Decomposition of pseudo-radioactive chemical products with a mathematical approach

The aim of this paper is to study the decomposition of pseudo–radioactive products that follow a dynamics determined by a trigonometric factor. In particular for maps of the form $e^{\cos (\pi t)}$ is proved that an asymptotic sampling recomposition property, generalizing the classical Shannon–Whittaker–Kotel’nikov Theorem, works.     

Mono- and Di-Fucosylated Glycans of the Parasitic Worm S. mansoni are Recognized Differently by the Innate Immune Receptor DC-SIGN

The parasitic worm, Schistosoma mansoni, expresses unusual fucosylated glycans in a stage-dependent manner that can be recognized by the human innate immune receptor DC-SIGN, thereby shaping host immune responses. We have developed a synthetic approach for mono- and bis-fucosylated LacdiNAc (LDN-F and LDN-DF, respectively), which are epitopes expressed on glycolipids and glycoproteins of S. mansoni. It is based on the use of monosaccharide building blocks having carefully selected amino-protecting groups, facilitating high yielding and stereoselective glycosylations. The molecular interaction between the synthetic glycans and DC-SIGN was studied by NMR and molecular modeling, which demonstrated that the α1,3-fucoside of LDN-F can coordinate with the Ca²⁺-ion of the canonical binding site of DC-SIGN allowing for additional interactions with the underlying LDN backbone. The 1,2-fucoside of LDN-DF can be complexed in a similar manner, however, in this binding mode GlcNAc and GalNAc of the LDN backbone are placed away from the protein surface resulting in a substantially lower binding affinity. Glycan microarray binding studies showed that the avidity and selectivity of binding is greatly enhanced when the glycans are presented multivalently, and in this format Le^x and LDN-F gave strong responsiveness, whereas no binding was detected for LDN-DF. The data indicates that S. mansoni has developed a strategy to avoid detection by DC-SIGN in a stage-dependent manner by the addition of a fucoside to a number of its ligands.     

Amino acid catalyzed neogenesis of carbohydrates: a plausible ancient transformation

Hexose sugars play a fundamental role in vital biochemical processes and their biosynthesis is achieved through enzyme-catalyzed pathways. Herein we disclose the ability of amino acids to catalyze the asymmetric neogenesis of carbohydrates by sequential cross-aldol reactions. The amino acids mediate the asymmetric de novo synthesis of natural L- and D-hexoses and their analogues with excellent stereoselectivity in organic solvents. In some cases, the four new stereocenters are assembled with almost absolute stereocontrol. The unique feature of these results is that, when an amino acid is employed as the catalyst, a single reaction sequence can convert a protected glycol aldehyde into a hexose in one step. For example, proline and its derivatives catalyze the asymmetric neogenesis of allose with >99 % ee in one chemical manipulation. Furthermore, all amino acids tested catalyzed the asymmetric formation of natural sugars under prebiotic conditions, with alanine being the smallest catalyst. The inherent simplicity of this catalytic process suggests that a catalytic prebiotic "gluconeogenesis" may occur, in which amino acids transfer their stereochemical information to sugars. In addition, the amino acid catalyzed stereoselective sequential cross-aldol reactions were performed as a two-step procedure with different aldehydes as acceptors and nucleophiles. The employment of two different amino acids as catalysts for the iterative direct aldol reactions enabled the asymmetric synthesis of deoxysugars with >99 % ee. In addition, the direct amino acid catalyzed C(2)+C(2)+C(2) methodology is a new entry for the short, highly enantioselective de novo synthesis of carbohydrate derivatives, isotope-labeled sugars, and polyketide natural products. The one-pot asymmetric de novo syntheses of deoxy and polyketide carbohydrates involved a novel dynamic kinetic asymmetric transformation (DYKAT) mediated by an amino acid.     

On the Differential Polynomial of a Graph

We introduce the differential polynomial of a graph. The differential polynomial of a graph G of order n is the polynomial B(G; x) :=∑?(G)k=-nB_k(G) x~(n+k), where B_k(G) denotes the number of vertex subsets of G with differential equal to k. We state some properties of B(G;x) and its coefficients.In particular, we compute the differential polynomial for complete, empty, path, cycle, wheel and double star graphs. We also establish some relationships between B(G; x) and the differential polynomials of graphs which result by removing, adding, and subdividing an edge from G.     

The Central Curve in Linear Programming

The central curve of a linear program is an algebraic curve specified by linear and quadratic constraints arising from complementary slackness. It is the union of the various central paths for minimizing or maximizing the cost function over any region in the associated hyperplane arrangement. We determine the degree, arithmetic genus and defining prime ideal of the central curve, thereby answering a question of Bayer and Lagarias. These invariants, along with the degree of the Gauss image of the curve, are expressed in terms of the matroid of the input matrix. Extending work of Dedieu, Malajovich and Shub, this yields an instance-specific bound on the total curvature of the central path, a quantity relevant for interior-point methods. The global geometry of central curves is studied in detail.     

The Ex-Post Evaluation of the Minimum Local Reliability Level: An Enhanced Probabilistic Location Set Covering Model

In order to evaluate the behavior of three probabilistic location set covering models we propose a new method that allows the ex-post measurement of the so called minimum local reliability level, both under the independence and under the dependence assumption. We show experimentally, by means of a set of test problems, that the proposed loss-system version of Ball and Lin's model (1993) does almost always achieve the required reliability level. Moreover, if we compare this new version with the other two already known probabilistic models and consider as a second additional criteria the least number of required vehicles, we show that the new version has a better behavior both under the independence and the dependence assumption. In this paper we further propose a new model with the aim of reducing the number of required vehicles while satisfying the fixed reliability level. Our new model is formulated like Ball and Lin's model incorporating the servers workload estimate of the Binomial PLSCP of ReVelle and Hogan (1988). Finally, we check the precision of our ex-post evaluation method over the four considered models through a simulation study.     

Exact Potts Model Partition Functions for Strips of the Square Lattice

We present exact calculations of the Potts model partition function Z(G, q, v) for arbitrary q and temperature-like variable v on n-vertex square-lattice strip graphs G for a variety of transverse widths L _t and for arbitrarily great length L , with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These have the form Z(G, q, v)= . We give general formulas for N _{Z, G, j} and its specialization to v=–1 for arbitrary L _t for both types of boundary conditions, as well as other general structural results on Z. The free energy is calculated exactly for the infinite-length limit of the graphs, and the thermodynamics is discussed. It is shown how the internal energy calculated for the case of cylindrical boundary conditions is connected with critical quantities for the Potts model on the infinite square lattice. Considering the full generalization to arbitrary complex q and v, we determine the singular locus , arising as the accumulation set of partition function zeros as L , in the q plane for fixed v and in the v plane for fixed q.     

Nonstoichiometric spinel ferrites obtained from alpha-NaFeO2 via molten media reactions

Different solid/liquid "exchange" reactions involving divalent cations, protons, or ammonium ions have been performed at low/moderate temperatures (between 80 and 500 degrees C) on alpha-NaFeO2 dipped in molten salts (or acid) media. Several ferrites have been obtained which are nonstoichiometric with partially inverse spinel structures. When sodium is replaced by divalent cations (Mg2+, Co2+, Ni2+, and Zn2+), the obtained ferrites are hyperstoichiometric (cation/oxygen ratio higher than 3/4) whereas proton or ammonium reactions result in hypostoichiometric materials (cation/oxygen lower than 3/4). All these ferrites present a platelet-like morphology and show ferrimagnetic, soft magnet behavior.