On the number of maximal bipartite subgraphs of a graph

We show new lower and upper bounds on the maximum number of maximal induced bipartite subgraphs of graphs with n vertices. We present an infinite family of graphs having 105^n/10 ≈ 1.5926ⁿ; such subgraphs show an upper bound of O(12^n/4) = O(1.8613ⁿ) and give an algorithm that finds all maximal induced bipartite subgraphs in time within a polynomial factor of this bound. This algorithm is used in the construction of algorithms for checking k‐colorability of a graph. © 2004 Wiley Periodicals, Inc. J Graph Theory 48: 127–132, 2005     

Functionalization of 2″‐C‐(Piperazinomethyl)‐2′,3′‐BcNA (Bicyclic Nucleic Acids) with Pyren‐1‐ylcarbonyl Units

Herein, we describe the incorporation of 2″‐C‐(piperazinomethyl)‐2′,3′‐BcNA (Bicyclic Nucleic Acids) into oligonucleotides via phosphoramidite chemistry and their subsequent solid‐phase functionalization with pyren‐1‐ylcarbonyl units after oligonucleotide synthesis. Thermal denaturation measurements showed that one modification led to increased thermal stability of the resulting duplex, and that two modifications could be incorporated in close proximity without decreasing the duplex stability (compared to the duplex stability of unmodified RNA). Fluorescence studies of the modified duplexes revealed that the structure and intensity of the fluorescence spectra were largely sequence‐dependent. Furthermore, molecular‐modeling studies showed that the pyrene moieties are placed in the major groove, and that the configuration at C(2″) is important for the thermal stability of the duplex.     

Fluoride‐Bridged {GdIII3MIII2} (M=Cr,Fe, Ga) Molecular Magnetic Refrigerants

The reaction of fac‐[M^IIIF₃(Me₃tacn)]?x H₂O with Gd(NO₃)₃?5H₂O affords a series of fluoride‐bridged, trigonal bipyramidal {Gd^III₃M^III₂} (M=Cr ( 1 ), Fe ( 2 ), Ga ( 3 )) complexes without signs of concomitant GdF₃ formation, thereby demonstrating the applicability even of labile fluoride‐complexes as precursors for 3d–4f systems. Molecular geometry enforces weak exchange interactions, which is rationalized computationally. This, in conjunction with a lightweight ligand sphere, gives rise to large magnetic entropy changes of 38.3 J kg^?1 K^?1 ( 1 ) and 33.1 J kg^?1 K^?1 ( 2 ) for the field change 7 T→0 T. Interestingly, the entropy change, and the magnetocaloric effect, are smaller in 2 than in 1 despite the larger spin ground state of the former secured by intramolecular Fe–Gd ferromagnetic interactions. This observation underlines the necessity of controlling not only the ground state but also close‐lying excited states for successful design of molecular refrigerants.     

[ReF6]2−: A Robust Module for the Design of Molecule‐Based Magnetic Materials

A facile synthesis of the [ReF₆]^2? ion and its use as a building block to synthesize magnetic systems are reported. Using dc and ac magnetic susceptibility measurements, INS and EPR spectroscopies, the magnetic properties of the isolated [ReF₆]^2? unit in (PPh₄)₂[ReF₆]?2 H₂O ( 1 ) have been fully studied including the slow relaxation of the magnetization observed below ca. 4 K. This slow dynamic is preserved for the one‐dimensional coordination polymer [Zn(viz)₄(ReF₆)]_∞ ( 2 , viz=1‐vinylimidazole), demonstrating the irrelevance of low symmetry for such magnetization dynamics in systems with easy‐plane‐type anisotropy. The ability of fluoride to mediate significant exchange interactions is exemplified by the isostructural [Ni(viz)₄(ReF₆)]_∞ ( 3 ) analogue in which the ferromagnetic Ni^II–Re^IV interaction (+10.8 cm^?1) dwarfs the coupling present in related cyanide‐bridged systems. These results reveal [ReF₆]^2? to be an unique new module for the design of molecule‐based magnetic materials.     

Palladium‐Catalyzed Carbonylative α‐Arylation of 2‐Oxindoles with (Hetero)aryl Bromides: Efficient and Complementary Approach to 3‐Acyl‐2‐oxindoles

An efficient Pd‐catalyzed carbonylative α‐arylation of 2‐oxindoles with aryl and heteroaryl bromides for the one‐step synthesis of 3‐acyl‐2‐oxindoles has been developed. This reaction proceeds efficiently under mild conditions and is complementary to the more common oxindole forming reactions. The transformation only requires a mild base and provides good to excellent yields even with heteroaromatic substrates. Employing a near stoichiometric amount of ¹³COgen, the methodology was easily extended to [¹³C] acyl labeling. The general applicability of the reaction conditions was demonstrated in the synthesis of a structure related to the pharmaceutically active 3‐acyl‐2‐oxindoles, tenidap.     

