Simple Constructions of Almost k-wise Independent Random Variables

We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is (2 + o(1)) (log log n + k/2 + log k + log 1/?), where ? is the statistical difference between the distribution induced on any k bit locations and the uniform distribution. This is asymptotically comparable to the construction recently presented by Naor and Naor (our size bound is better as long as ? < 1/(k log n)). An additional advantage of our constructions is their simplicity.     

Discussion of “Copulas: Tales and facts”, by Thomas Mikosch

As Prof. Mikosch correctly points out, there exists very little sound statistical theory on modelling dependence using copulas. In this contribution, an open problem is presented concerning the efficient estimation of the parameter of a copula when no parametric assumptions are made regarding the marginal distributions.     

A counterexample to the strong subadditivity of extremal plurisubharmonic functions

A simple example is given which shows that one way have $$h_E (z^0 ) + h_F (z^0 ) > h_{E \cup F} (z^0 ) + h_{E \cap F} (z^0 )$$ for some pointz ⁰∈ω, where $$h_E (z) = \sup \{ u(z):u \in PSH (\Omega ),u \leqslant 0 on E,u \leqslant 1 in \Omega \} ,z \in \Omega ,$$ is the extremal function often studied in complex analysis.     

BIOLOGICAL ACTIVITIES OF PHTHALOCYANINES-X. SYNTHESES AND ANALYSES OF SULFONATED PHTHALOCYANINES

Abstract— Synthetic methods to obtain selectively sulfonated metallo phthalocyanines are compared. Both condensation and direct sulfonation procedures lead to mixtures of mono- to tetrasulfonated products which are resolved by reverse phase liquid chromatography in buffered aqueous-methanol. The proportion of sulfonated derivatives is examined as a function of the starting reagents in the case of the condensation method, and as a function of the temperature and reaction time in the case of the direct sulfonation procedure. The number of sulfonate groups per phthalocyanine molecule is determined by oxidative degradation of the phthalocyanine ring followed by quantitative chromatographic analysis of the sulfophthalamide and phthalamide fragments.     

Application of Horner–Emmons Olefination to the Crown-Ether Derivatives

An effective synthetic approach to the preparation of a new crown-ether vinylogs involving the Horner–Emmons olefination of carbonyl precursors with the use of C₂- and C₅-phosphonates was proposed. The effects of the conjugation chain length and the nature of the terminal polar functions in the phosphonate reagent on the yield and process stereoselectivity were discussed.     

THE PHOTOCHEMICAL YIELD OF SINGLET OXYGEN FROM PORPHYRINS IN DIFFERENT STATES OF AGGREGATION

Abstract— Aqueous solutions of hematoporphyrin and hematoporphyrin derivatives were exposed to light. When present in such solutions tryptophan is degraded by a singlet oxygen mechanism. This is true for excitation at 396 nm, where porphyrin monomers have their absorption maximum, as well as for excitation at 360 nm, where porphyrin aggregates seem to absorb strongly. The quantum yield of singlet oxygen production is similar within 25% for excitation at 396 and 360 nm while the fluorescence quantum yield is more than a factor 2 lower for excitation at 360 nm than for excitation at 396 nm. Photoexcitation of the clinically used hematopotophyrin derivatives photofrin I and photofrin II produces singlet oxygen with significantly smaller yields than photoexcitation of hematoporphyrin. Thus, the aggregates present in solutions of photofrin I and photofrin II are of a different nature than those present in aqueous solutions of hematoporphyrin.     

SULFOPHTHALOCYANINES FOR PHOTODYNAMIC INACTIVATION OF VIRUSES IN BLOOD PRODUCTS: EFFECT OF STRUCTURAL MODIFICATIONS

Abstract— Transmission of infectious diseases through blood transfusions is well known. Ultraviolet irradiation, solvents and detergents provide a means of sterilizing noncellular blood components. However these harsh methods are not applicable to cellular blood products. Recently, attempts have been made to sterilize biological fluids using photodynamic treatment and phthalocyanine (Pc) dyes have been advanced as photosensitizers for this purpose. We have evaluated a series of water-soluble Pc, chelated with different central metal ions, substituted to different degrees with sulfonato and r-butyl groups, for their effectiveness to reduce virus infectivity in red blood cell suspensions. Vaccinia virus cytopathogenicity was determined by endpoint serial dilutions in the CV-1 cell line. Anti-viral activity increased with the central metal ion in the following order: Ga(III) < Al(III) < Zn(II), and varied inversely with the degree of sulfonation. Furthermore, addition of a t -butyl group onto the trisulfonated dyes (PcS₃[ t -Bul) resulted in a 5–40-fold increase in anti-viral potency, suggesting that amphiphilicity enhances the photodynamic activity of the dye. Strong anti-viral photosensitizing properties cannot be the sole selection criterion. Of equal importance is the preservation of blood component integrity. Accordingly, the photohemolytic activity of the dyes was evaluated using the rate of hemolysis as a parameter and a toxicity index was defined. Among the most active dyes, the AlPcS₃( t -Bu) complex exhibited the most favorable anti-viral properties combined with a low toxicity index. Our results suggest that trisulfophthalocyanines, bearing an additional t -butyl group to enhance amphiphilicity, are particularly promising dyes for photodynamic blood sterilization.     

Dielectric relaxation studies of 1-hexanol and 1,2-hexanediol in heptane

Solutions of 1-hexanol and 1,2-hexanediol in heptane have been investigated tigated by means of dielectric time domain spectroscopy (TDS). The permittivity spectrum of 1-hexanol in heptane is characterized by a model function containing a sum of three elementary Debye dispersions, while 1,2-hexanediol in heptane is best described by a Cole-Davidson model function. It is shown that dilute solutions of 1-hexanol in heptane have a completely different behavior to that of 1,2-hexanediol. For the diol, the relaxation time levels off at a high value indicating an existence of higher hydrogen bonded complexes. It is possible to quantify the relative amount of monomeric 1-alcohol molecules from the dielectric spectrum. The monomerization rate for 1-hexanol upon dilution with heptane is initially low, but increases rapidly for mole fractions of heptane exceeding 0.4.     

Superpositioned dielectrophoresis for enhanced trapping efficiency

One of the major applications for dielectrophoresis is selective trapping and fractionation of particles. If the surrounding medium is of low conductivity, the trapping force is high, but if the conductivity increases, the attraction decreases and may even become negative. However, high-conductivity media are essential when working with biological material such as living cells. In this paper, some basic calculations have been performed, and a model has been developed which employs both positive and negative dielectrophoresis in a channel with interdigitated electrodes. The finite element method was utilized to predict the trajectories of Escherichia coli bacteria in the superpositioned electrical fields. It is shown that a drastic improvement of trapping efficiency can be obtained in this way, when a high conductivity medium is employed.