Extended formulations in combinatorial optimization

This survey is concerned with the size of perfect formulations for combinatorial optimization problems. By “perfect formulation”, we mean a system of linear inequalities that describes the convex hull of feasible solutions, viewed as vectors. Natural perfect formulations often have a number of inequalities that is exponential in the size of the data needed to describe the problem. Here we are particularly interested in situations where the addition of a polynomial number of extra variables allows a formulation with a polynomial number of inequalities. Such formulations are called “compact extended formulations”. We survey various tools for deriving and studying extended formulations, such as Fourier’s procedure for projection, Minkowski-Weyl’s theorem, Balas’ theorem for the union of polyhedra, Yannakakis’ theorem on the size of an extended formulation, dynamic programming, and variable discretization. For each tool that we introduce, we present one or several examples of how this tool is applied. In particular, we present compact extended formulations for several graph problems involving cuts, trees, cycles and matchings, and for the mixing set, and we present the proof of Fiorini, Massar, Pokutta, Tiwary and de Wolf of an exponential lower bound for the cut polytope. We also present Bienstock’s approximate compact extended formulation for the knapsack problem, Goemans’ result on the size of an extended formulation for the permutahedron, and the Faenza-Kaibel extended formulation for orbitopes.     

“Through-Space” Relativistic Effects on NMR Chemical Shifts of Pyridinium Halide Ionic Liquids

We have investigated, using two-component relativistic density functional theory (DFT) at ZORA-SO-BP86 and ZORA-SO-PBE0 level, the occurrence of relativistic effects on the ¹H, ¹³C, and ¹⁵N NMR chemical shifts of 1-methylpyridinium halides [MP][X] and 1-butyl-3-methylpyridinium trihalides [BMP][X₃] ionic liquids (ILs) (X=Cl, Br, I) as a result of a non-covalent interaction with the heavy anions. Our results indicate a sizeable deshielding effect in ion pairs when the anion is I⁻ and I₃⁻. A smaller, though nonzero, effect is observed also with bromine while chlorine based anions do not produce an appreciable relativistic shift. The chemical shift of the carbon atoms of the aromatic ring shows an inverse halogen dependence that has been rationalized based on the little C-2s orbital contribution to the σ-type interaction between the cation and anion. This is the first detailed account and systematic theoretical investigation of a relativistic heavy atom effect on the NMR chemical shifts of light atoms in the absence of covalent bonds. Our work paves the way and suggests the direction for an experimental investigation of such elusive signatures of ion pairing in ILs.     

Memory effects in quantum channel discrimination

We consider quantum-memory assisted protocols for discriminating quantum channels. We show that for optimal discrimination of memory channels, memory assisted protocols are needed. This leads to a new notion of distance for channels with memory, based on the general theory of quantum testers. For discrimination and estimation of sets of independent unitary channels, we prove optimality of parallel protocols among all possible architectures.     

Use of Nitrogen-Doped Carbon Nanodots for the Photocatalytic Fluoroalkylation of Organic Compounds

The use of amine-rich N-doped carbon nanodots (NCNDs) for the photochemical radical perfluoroalkylation of organic compounds is reported. This operationally simple approach occurs under mild conditions producing valuable new C−C bonds. The chemistry is driven by the ability of NCNDs to directly reach an electronically excited state upon light absorption, thereby successively triggering the formation of reactive radical species from simple perfluoroalkyl iodides. Preliminary mechanistic studies are also reported.     