PHAISTOS: A framework for Markov chain Monte Carlo simulation and inference of protein structure

We present a new software framework for Markov chain Monte Carlo sampling for simulation, prediction, and inference of protein structure. The software package contains implementations of recent advances in Monte Carlo methodology, such as efficient local updates and sampling from probabilistic models of local protein structure. These models form a probabilistic alternative to the widely used fragment and rotamer libraries. Combined with an easily extendible software architecture, this makes PHAISTOS well suited for Bayesian inference of protein structure from sequence and/or experimental data. Currently, two force‐fields are available within the framework: PROFASI and OPLS‐AA/L, the latter including the generalized Born surface area solvent model. A flexible command‐line and configuration‐file interface allows users quickly to set up simulations with the desired configuration. PHAISTOS is released under the GNU General Public License v3.0. Source code and documentation are freely available from http://phaistos.sourceforge.net . The software is implemented in C++ and has been tested on Linux and OSX platforms. © 2013 Wiley Periodicals, Inc.     

A Stable Homoleptic Organometallic Iron(IV) Complex

A homoleptic organometallic Fe^IV complex that is stable in both solution and in the solid state at ambient conditions has been synthesized and isolated as [Fe(phtmeimb)₂](PF₆)₂ (phtmeimb=[phenyl(tris(3-methylimidazolin-2-ylidene))borate]⁻). This Fe^IV N-heterocyclic carbene (NHC) complex was characterized by ¹H NMR, HR-MS, elemental analysis, scXRD analysis, electrochemistry, Mößbauer spectroscopy, and magnetic susceptibility. The two latter techniques unequivocally demonstrate that [Fe(phtmeimb)₂](PF₆)₂ is a triplet Fe^IV low-spin S=1 complex in the ground state, in agreement with quantum chemical calculations. The electronic absorption spectrum of [Fe(phtmeimb)₂](PF₆)₂ in acetonitrile shows an intense absorption band in the red and near IR, due to LMCT (ligand-to-metal charge transfer) excitation. For the first time the excited state dynamics of a Fe^IV complex was studied and revealed a ≈0.8 ps lifetime of the ³LMCT excited state of [Fe(phtmeimb)₂](PF₆)₂ in acetonitrile.     

Hybrid vertical‐cavity laser with lateral emission into a silicon waveguide

We experimentally demonstrate an optically‐pumped III‐V/Si vertical‐cavity laser with lateral emission into a silicon waveguide. This on‐chip hybrid laser comprises a distributed Bragg reflector, a III‐V active layer, and a high‐contrast grating reflector, which simultaneously funnels light into the waveguide integrated with the laser. This laser has the advantages of long‐wavelength vertical‐cavity surface‐emitting lasers, such as low threshold and high side‐mode suppression ratio, while allowing integration with silicon photonic circuits, and is fabricated using CMOS compatible processes. It has the potential for ultrahigh‐speed operation beyond 100 Gbit/s and features a novel mechanism for transverse mode control.

     

Nonreciprocal transmission in a nonlinear photonic‐crystal Fano structure with broken symmetry

Nanostructures that feature nonreciprocal light transmission are highly desirable building blocks for realizing photonic integrated circuits. Here, a simple and ultracompact photonic‐crystal structure, where a waveguide is coupled to a single nanocavity, is proposed and experimentally demonstrated, showing very efficient optical diode functionality. The key novelty of the structure is the use of cavity‐enhanced material nonlinearities in combination with spatial symmetry breaking and a Fano resonance to realize nonreciprocal propagation effects at ultralow power and with good wavelength tunability. The nonlinearity of the device relies on ultrafast carrier dynamics, rather than the thermal effects usually considered, allowing the demonstration of nonreciprocal operation at a bit‐rate of 10 Gbit s⁻¹ with a low energy consumption of 4.5 fJ bit⁻¹.

     

Global weak solutions for a viscous liquid–gas model with transition to single-phase gas flow and vacuum

This work deals with a viscous two-phase liquid–gas model relevant to the flow in wells and pipelines. The liquid is treated as an incompressible fluid whereas the gas is assumed to be polytropic. The model is rewritten in terms of Lagrangian coordinates and is studied in a free boundary setting where the liquid and gas masses are of compact support initially, and continuous at the boundary. Consequently, the initial masses involve a transition to single-phase gas flow and vacuum at the boundary. An appropriate balance between pressure and viscous forces is identified which allows obtaining pointwise upper and lower estimates of masses. These estimates rely on the assumption of a certain relation between the rate of degeneracy of the viscosity coefficient and the rate that determines how fast the initial masses are vanishing at the boundary. By combining these estimates with basic energy type of estimates, higher order regularity estimates are obtained. The existence of global weak solutions is then proved by showing compactness for a class of semi-discrete approximations.