Erratum: Long‐range JCH heteronuclear coupling constants in cyclopentane derivatives. Part II

The original article to which this Erratum refers was published in Magnetic Resonance in volume 45 issue 1.     

A Lower Bound for the Determinantal Complexity of a Hypersurface

We prove that the determinantal complexity of a hypersurface of degree \(d > 2\) is bounded below by one more than the codimension of the singular locus, provided that this codimension is at least 5. As a result, we obtain that the determinantal complexity of the \(3 \times 3\) permanent is 7. We also prove that for \(n> 3\), there is no nonsingular hypersurface in \({\mathbb {P}}^n\) of degree d that has an expression as a determinant of a \(d \times d\) matrix of linear forms, while on the other hand for \(n \le 3\), a general determinantal expression is nonsingular. Finally, we answer a question of Ressayre by showing that the determinantal complexity of the unique (singular) cubic surface containing a single line is 5.     

Cluster Partition Function and Invariants of 3-Manifolds

The author reviews some recent developments in Chern-Simons theory on a hyperbolic 3-manifold M with complex gauge group G.The author focuses on the case of G =SL(N,C) and M being a knot complement:M =S3 \ k.The main result presented in this note is the cluster partition function,a computational tool that uses cluster algebra techniques to evaluate the Chern-Simons path integral for G =SL(N,C).He also reviews various applications and open questions regarding the cluster partition function and some of its relation with string theory.     

Cleft extensions of a family of braided Hopf algebras

We introduce a family of braided Hopf algebras that (in characteristic zero) generalizes the rank 1 Hopf algebras introduced by Krop and Radford and we study its cleft extensions.     

Hydrogen bonding interactions between α-, β-glucose,and methacrylic acid

Intermolecular interactions between α-, β-glucose, and methacrylic acid (MAA) have been investigated. Twenty-two possible conformations have been optimized at the DFT(B3LYP) level of theory with the 6-31G(d) basis set. The geometrical parameters for the most stable configurations of hydrogen bonding sites in the optimized systems have been determined. The binding energies ΔE _bind have been calculated at the MP2/6-311++G(d,p) level of approximation taking into account the basis set superposition error (BSSE) and the zero-point vibrational energies corrections. Results indicate that the most stabilized complexes form hydrogen bonds either through carboxylic and hemiacetal oxygen atoms acting as proton acceptors. Both, α- and β-anomers are studied in the pyranose six-membered ring. In all complexes, the nuclear quadrupole coupling constants (χ) for ¹⁷O nuclei were obtained about 10.0 MHz, while for the ²H atoms they vary from ≈200.0 to ≈350.0 kHz.     

Solving the vendor–buyer integrated inventory system with arithmetic–geometric inequality

In the past, economic order quantity (EOQ) and economic production quantity (EPQ) were treated independently from the viewpoints of the buyer or the vendor. In most cases, the optimal solution for one player was non-optimal to the other player. In today’s competitive markets, close cooperation between the vendor and the buyer is necessary to reduce the joint inventory cost and the response time of the vendor–buyer system. The successful experiences of National Semiconductor, Wal-Mart, and Procter and Gamble have demonstrated that integrating the supply chain has significantly influenced the company’s performance and market share (Simchi-Levi et al. (2000) [1]). Recently, Yang et al. (2007) [2] presented an inventory model to determine the economic lot size for both the vendor and buyer, and the number of deliveries in an integrated two stage supply chain. In this paper, we present an alternative approach to determine the global optimal inventory policy for the vendor–buyer integrated system using arithmetic–geometric inequality.     

Huddling behavior as critical phase transition triggered by low temperatures

Huddling is a grouping behavior where animals maintain close bodily contact and save energy. We tested the hypothesis that this thermoregulatory behavior behaves as a system with continuous (second‐order phase) transition called critical when the environmental temperature (driving parameter) is near a critical value. To do so, we followed theoretical and experimental approaches, examining data from geometrical models, metabolic rate during huddling in small mammals, and also conducting an experiment on thermoregulatory huddling behavior with white mice. Our results support all predictions for systems under continuous‐phase transition triggered by low temperatures, a phenomenon reported for first time in a biological system. We suggest that huddling behavior in social animals, a recognized adaptive behavior, may be considered a self‐organized system coupled with an external driving parameter. © 2011 Wiley Periodicals, Inc. Complexity, 2011     

Phenotypic and Target-Directed Screening Yields New Acaricidal Alternatives for the Control of Ticks

Rhipicephalus microplus, the “common cattle tick”, is the most important ectoparasite in livestock worldwide due to the economic and health losses it produces. This tick is a vector for pathogens of several tick-borne diseases. In Latin American countries, damages reach approximately USD 500 million annually due to tick infections, as well as tick-borne diseases. Currently, resistant populations for every chemical group of acaricides have been reported, posing a serious problem for tick control. This study aims to find new alternatives for controlling resistant ticks with compounds derived from small synthetic organic molecules and natural origins. Using BME26 embryonic cells, we performed phenotypic screening of 44 natural extracts from 10 Mexican plants used in traditional medicine, and 33 compounds selected from our chemical collection. We found 10 extracts and 13 compounds that inhibited cell growth by 50% at 50 µg/mL and 100 µM, respectively; the dose-response profile of two of them was characterized, and these compounds were assayed in vitro against different life stages of Rhipicephalus microplus. We also performed a target-directed screening of the activity of triosephosphate isomerase, using 86 compounds selected from our chemical collection. In this collection, we found the most potent and selective inhibitor of tick triosephosphate isomerase reported until now. Two other compounds had a potent acaricidal effect in vitro using adults and larvae when compared with other acaricides such as ivermectin and Amitraz. Those compounds were also selective to the ticks compared with the cytotoxicity in mammalian cells like macrophages or bovine spermatozoids. They also had a good toxicological profile, resulting in promising acaricidal compounds for tick control in cattle raising.