An Analogue of Distributivity for Ungraded Lattices

In this paper, we study lattices that posess both the properties of being extremal (in the sense of Markowsky) and of being left modular (in the sense of Blass and Sagan). We call such lattices trim and show that they posess some additional appealing properties, analogous to those of a distributive lattice. For example, trimness is preserved under taking intervals and suitable sublattices. Trim lattices satisfy a weakened form of modularity. The order complex of a trim lattice is contractible or homotopic to a sphere; the latter holds exactly if the maximum element of the lattice is a join of atoms. Any distributive lattice is trim, but trim lattices need not be graded. The main example of ungraded trim lattices are the Tamari lattices and generalizations of them. We show that the Cambrian lattices in types A and B defined by Reading are trim; we conjecture that all Cambrian lattices are trim.     

New Combinatorial Descriptions of the Triangulations of Cyclic Polytopes and the Second Higher Stasheff–Tamari Posets

This paper is concerned with the d-dimensional cyclic polytope with n vertices, C(n,d), and the set of its triangulations, S(n,d). We show that there is a bijection between S(n,d) and certain partitions of the set of increasing d-tuples on the integers 1 to n–1. We give a combinatorial characterization of the second higher Stasheff–Tamari poset, which is a partial ordering of S(n,d), and we determine its 2-dimension. There is a well-known representation of triangulations of an n-gon by right bracket vectors. We generalize this to cyclic polytopes of higher dimensions.     

THE PRESENCE OF PHOTOREACTIVE β-CARBOLINE FLUOROPHORES IN WEATHERED WOOL KERATIN

Abstract Solvent-cleaned Merino wool, which was enzymatically digested with protease K, displayed a fluorescence maximum at 500 nm when excited at 430 nm. The yield of this emission was approximately 15 times greater for a fiber tips digest than for a digest of the mid-length region of the same fibers.
Separation of the components in the wool tip digest by silica gel thin-layer chromatography revealed the presence of several fluorescent species. The chromatographic mobility of these species was similar to the behavior observed in a preparation of authentic 1-methyltetrahydro-P-carboline, 1,3-dicarboxylic acid.
Mass spectroscopy of the fluorescent compounds in the wool tip digest displayed molecular ions, [M + H]⁺ with m/z = 273.0890 and 257.0560, and molecular weights that define the formulae C₁₄H₁₂N₂O₄ and C₁₁H₈O₄N₂, respectively, which correspond to β-carboline 1,3-dicarboxylic acids. Mass spectral evidence also indicates the presence of two other β-carbolines.     

S1P1-selective in vivo-active agonists from high-throughput screening: off-the-shelf chemical probes of receptor interactions, signaling, and fate

The essential role of the sphingosine 1-phosphate (S1P) receptor S1P(1) in regulating lymphocyte trafficking was demonstrated with the S1P(1)-selective nanomolar agonist, SEW2871. Despite its lack of charged headgroup, the tetraaromatic compound SEW2871 binds and activates S1P(1) through a combination of hydrophobic and ion-dipole interactions. Both S1P and SEW2871 activated ERK, Akt, and Rac signaling pathways and induced S1P(1) internalization and recycling, unlike FTY720-phosphate, which induces receptor degradation. Agonism with receptor recycling is sufficient for alteration of lymphocyte trafficking by S1P and SEW2871. S1P(1) modeling and mutagenesis studies revealed that residues binding the S1P headgroup are required for kinase activation by both S1P and SEW2871. Therefore, SEW2871 recapitulates the action of S1P in all the signaling pathways examined and overlaps in interactions with key headgroup binding receptor residues, presumably replacing salt-bridge interactions with ion-dipole interactions.     

A public-key cryptosystem utilizing cyclotomic fields

While it is well-known that the RSA public-key cryptosystem can be broken if its modulusN can be factored, it is not known whether there are other ways of breaking RSA. This paper presents a public-key scheme which necessarily requires knowledge of the factorization of its modulus in order to be broken. Rabin introduced the first system whose security is equivalent to the difficulty of factoring the modulus. His scheme is based on squaring (cubing) for encryption and extracting square (cube) roots for decryption. This introduces a 14 (19) ambiguity in the decryption. Various schemes which overcome this problem have been introduced for both the quadratic and cubic case. We generalize the ideas of Williams' cubic system to larger prime exponents. The cases of higher prime order introduce a number of problems not encountered in the quadratic and cubic cases, namely the existence of fundamental units in the underlying cyclotomic field, the evaluation of higher power residue symbols, and the increased difficulty of Euclidean division in the field.     

