Betti numbers of Stanley–Reisner rings determine hierarchical Markov degrees

There are two seemingly unrelated ideals associated with a simplicial complex Δ: one is the Stanley–Reisner ideal I _Δ , the monomial ideal generated by minimal non-faces of Δ, well-known in combinatorial commutative algebra; the other is the toric ideal I _M(Δ) of the facet subring of Δ, whose generators give a Markov basis for the hierarchical model defined by Δ, playing a prominent role in algebraic statistics. In this note we show that the complexity of the generators of I _M(Δ) is determined by the Betti numbers of I _Δ . The unexpected connection between the syzygies of the Stanley–Reisner ideal and degrees of minimal generators of the toric ideal provide a framework for further exploration of the connection between the model and its many relatives in algebra and combinatorics.     

Q-Complete domains with corners in {\mathbb{P}^n} and extension of line bundles

We show that if a compact set X in ${\mathbb P^n}$ is laminated by holomorphic submanifolds of dimension q, then ${\mathbb P^n{\setminus}X}$ is (q + 1)-complete with corners. Consider a manifold U, q-complete with corners. Let ${\mathcal N}$ be a holomorphic line bundle in the complement of a compact in U. We study when ${\mathcal N}$ extends as a holomorphic line bundle in U. We give applications to the non existence of some Levi-flat foliations in open sets in ${\mathbb P^n}$ . The results apply in particular when U is a Stein manifold of dimension n ≥ 3, then every holomorphic line bundle in the complement of a compact extends holomorphically to U.     

Integrating restoration and scheduling decisions for disrupted interdependent infrastructure systems

We consider the problem faced by managers of critical civil interdependent infrastructure systems of restoring essential public services after a non-routine event causes disruptions to these services. In order to restore the services, we must determine the set of components (or tasks) that will be temporarily installed or repaired, assign these tasks to work groups, and then determine the schedule of each work group to complete the tasks assigned to it. These restoration planning and scheduling decisions are often undertaken in an independent, sequential manner. We provide mathematical models and optimization algorithms that integrate the restoration and planning decisions and specifically account for the interdependencies between the infrastructure systems. The objective function of this problem provides a measure of how well the services are being restored over the horizon of the restoration plan, rather than just focusing on the performance of the systems after all restoration efforts are complete. We test our methods on realistic data representing infrastructure systems in New York City. Our computational results demonstrate that we can provide integrated restoration and scheduling plans of high quality with limited computational resources. We also discuss the benefits of integrating the restoration and scheduling decisions.     

Symbolic Differential Elimination for Symmetry Analysis

Differential problems are ubiquitous in mathematical modeling of physical and scientific problems. Algebraic analysis of differential systems can help in determining qualitative and quantitative properties of solutions of such systems. In this tutorial paper we describe several algebraic methods for investigating differential systems.     

Unique origin of colors of armchair carbon nanotubes

The colors of suspended metallic colloidal particles are determined by their size-dependent plasma resonance, while those of semiconducting colloidal particles are determined by their size-dependent band gap. Here, we present a novel case for armchair carbon nanotubes, suspended in aqueous medium, for which the color depends on their size-dependent excitonic resonance, even though the individual particles are metallic. We observe distinct colors of a series of armchair-enriched nanotube suspensions, highlighting the unique coloration mechanism of these one-dimensional metals.     

Insights in the plasma-assisted growth of carbon nanotubes through atomic scale simulations: effect of electric field

Carbon nanotubes (CNTs) are nowadays routinely grown in a thermal CVD setup. State-of-the-art plasma-enhanced CVD (PECVD) growth, however, offers advantages over thermal CVD. A lower growth temperature and the growth of aligned freestanding single-walled CNTs (SWNTs) makes the technique very attractive. The atomic scale growth mechanisms of PECVD CNT growth, however, remain currently entirely unexplored. In this contribution, we employed molecular dynamics simulations to focus on the effect of applying an electric field on the SWNT growth process, as one of the effects coming into play in PECVD. Using sufficiently strong fields results in (a) alignment of the growing SWNTs, (b) a better ordering of the carbon network, and (c) a higher growth rate relative to thermal growth rate. We suggest that these effects are due to the small charge transfer occurring in the Ni/C system. These simulations constitute the first study of PECVD growth of SWNTs on the atomic level.     

Synthesis of bispecific antibodies using genetically encoded unnatural amino acids

Bispecific antibodies were constructed using genetically encoded unnatural amino acids with orthogonal chemical reactivity. A two-step process afforded homogeneous products in excellent yield. Using this approach, we synthesized an anti-HER2/anti-CD3 bispecific antibody, which efficiently cross-linked HER2+ cells and CD3+ cells. In vitro effector-cell mediated cytotoxicity was observed at picomolar concentrations.     

The double sign of a real division algebra of finite dimension greater than one

For any real division algebra A of finite dimension greater than one, the signs of the determinants of left multiplication and right multiplication by an element a ∈ A?{0} are shown to form an invariant of A, called its double sign. For each n ∈ {2, 4, 8}, the double sign causes the category $\mathbb {D}_nFor any real division algebra A of finite dimension greater than one, the signs of the determinants of left multiplication and right multiplication by an element a ∈ A?{0} are shown to form an invariant of A, called its double sign. For each n ∈ {2, 4, 8}, the double sign causes the category $\mathbb {D}_n$ of all n‐dimensional real division algebras to decompose into four blocks. The structures of these blocks are closely related, and their relationship is made precise for a sample of full subcategories of $\mathscr {D}_n$.     

Development and validation of an SPE HG-AAS method for determination of inorganic arsenic in samples of marine origin

The present paper describes a novel method for the quantitative determination of inorganic arsenic (iAs) in food and feed of marine origin. The samples were subjected to microwave-assisted extraction using diluted hydrochloric acid and hydrogen peroxide, which solubilised the analytes and oxidised arsenite (As(III)) to arsenate (As(V)). Subsequently, a pH buffering of the sample extract at pH 6 enabled selective elution of As(V) from a strong anion exchange solid-phase extraction (SPE) cartridge. Hydride generation atomic absorption spectrometry (HG-AAS) was applied to quantify the concentration of iAs (sum of As(III) and As(V)) as the total arsenic (As) in the SPE eluate. The results of the in-house validation showed that mean recoveries of 101-104% were achieved for samples spiked with iAs at 0.5, 1.0 and 1.5 mg·kg(-1), respectively. The limit of detection was 0.08 mg kg(-1), and the repeatability (RSD(r)) and intra-laboratory reproducibility (RSD(IR)) were less than 8% and 13%, respectively, for samples containing 0.2 to 1.5 mg kg(-1) iAs. The trueness of the SPE HG-AAS method was verified by confirming results obtained by parallel analysis using high-performance liquid chromatography coupled to inductively coupled plasma mass spectrometry. It was demonstrated that the two sets of results were not significantly different (P < 0.05). The SPE HG-AAS method was applied to 20 marine food and feed samples, and concentrations of up to 0.14 mg kg(-1) of iAs were detected.