method for the latter is the periodogram, or spectral analysis, approach. This is a parametric method which is sensitive to the form, in particular the number of peaks per cycle, of the intensity. We construct a family of nonparametric estimators for the period of a cyclic Poisson process, with the object of robustness against the form of the intensity. These are tested, along with the standard periodogram estimate and an earlier nonparametric estimator, on simulated data from a range of intensity functions. While the nonparametric estimators presently lack the well-developed asymptotic and statistical properties of the periodogram, the best of them is almost as accurate as the periodogram for the unimodal intensity cycles on which the latter is based. Whereas the periodogram cannot handle multimodal cycles at all, the better nonparametric estimators are reasonably accurate, and sometimes err by estimating multiples of the period rather than divisors, errors that are arguably less damaging. We conclude with some remarks concerning the derivation of asymptotic properties for our nonparametric estimator.     

Two-photon photodynamic therapy of C6 cells by means of 5-aminolevulinic acid induced protoporphyrin IX

Photodynamic therapy (PDT) has received increased attention as a treatment modality for malignant tumors as well as non-oncologic diseases such as age-related macular degeneration (AMD). An alternative to excite the photosensitizer by the common one-photon absorption is the method of two-photon excitation (TPE). This two-photon photodynamic therapy has the potential of improving the therapeutic outcome due to a highly localized photodynamic effect. The present study investigated the two-photon excited PDT performing in vitro experiments where C6 rat glioma cells were irradiated with a pulsed and focused fs Ti:sapphire laser emitting light at 800 nm. The irradiance distribution of the laser beam was carefully analyzed before the experiment and the applied irradiance was known for each position within the irradiated cell layer. Cells were divided into four groups and one group was incubated with 5-ALA and irradiated 4-5h later. The survival of this group was tested after irradiation by means of ethidium bromide and acridine orange staining and compared to a control group, which was irradiated under the same conditions, but not incubated with 5-ALA before. Both groups showed necrotic areas depending on the applied irradiance, the value of which at the margin of the necrotic area could be deduced from its size. 5-ALA incubated cells became necrotic after irradiation with a mean irradiance above 6.1 x 10(10) W/cm(2), while non-incubated cells remained viable. Cells of both groups became necrotic when treated with an irradiance above 10.9 x 10(10) W/cm(2). The observed affected area of the cell layers was between 0.13 mm(2) and 1.10 mm(2). Since the irradiation of non-incubated cells below the mean power density of 10.9 x 10(10) W/cm(2) induced no necrosis, apparently no thermal damage was induced in the cells and necrosis of the 5-ALA incubated cells can be ascribed to the photodynamic effect induced by two-photon excitation. The successful photodynamic treatment of a large area of a monolayer cell culture induced by two-photon excitation offers new perspectives for photodynamic treatment modalities.     

Searching for and Quantifying Nonconvexity Regions of Functions*

Lithuanian Mathematical Journal - Convexity plays a prominent role in a number of areas, but practical considerations often lead to nonconvex functions. We suggest a method for determining regions...     

Confidence regions for the intensity function of a cyclic Poisson process

A classical approach to constructing simultaneous confidence intervals (i.e., confidence bands or regions) for a function is via establishing a limiting process of the appropriately normalized difference between the function and its empirical estimator. In the present paper we depart from this approach and construct confidence bands for the intensity function of a cyclic Poisson process via extreme value type asymptotic results for the appropriately normalized supremum of the difference between the intensity function and its empirical estimator.