Interactions of benzoic acid and phosphates with iron oxide colloids using chemical force titration

Colloidal iron oxides are an important component in soil systems and in water treatment processes. Humic-based organic compounds, containing both phenol and benzoate functional groups, are often present in these systems and compete strongly with phosphate species for binding sites on the iron oxide surfaces. Here, we examine the interaction of benzoate and phenolic groups with various iron oxide colloids using atomic force microscopy (AFM) chemical force titration measurements. Self-assembled monolayers (SAMs) of 4-(12-mercaptododecyloxy)benzoic acid and 4-(12-mercaptododecyloxy)phenol were used to prepare chemically modified Au-coated AFM tips, and these were used to probe the surface chemistry of a series of iron oxide colloids. The SAMs formed were also characterized using scanning tunneling microscopy, reflection-absorption infrared spectroscopy, and X-ray photoelectron spectroscopy. The surface pK(a) of 4-(12- mercaptododecyloxy)benzoic acid has been determined to be 4.0 +/- 0.5, and the interaction between the tip and the sample coated with a SAM of this species is dominated by hydrogen bonding. The chemical force titraton profile for an AFM probe coated with 4-(12- mercaptododecyloxy)benzoic acid and a bare iron oxide colloid demonstrates that the benzoic acid function group interacts with all three types of iron oxide sites present on the colloid surface over a wide pH range. Similar experiments were carried out on colloids precipitated in the presence of phosphoric, gallic, and tannic acids. The results are discussed in the context of the competitive binding interactions of solution species present in soils or in water treatment processes.     

An evaluation of acid digestion methods for amniotic fluid phospholipids

Five methods of acid digestion of amniotic fluid phospholipids for inorganic phosphate release were evaluated at a temperature of 225 °C and a heating time of 30 min. The methods used the following digestants: (A (perchloric acid), B (perchloric acid containing molybdate), C (sulfuric acid, 30% hydrogen peroxide, 5% urea), D (sulfuric-perchloric acids), and E (sulfuric-perchloric acids with vanadium pentoxide). After digestion and dilution with water, a hydrogen ion concentration of about 2.5 mol/ liter was obtained that permitted the use of stannous chloride-hydrazine sulfate as the reducing agent for phosphate color development. Recoveries of the different amniotic fluid phospholipids and aqueous phosphate standards were quantitative for all methods. A comparative study with amniotic fluids showed similar results for all methods. Since all methods were found to be equivalent under the specified conditions described, the choice was dependent upon the user's preference.     

Potentiometric, luminescence and NMR study of the interaction of Eu with glyceryl phosphates

Complexation of europium(III) with glyceryl-1- and -2-phosphates has been studied by metal ion luminescence, ¹H and ¹³C NMR spectroscopy and potentiometry. From the luminescence and NMR studies, the formation of a 1:1 inner-sphere complex, in which the glyceryl phosphate is directly bound to the metal, is confirmed. Similar apparent binding constants at pH 2 were obtained by the three methods. Values obtained by NMR at pH 2 are 53 M⁻¹ and 12 M⁻¹ for glyceryl-1- and -2-phosphate, respectively. By comparison with literature data on related systems it is suggested that the ligands bind through the phosphate group. To obtain structural information from the NMR data, complexation has also been studied with the lanthanide ions Dy(III), Er(III) and Gd(III) using both chemical shift and relaxation data. From this, metal-proton distance ratios have been calculated. Comparison of ¹H and ¹³C NMR spectral data in the presence of paramagnetic lanthanides suggests conformational equilibria in the solutions. From the potentiometric studies, global formation constants have been determined, and speciation diagrams obtained over the pH range 1.5pH7.0 for ligand/metal ratios of 1 and 30. Implications of these results on lanthanide induced fusion of phospholipid membranes are discussed.     

Chemical force titrations of amine- and sulfonic acid-modified poly(dimethylsiloxane)

Chemical force titrations-measurements of the adhesive interaction between a pair of suitably chemically modified atomic force microscopy (AFM) tip and sample surfaces as a function of pH-have been carried out for various combinations of silanol, amine, carboxylic acid, and sulfonic acid functional groups on both tip and sample. The primary surface material studied was poly(dimethylsiloxane) (PDMS). Surface modification was carried out using a plasma oxidation process to form silanol sites; further modification with amine or sulfonic acid sites was carried out by reaction of the silanol sites with the appropriate trialkoxysilane derivative. AFM tips were also modified using trialkoxysilane compounds. In the cases of tip/sample combinations with the same functional group on each, surface pK(1/2) values could be determined. In several "mixed" tip/sample combinations, a peak appeared in the titration curve midway between the surface pK(1/2) values of the tip and sample, consistent with an ionic H-bonding model for the interactions. The amine/sulfonic acid pair showed more complex behavior; the amine-terminated tip/sulfonic acid-terminated PDMS surface force titration curve consisted of two peaks centered at pH 4 and pH 8. Reversing the tip/sample pair resulted in the peak positions being shifted upward by 1.0 pH unit. The peak appearing at lower pH is assigned to electrostatic interactions between the two oppositely charged surfaces, whereas the higher pH peak is believed to arise due to ionic H-bonding interactions. AFM images show the effects on surface patterning of amine- and sulfonic acid-modified PDMS surfaces that have undergone two different oxidation methods (air plasma oxidation and Tesla coil oxidation). The surface morphologies of freshly prepared and 24 h aged air plasma oxidized PDMS are also discussed in this study.