The Computational Complexity of the Chow Form

We present a bounded probability algorithm for the computation of the Chowforms of the equidimensional components of an algebraic variety. In particular, this gives an alternative procedure for the effective equidimensional decomposition of the variety, since each equidimensional component is characterized by its Chow form. The expected complexity of the algorithm is polynomial in the size and the geometric degree of the input equation system defining the variety. Hence it improves (or meets in some special cases) the complexity of all previous algorithms for computing Chow forms. In addition to this, we clarify the probability and uniformity aspects, which constitutes a further contribution of the paper. The algorithm is based on elimination theory techniques, in line with the geometric resolution algorithm due to M. Giusti, J. Heintz, L. M. Pardo, and their collaborators. In fact, ours can be considered as an extension of their algorithm for zero-dimensional systems to the case of positive-dimensional varieties. The key element for dealing with positive-dimensional varieties is a new Poisson-type product formula. This formula allows us to compute the Chow form of an equidimensional variety from a suitable zero-dimensional fiber. As an application, we obtain an algorithm to compute a subclass of sparse resultants, whose complexity is polynomial in the dimension and the volume of the input set of exponents. As another application, we derive an algorithm for the computation of the (unique) solution of a generic overdetermined polynomial equation system.     

Group algebras of Kleinian type and groups of units

The algebras of Kleinian type are finite-dimensional semisimple rational algebras A such that the group of units of an order in A is commensurable with a direct product of Kleinian groups. We classify the Schur algebras of Kleinian type and the group algebras of Kleinian type. As an application, we characterize the group rings RG, with R an order in a number field and G a finite group, such that the group of units of RG is virtually a direct product of free-by-free groups.     

Determination of the partition coefficients of the nonionic detergent C12E7 between lipid-detergent mixed membranes and water by means of Laurdan fluorescence spectroscopy

The membrane-water partition coefficient of the detergent C₁₂E₇ between water and C₁₂E₇/POPC mixed membranes has been determined by means of steady-state fluorescence spectroscopy. The emission spectra of the fluorescent probe Laurdan were used as an indicator of membrane composition at different membrane concentrations in the sample. The partition coefficient expressed as the ratio of the mole fractions of the detergent in the membrane and water phases is about 6^*10⁵ at low molar ratios of C₁₂E₇/POPC (R _c ) and decreases rapidly with increasingR _c . The limiting detergent content of the lamellar phase (R _c ^* >0.8) is indicated by a minimum ofP(R _c ).     

A fluorescence-based method for direct measurement of submicrosecond intramolecular contact formation in biopolymers: an exploratory study with polypeptides.

A fluorescent amino acid derivative (Fmoc-DBO) has been synthesized, which contains 2,3-diazabicyclo[2.2.2]oct-2-ene (DBO) as a small, hydrophilic fluorophore with an extremely long fluorescence lifetime (325 ns in H2O and 505 ns in D2O under air). Polypeptides containing both the DBO residue and an efficient fluorescence quencher allow the measurement of rate constants for intramolecular end-to-end contact formation. Bimolecular quenching experiments indicated that Trp, Cys, Met, and Tyr are efficient quenchers of DBO (k(q) = 20, 5.1, 4.5, and 3.6 x 10(8) M(-1) x s(-1) in D2O), while the other amino acids are inefficient. The quenching by Trp, which was selected as an intrinsic quencher, is presumed to involve exciplex-induced deactivation. Flexible, structureless polypeptides, Trp-(Gly-Ser)n-DBO-NH2, were prepared by standard solid-phase synthesis, and the rates of contact formation were measured through the intramolecular fluorescence quenching of DBO by Trp with time-correlated single-photon counting, laser flash photolysis, and steady-state fluorometry. Rate constants of 4.1, 6.8, 4.9, 3.1, 2.0, and 1.1 x 10(7) s(-1) for n = 0, 1, 2, 4, 6, and 10 were obtained. Noteworthy was the relatively slow quenching for the shortest peptide (n = 0). The kinetic data are in agreement with recent transient absorption studies of triplet probes for related peptides, but the rate constants are significantly larger. In contrast to the flexible structureless Gly-Ser polypeptides, the polyproline Trp-Pro4-DBO-NH2 showed insignificant fluorescence quenching, suggesting that a high polypeptide flexibility and the possibility of probe-quencher contact is essential to induce quenching. Advantages of the new fluorescence-based method for measuring contact formation rates in biopolymers include high accuracy, fast time range (100 ps-1 micros), and the possibility to perform measurements in water under air.     

