The threshold for random -SAT is

Let be a random -CNF formula formed by selecting uniformly and independently out of all possible -clauses on variables. It is well known that if , then is unsatisfiable with probability that tends to 1 as . We prove that if , where , then is satisfiable with probability that tends to 1 as .

Our technique, in fact, yields an explicit lower bound for the random -SAT threshold for every . For our bounds improve all previously known such bounds.

     

Equivalence of positive Hausdorff measure and the open set condition for self-conformal sets

A compact set is self-conformal if it is a finite union of its images by conformal contractions. It is well known that if the conformal contractions satisfy the ``open set condition' (OSC), then has positive -dimensional Hausdorff measure, where is the solution of Bowen's pressure equation. We prove that the OSC, the strong OSC, and positivity of the -dimensional Hausdorff measure are equivalent for conformal contractions; this answers a question of R. D. Mauldin. In the self-similar case, when the contractions are linear, this equivalence was proved by Schief (1994), who used a result of Bandt and Graf (1992), but the proofs in these papers do not extend to the nonlinear setting.

     

Excited-state intermolecular proton transfer of firefly luciferin III. Proton transfer to a mild base

Steady-state and time-resolved techniques were employed to study the excited-state proton transfer (ESPT) from d-luciferin, the natural substrate of the firefly luciferase, to the mild acetate base in aqueous solutions. We found that in 1 M aqueous solutions of acetate or higher, a proton transfer (PT) process to the acetate takes place within 30 ps in both H(2)O and D(2)O solutions. The time-resolved emission signal is composed of three components. We found that the short-time component decay time is 300 and 600 fs in H(2)O and D(2)O, respectively. This component is attributed either to a PT process via the shortest water bridged complex available, ROH··H(2)O··Ac(-), or to PT taking place within a contact ion pair. The second time component of 2000 and 3000 fs for H(2)O and D(2)O, respectively, is attributed to ROH* acetate complex, whose proton wire is longer by one water molecule. The decay rate of the third, long-time component is proportional to the acetate concentration. We attribute it to the diffusion-assisted reaction as well as to PT process to the solvent.     

Gate‐Induced Modification of Water Adsorption on Dielectrics Probed by EFM and Carbon Nanotube FETs

Humidity plays an important role in molecular electronics. It facilitates charge movement on top of dielectric layers and modifies the device transfer characteristics. Using two different methods to probe temporal charge redistribution on the surface of dielectrics, we were able to extract the surface humidity for the first time. The first method is based on the relaxation time constants of the current through carbon nanotube field‐effect transistors (CNTFETs), and the second is based on electric force microscopy (EFM) measurements. Moreover, we found that applying external gate biases modifies the surface humidity. A theoretical model based on dielectrophoretic attraction between the water molecules and the substrate is introduced to explain this observation, and the results support our hypothesis. Furthermore, it is found that upon the adsorption of two to three layers of water the surface conductivity saturates.     

Interaction of scanning probes with semiconductor nanocrystals; physical mechanism and basis for near-field optical imaging

We investigate the modification of photoluminescence (PL) from single semiconductor nanocrystal quantum dots (NCs) in the proximity of metal and semiconducting atomic force microscope (AFM) tips. The presence of the tip alters the radiative decay rate of an emitter via interference and opens efficient nonradiative decay channels via energy transfer to the tip material. These effects cause quenching (or enhancement) of the emitter's PL intensity as a function of its distance from the interacting tip. We take advantage of this highly distance-dependent effect to realize a contrast mechanism for high-resolution optical imaging. AFM tips are optimized as energy acceptors by chemical functionalization with InAs NCs to achieve optical resolution down to 30 nm. The presented experimental scheme offers high-resolution optical information while maintaining the benefits of traditional AFM imaging. We directly measure the PL intensity of single NCs as a function of the tip distance. Our results are in good agreement with calculations made by a classical theoretical model describing an oscillating dipole interacting with a planar mirror.     

