The unsatisfiability threshold revisited

The problem of determining the unsatisfiability threshold for random 3-SAT formulas consists in determining the clause to variable ratio that marks the experimentally observed abrupt change from almost surely satisfiable formulas to almost surely unsatisfiable. Up to now, there have been rigorously established increasingly better lower and upper bounds to the actual threshold value. In this paper, we consider the problem of bounding the threshold value from above using methods that, we believe, are of interest on their own right. More specifically, we show how the method of local maximum satisfying truth assignments can be combined with results for the occupancy problem in schemes of random allocation of balls into bins in order to achieve an upper bound for the unsatisfiability threshold less than 4.571. In order to obtain this value, we establish a bound on the q-binomial coefficients (a generalization of the binomial coefficients). No such bound was previously known, despite the extensive literature on q-binomial coefficients. Finally, to prove our result we had to establish certain relations among the conditional probabilities of an event in various probabilistic models for random formulas. It turned out that these relations were considerably harder to prove than the corresponding ones for unconditional probabilities, which were previously known.     

Scattering of Magnetic Edge States

We consider a charged particle following the boundary of a two dimensional domain because a homogeneous magnetic field is applied. We develop the basic scattering theory for the corresponding quantum mechanical edge states. The scattering operator attains a limit for large magnetic fields which preserves Landau bands. We interpret the corresponding scattering phases in terms of classical trajectories. Communicated by Yosi Avron submitted 23/02/05, accepted 3/05/05     

New pi-extended water-soluble squaraines as singlet oxygen generators

[graph: see text] Condensation of squaric acid with a number of differently substituted 2-pyrrolyl derivatives afforded three new classes of squaraines. Their sharp and intense absorption bands in the biological window (700-900 nm), inherent singlet oxygen generation capabilities, together with proper functionalization allowing good water solubility make them suitable candidates as new non-porphyrinic singlet oxygen photosensitizers for photodynamic therapy (PDT).     

Primate beta-defensins--structure, function and evolution

Host defense peptides (HDPs) are endogenous antibiotics that play a multifunctional role in the innate immunity of mammals. Among these, beta-defensins contribute to mucosal and epithelial defense, also acting as signal molecules for cellular components of innate and adaptive immunity. Numerous members of this family have been identified in mammalian and avian species, and genomic studies in human and mouse indicate a considerable complexity in their gene organization. Recent reports on the evolution of primate and rodent members of this family indicate quite a complex pattern of variation. In this review we briefly discuss the evolution of mammalian beta-defensins in relation to other types of defensins, and then concentrate on the evolution of beta-defensins 1 to 4 in primates. In particular, the surprisingly varied patterns of evolution, which range from neutral or weakly purifying, to positive selection to a high level of conservation are analyzed in terms of possible genetics, structural or functional implications, as well as to observed variations on the antimicrobial activity in vitro. The role of polymorphisms in the genes encoding for these host defense peptides in determining susceptibility to human diseases are also briefly considered.     

X-ray structure and circular dichroism of pure rotamers of bis[guanosine-5'-monophosphate(-1)](N,N,N',N'-tetramethylcyclohexyl-1,2-diamine)platinum(II) complexes that have R,R and S,S configurations at the asymmetric diamine