Electrochemically deposited ZnO films: an XPS study on the evolution of their surface hydroxide and defect composition upon thermal annealing

Electrodeposition from ZnCl₂ aqueous solution was performed to grow ZnO thin films on the surface of polycrystalline copper plates. Electrochemical parameters for deposition were optimized by means of cyclic voltammetry (CV). The morphology of the deposits was studied via scanning electron microscopy (SEM), and their chemical composition was ascertained by means of X-ray photoelectron spectroscopy (XPS). The effects of changing the deposition bath temperature (T _bath) and the role played by post-deposition treatments, such as temperature and time of annealing in air, were studied. SEM images of freshly deposited vs. annealed samples have shown that in the former case the films display a rough morphology with mixed grain/hexagonal platelets structures and in the latter smaller but more uniformly dispersed cubic grains. T _bath is found to be the key parameter to induce the different morphology in the deposited films, which reflects in a different chemical reactivity of surface species, as found on the basis of the binding energies and relative quantitative ratios between Zn 2p and O 1s peaks. In fact, a higher T _bath favours a more efficient desorption of OH groups upon annealing, the O 1s peak resulting to much more drastically modified oxide/hydroxide intensity ratio with respect to the case of the sample deposited at lower T _bath.     

1,2‐Dimethoxyethane Degradation Thermodynamics in Li−O2 Redox Environments

The reaction thermodynamics of the 1,2‐dimethoxyethane (DME), a model solvent molecule commonly used in electrolytes for Li?O₂ rechargeable batteries, has been studied by first‐principles methods to predict its degradation processes in highly oxidizing environments. In particular, the reactivity of DME towards the superoxide anion O₂^? in oxygen‐poor or oxygen‐rich environments is studied by density functional calculations. Solvation effects are considered by employing a self‐consistent reaction field in a continuum solvation model. The degradation of DME occurs through competitive thermodynamically driven reaction paths that end with the formation of partially oxidized final products such as formaldehyde and methoxyethene in oxygen‐poor environments and methyl oxalate, methyl formate, 1‐formate methyl acetate, methoxy ethanoic methanoic anhydride, and ethylene glycol diformate in oxygen‐rich environments. This chemical reactivity indirectly behaves as an electroactive parasitic process and therefore wastes part of the charge exchanged in Li?O₂ cells upon discharge. This study is the first complete rationale to be reported about the degradation chemistry of DME due to direct interaction with O₂^?/O₂ molecules. These findings pave the way for a rational development of new solvent molecules for Li?O₂ electrolytes.     

Hardware-in-the-loop simulation of wave energy converters based on dielectric elastomer generators

Dielectric elastomer generators (DEGs) are soft electrostatic generators based on low-cost electroactive polymer materials. These devices have attracted the attention of the marine energy community as a promising solution to implement economically viable wave energy converters (WECs). This paper introduces a hardware-in-the-loop (HIL) simulation framework for a class of WECs that combines the concept of the oscillating water columns (OWCs) with the DEGs. The proposed HIL system replicates in a laboratory environment the realistic operating conditions of an OWC/DEG plant, while drastically reducing the experimental burden compared to wave tank or sea tests. The HIL simulator is driven by a closed-loop real-time hydrodynamic model that is based on a novel coupling criterion which allows rendering a realistic dynamic response for a diversity of scenarios, including large scale DEG plants, whose dimensions and topologies are largely different from those available in the HIL setup. A case study is also introduced, which simulates the application of DEGs on an OWC plant installed in a mild real sea laboratory test-site. Comparisons with available real sea-test data demonstrated the ability of the HIL setup to effectively replicate a realistic operating scenario. The insights gathered on the promising performance of the analysed OWC/DEG systems pave the way to pursue further sea trials in the future.

     

Perspectives in paramagnetic NMR of metalloproteins

NMR experiments and tools for the characterization of the structure and dynamics of paramagnetic proteins are presented here. The focus is on the importance of (13)C direct-detection NMR for the assignment of paramagnetic systems in solution, on the information contained in paramagnetic effects observed both in solution and in the solid state, and on novel paramagnetism-based tools for the investigation of conformational heterogeneity in protein-protein complexes or in multi-domain proteins.     

The triazine ring as a scaffold for the synthesis of new organogelators

The synthesis of new organogelators based on a triazine nucleus is described together with the analysis of the properties of the main compound 15. This compound revealed an efficient organogelator in both polar and apolar solvents and represents a promising precursor of other functionalized organogelators.