Unifying Optimal Partition Approach to Sensitivity Analysis in Conic Optimization

We study convex conic optimization problems in which the right-hand side and the cost vectors vary linearly as functions of a scalar parameter. We present a unifying geometric framework that subsumes the concept of the optimal partition in linear programming (LP) and semidefinite programming (SDP) and extends it to conic optimization. Similar to the optimal partition approach to sensitivity analysis in LP and SDP, the range of perturbations for which the optimal partition remains constant can be computed by solving two conic optimization problems. Under a weaker notion of nondegeneracy, this range is simply given by a minimum ratio test. We discuss briefly the properties of the optimal value function under such perturbations.     

On some closed sets in ideal minimal spaces

The purpose of this paper is to introduce ideal minimal spaces and to investigate the relationships between minimal spaces and ideal minimal spaces. We define some closed sets in these spaces to establish their relationships. Basic properties and characterizations related to these sets are given.     

Competing magnetic phases on a kagomé staircase

We present thermodynamic and neutron data on Ni3V2O8, a spin-1 system on a kagomé staircase. The extreme degeneracy of the kagomé antiferromagnet is lifted to produce two incommensurate phases at finite T--one amplitude modulated, the other helical--plus a commensurate canted antiferromagnet for T-->0. The H-T phase diagram is described by a model of competing first and second neighbor interactions with smaller anisotropic terms. Ni3V2O8 thus provides an elegant example of order from subleading interactions in a highly frustrated system.     

Dendron–polymer conjugates via the diels–alder “click” reaction of novel anthracene‐based dendrons

Diblock and triblock dendron–polymer conjugates containing biodegradable polyester dendron blocks and polyethylene glycol (PEG) polymer were synthesized using the Diels–Alder “click” cycloaddition reaction. PEG polymers with furan‐protected maleimide functionality were synthesized and reacted with biodegradable polyester dendrons containing an anthracene moiety at their focal point. First through third generations of biodegradable polyester dendrons containing an anthracene unit at their focal point were synthesized using a divergent strategy. Efficient conjugation of the dendrons to polymers was demonstrated using ¹HNMR and size exclusion chromatography. This modular approach provides an easy access to the design of multivalent PEG conjugates. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 3191–3201     

Solvent‐Catalyzed Ring–Chain–Ring Tautomerization in Axially Chiral Compounds

The mechanism of ring–chain–ring tautomerization and the prominent effect of the solvent environment have been computationally investigated in an effort to explain the enantiomeric interconversion observed in 2‐oxazolidinone derivatives, heterocyclic analogues of biphenyl atropisomers, which were isolated as single stable enantiomers and have the potential to be used as axially chiral catalysts. This study has shed light on the identity of the intermediate species involved in the ring–chain–ring tautomerization process as well as the catalytic effect of polar protic solvents. These mechanistic details will prove very useful in predicting and understanding ring–chain tautomeric equilibria in similar heterocyclic systems and will further enable experimentalists to devise appropriate experimental conditions in which axially chiral catalysts remain stable as single enantiomers.     

An Online Expectation–Maximization Algorithm for Changepoint Models

Changepoint models are widely used to model the heterogeneity of sequential data. We present a novel sequential Monte Carlo (SMC) online expectation–maximization (EM) algorithm for estimating the static parameters of such models. The SMC online EM algorithm has a cost per time which is linear in the number of particles and could be particularly important when the data is representable as a long sequence of observations, since it drastically reduces the computational requirements for implementation. We present an asymptotic analysis for the stability of the SMC estimates used in the online EM algorithm and demonstrate the performance of this scheme by using both simulated and real data originating from DNA analysis. The supplementary materials for the article are available online.     

Structural studies and cytotoxic activity of a new dinuclear coordination compound of palladium(II)–2,2′:6′,2″‐terpyridine with rigid dianionic 1,2,4‐triazole‐3‐sulfonate linker

A new dinuclear coordination compound of palladium(II), [Pd₂(terpy)₂(μ‐tas‐N¹,N⁴)]SO₄?11H₂O ( 1 ), was synthesized by tethering a doubly deprotonated 1,2,4‐triazole‐3‐sulfonate (tas) linker generated in situ via oxidation of 1,2,4‐triazole‐3‐thione (tat) under the synthetic conditions. X‐ray diffraction analysis reveals that tat molecules adopt the thione form in the solid state, and are combined in infinite chains by symmetrically related classical intermolecular hydrogen bonds N1─H1???S1, N3─H3???N2 to give rise to R₂²(7) pattern in one‐dimensional chains along the b‐axis propagating along the a‐axis. Further short contacts through lone pairs of N2???S1 on the rings between the adjacent chains along the a‐axis lead to a two‐dimensional network structure. Compound 1 was characterized using infrared, ¹H NMR and UV–visible spectroscopies, electrospray ionization mass spectrometry and X‐ray crystallography. The crystal structure determination of 1 reveals that the Pd(II) ions are coordinated with four nitrogen atoms: three from terpy and one from tas acting as an end‐to‐end (μ‐1,4) bridging ligand. The Pd(II) ions in 1 adopt a distorted square planar geometry. The anti‐growth effect of 1 was tested on colorectal cancer (HCT‐15), non‐small‐cell lung cancer (A549), prostate cancer (PC‐3) and cervical cancer (HeLa) cell lines using sulforhodamine B viability assay. The cytotoxic effect was further confirmed using adenosine triphosphate viability assay. Compound 1 shows a promising cytotoxic activity in the diverse cancer cell models in vitro (p <0.0001).     

Ligase-Independent Cloning of Amylase Gene from a Local Bacillus subtilis Isolate and Biochemical Characterization of the Purified Enzyme

Five hundred ninety-seven bacterial isolates from Turkish hot spring water sources were screened for their ability to produce extracellular α-amylase. Among them, a high enzyme-producing Bacillus subtilis isolate, A28, was selected, and its α-amylase gene was cloned and expressed in Escherichia coli by a ligase-independent method. α-Amylase from the recombinant strain was purified to homogeneity by Q-Sepharose anion exchange and Sephacryl S-100 gel filtration chromatographies. The final yield of the enzyme was about 22.5 % of the initial activity, with a 16.4-fold increase in specific activity compared with the culture lysate. The optimum temperature and pH of the enzyme were 70 °C and 6.0, respectively. The enzyme was highly active at acidic-neutral pH range of 4.5–7.0. The amy28 α-amylase retained 100 % of its activity after incubation at 50 °C for 90 min. Co⁺², Cu²⁺, Fe²⁺, Fe³⁺, Ni⁺², and Zn⁺² caused significant inhibition in enzyme activity, which was not affected by Na⁺, Mg²⁺, Li⁺, and Ba²⁺. The activity was inhibited about 70 % upon treatment of the enzyme with 10 mM ethylenediaminetetraacetic acid. However, Ca²⁺ ions known as high temperature stabilizer for other amylases did not stimulate the activity of the enzyme. Due to pH stability and thermostability of the recombinant amylase, this enzyme may be suitable in starch processing, brewing, and food industries.