The use of a sterically hindered diamine ligand (Me(4)DACH) has allowed for the first time, the isolation and characterization, both in the solid state (X-ray crystallography) and in solution (circular dichroism), of pure DeltaHT rotamers of [Pt(Me(4)dach)(5'-GMP)(2)] (compounds 1 and 2 for R,R and S,S configurations of the Me(4)DACH ligand, respectively). Comparison of the CD spectra obtained for each rotamer, which differ only in the chirality of the Me(4)DACH ligand (R,R or S,S) or in the chirality of the HT conformation (Delta or Lambda), allowed us to conclude that, in the 200-350 nm range, the contributions to the overall CD spectrum that stem from diamine chirality and diamine-induced chirality of platinum d--d transitions or from sugar chirality are negligible relative to the exciton chiral coupling that occurs for pi-pi* transitions of the cis guanines. Accurate molecular structures of 1.10 D(2)O and 2.14 D(2)O (conventional crystallographic agreement indexes R(1) convergent to 2.07 % and 2.18 %, respectively) revealed that the crystallized rotamers have a DeltaHT conformation that is in agreement with all previously reported X-ray structures of [Pt(diamine)(nucleos(t)ide)(2)] complexes. This conformation allows the 5'-phosphate to be located in proximity to the Me(4)DACH ligand so that (P)O...HC(N) hydrogen-bond interactions exists in both complexes. For both structures, the canting of the guanine planes on the coordination plane is right-handed (R; canting angle (Phi) of 80.9 degrees and 73.2 degrees, respectively); this indicates that the canting direction is driven by the HT conformation chirality (Delta for both compounds) and not by the chirality of the carrier ligand (different for the two compounds). Density functional theory analysis of the conformational space as a function of Phi indicated a good agreement between the computed and experimental structures. The increase in energy for Phi values below 65 degrees and 55 degrees (for 1 and 2, respectively) is mainly due to the short intramolecular contacts between C(8)H and the cis N-Me groups on the same side of the platinum coordination plane.     

Synthesis of Phosphaformamidines and Phosphaformamidinates

A large‐scale synthetic route to a variety of phosphaformamidines and phosphaformamidinates, a type of derivative that was not accessible by the methods previously known for preparing phosphaamidines and phosphaamidinates, is reported. Thermally stable ethyl N‐arylformimidates 1 (ArN?CH(OEt), Ar=2,4,6‐(Me)₃Ph or 2,6‐(iPr)₂Ph) readily reacted with lithium dialkyl‐ and diarylphosphanides to afford the corresponding N‐aryl phosphaformamidines in 80 and 60 % yield, respectively, whereas with lithium (aryl)(silyl)phosphanide, the N‐aryl‐N‐silylphosphaformamidine (60 % yield) was obtained. Addition of primary lithium arylphosphanides to 1 followed by addition of a stoichiometric amount of nBuLi gave rise to the respective phosphaformamidinates (70–88 % yield). Methanolysis of the products afforded the N‐aryl‐N‐hydrogenophosphaformamidines (90–95 % yield). The solid‐state structure of one of the phosphaformamidinates is also presented.     

Effects of deformability, uneven surface charge distributions, and multipole moments on biocolloid electrophoretic migration

Liposomes have been widely used as cellular and bioparticle mimics due to their lipid bilayer structure and relative ease of production and manipulation. Such biocolloids are frequently characterized by capillary electrophoresis (CE), which promises a wealth of information about such properties as surface charge, composition, and rigidity. The applicability of this information is somewhat limited, however, since it is interpreted with colloidal theories that do not account for the unique properties of biocolloids. In this work, the effects of deformability, mobile surface charges, intrinsic polarizability, and uneven surface charge distributions are incorporated into colloidal theories in order to better model the electrophoretic behaviors of liposomes.     

Light-emitting molecular machines: pH-induced intramolecular motions in a fluorescent nickel(II) scorpionate complex

A cyclam-like macrocycle has been synthesized with a pendant arm containing a dansylamide group. In the corresponding nickel(II) complex, binding of the pendant arm to the metal is pH controlled. In particular, at pH 4.3, the sulfonamide group deprotonates and coordinates the NiII center, giving rise to a complex of trigonal bipyramidal stereochemistry, as shown by X-ray diffraction studies performed on the crystalline complex salt. At pH 7.5, an OH- ion binds the metal and a six-coordinate species forms. The binding-detachment of the pendant arm to/from the NiII center is signaled by changes in the emission properties of the dansyl subunit in the side chain; the fluorescence of this side chain is high when the pendant arm is not coordinated and low when the sulfonamide group is bound to the metal. The system investigated represents the prototype of a light-emitting molecular machine, driven by a pH change.