Evaluation of healthy and sensory indexes of sweetened beverages using an electronic tongue

Overconsumption of sugar-sweetened beverages may increase the risk of health problems and so, the evaluation of their glycemic load and fructose-intolerance level is essential since it may allow establishing possible relations between physiologic effects of sugar-rich beverages and health. In this work, an electronic tongue was used to accurately classify beverages according to glycemic load (low, medium or high load) as well to their adequacy for people suffering from fructose malabsorption syndrome (tolerable or not): 100% of correct classifications (leave-one-out cross-validation) using linear discriminant models based on potentiomentric signals selected by a meta-heuristic simulated annealing algorithm. These results may be partially explained by the electronic tongue’s capability to mimic the human sweetness perception and total acid flavor of beverages, which can be related with glycemic load and fructose-intolerance index. Finally, the E-tongue was also applied to quantify, accurately, healthy and sensory indexes using multiple linear regression models (leave-one-out cross-validation: R_adj > 0.99) in the following dynamic ranges: 4.7 < glycemic load ≤ 30; 0.4 < fructose intolerance index ≤ 1.5; 32 < sweetness perception < 155; 1.3 < total acid flavor, g L⁻¹ < 8.3; and, 5.8 < well-balanced flavor ≤ 74. So, the proposed electronic tongue could be used as a practical, fast, low-cost and green tool for beverage’s healthy and sensory evaluation.     

Histopathological Analysis of UVB and IR Interaction in Rat Skin

To determine the chronic skin effects caused by the interaction of infrared and ultraviolet B radiations, male Rattus norvegicus (Wistar) (2 months old) were exposed for 15 days to infrared radiation (600–1500 nm, with a peak at 1000 nm, n = 12) for 30 min (1080 J cm^?2) (IRo); to ultraviolet B radiation (peak emission at 313 nm, n = 9) for 90 min (55.08 J cm^?2) (UVB); to infrared radiation followed after 90 min by ultraviolet B (n = 6) (IRUVB) and to ultraviolet B followed after 90 min by infrared radiation (n = 9) (UVBIR). Skin samples were collected and histopathological analysis showed the presence of acanthosis, parakeratotic and orthokeratotic hyperkeratosis, intraepidermal pustules, keratin pearls, detachment of epidermis, collagen necrosis, inflammatory infiltrate, vasodilation, basal cell vacuolization and superficial dermis degeneration both in UVB and UVBIR treatments. IRUVB animals showed the same characteristics as above except for parakeratotic hyperkeratosis, keratin pearls and superficial dermis degeneration. To conclude, infrared radiation exposure after ultraviolet B irradiation increases skin damage without protecting the tissue, while infrared radiation exposure before ultraviolet B irradiation showed a protective effect against ultraviolet skin damage.     

Exploring the functional interaction between POSH and ALIX and the relevance to HIV-1 release

Background

The ALG2-interacting protein X (ALIX)/AIP1 is an adaptor protein with multiple functions in intracellular protein trafficking that plays a central role in the biogenesis of enveloped viruses. The ubiquitin E3-ligase POSH (plenty of SH3) augments HIV-1 egress by facilitating the transport of Gag to the cell membrane. Recently, it was reported, that POSH interacts with ALIX and thereby enhances ALIX mediated phenotypes in Drosophila.

Results

In this study we identified ALIX as a POSH ubiquitination substrate in human cells: POSH induces the ubiquitination of ALIX that is modified on several lysine residues in vivo and in vitro. This ubiquitination does not destabilize ALIX, suggesting a regulatory function. As it is well established that ALIX rescues virus release of L-domain mutant HIV-1, HIV-1Δ_PTAP, we demonstrated that wild type POSH, but not an ubiquitination inactive RING finger mutant (POSH^V14A), substantially enhances ALIX-mediated release of infectious virions derived from HIV-1Δ_PTAP L-domain mutant (YPX_nL-dependent HIV-1). In further agreement with the idea of a cooperative function of POSH and ALIX, mutating the YPX_nL-ALIX binding site in Gag completely abrogated augmentation of virus release by overexpression of POSH. However, the effect of the POSH-mediated ubiquitination appears to be auxiliary, but not necessary, as silencing of POSH by RNAi does not disturb ALIX-augmentation of virus release.

Conclusion

Thus, the cumulative results identified ALIX as an ubiquitination substrate of POSH and indicate that POSH and ALIX cooperate to facilitate efficient virus release. However, while ALIX is obligatory for the release of YPX_nL-dependent HIV-1, POSH, albeit rate-limiting, may be functionally interchangeable.