The First Online Capillary Electrophoresis-Microscale Thermophoresis (CE-MST) Method for the Analysis of Dynamic Equilibria—The Determination of the Acidity Constant of Fluorescein Isothiocyanate

This article presents the first successful application of a capillary electrophoresis-microscale thermophoresis tandem technique (CE-MST) for determining the values of equilibrium constant, realized by connecting online the CE and MST instruments using a fused-silica capillary. The acid-base dissociation of fluorescein isothiocyanate, expressed by the acidity constant value (pK_a), was used as a model. The measurement procedure consisted of introducing a mixture containing the analyte and a deliberately added interferent into the CE capillary, electrophoretic separation of the analyte from the interferent, the detection of the analyte with a CE-integrated detector, detection with a MST detector, and then stopping the flow temporarily by turning off the voltage source to conduct the thermophoretic measurement. The analysis of migration times, peak areas and MST responses obtained concurrently for the same sample allowed us to determine the pK_a value using three independent methods integrated within one instrumentation. The analyte was effectively separated from the interferent, and the acidity values turned out to be consistent with each other. An attempt was also made to replace the standard commercial CE instrument with a home-made portable CE setup. As a result, the similar pK_a value was obtained, at the same time proving the possibility of increasing cost efficiency and reducing energy consumption. Overall, the CE-MST technique has a number of limitations, but its unique analytical capabilities may be beneficial for some applications, especially when sample separation is needed prior to the thermophoretic measurement.     

Leptin in Human Milk—One of the Key Regulators of Nutritional Programming

Breast milk is the optimal food for infants and toddlers, providing basic nutrients. It is also a source of many biologically active substances. Among them are hormones responsible for metabolic balance. One of the hormones taken in with breast milk by a breastfed baby is leptin. This hormone is involved in the regulation of appetite, informing the brain about the body’s energy resources. Having the correct mechanisms related to the action of leptin is a factor reducing the risk of obesity. The natural presence of leptin in the composition of breast milk suggests that it has a specific role in shaping the health of a breastfed child. Obesity as a disease of civilization affects more and more people, including children. The development of this disease is multifaceted and determined by many factors, including genetic and environmental factors such as eating habits and low physical activity. Behind obesity, there are complex mechanisms in which many elements of the human body are involved. Understanding the effects of breastfeeding as a natural source of leptin can help prevent childhood obesity and development of this disease in future life.     

Ultrasound-assisted microencapsulation of jackfruit extract in eco-friendly powder particles: characterization and antiproliferative activity

The aim of the article was to develop stable and safe eco-friendly microcapsules and evaluate their physicochemical properties and their efficiency to protect a jackfruit extract. Eco-friendly microcapsules were produced by ultrasound and spray drying using only three safe ingredients: sucrose ester (SE), miglyol and maltodextrin (DE = 10). Some physicochemical properties, particle morphology, FT-IR, differential scanning calorimetry and antiproliferative activity were determined for microcapsules loaded or not with the jackfuit extract. The results revealed that the encapsulation process by spray drying produced stable microcapsules, with adequate physicochemical and fluid properties for a powder product. The cell viability on the proliferation of M12.C3.F6 cell line was not affected by powder microcapsules without jackfruit extract, indicating that capsules are not toxic for these cells. However, microcapsules with jackfruit extract (100 μg/ml) were able to inhibit significantly the proliferation of M12.C3.F6 cells. These microcapsules can be used for the protection of different compounds sensitive to light, oxygen and/or heat and displaying a very low aqueous solubility.