Optimization Over the Boolean Hypercube Via Sums of Nonnegative Circuit Polynomials

Various key problems from theoretical computer science can be expressed as polynomial optimization problems over the boolean hypercube. One particularly successful way to prove complexity bounds for these types of problems is based on sums of squares (SOS) as nonnegativity certificates. In this article, we initiate optimization problems over the boolean hypercube via a recent, alternative certificate called sums of nonnegative circuit polynomials (SONC). We show that key results for SOS-based certificates remain valid: First, for polynomials, which are nonnegative over the n-variate boolean hypercube with constraints of degree d there exists a SONC certificate of degree at most \(n+d\). Second, if there exists a degree d SONC certificate for nonnegativity of a polynomial over the boolean hypercube, then there also exists a short degree d SONC certificate that includes at most \(n^{O(d)}\) nonnegative circuit polynomials. Moreover, we prove that, in opposite to SOS, the SONC cone is not closed under taking affine transformation of variables and that for SONC there does not exist an equivalent to Putinar’s Positivstellensatz for SOS. We discuss these results from both the algebraic and the optimization perspective.

     

Activation of SO2 by N/Si+ and N/B Frustrated Lewis Pairs: Experimental and Theoretical Comparison with CO2 Activation

The guanidine 1,5,7-triazabicyclo[4.4.0]dec-5-ene (TBD) and the substituted derivatives [TBD–SiR₂]⁺ and TBD–BR₂ reacted with SO₂ to give different FLP–SO₂ adducts. Molecular structures, elucidated by X-ray diffraction, showed some structural similarities with the analogous CO₂ adducts. Thermodynamic stabilities were both experimentally evidenced and computed through DFT calculations. The underlying parameters governing the relative stabilities of the different SO₂ and CO₂ adducts were discussed from a theoretical standpoint, with a focus on the influence of the Lewis acidic moiety.     

Iron Porphyrin Allows Fast and Selective Electrocatalytic Conversion of CO2 to CO in a Flow Cell

Molecular catalysts have been shown to have high selectivity for CO₂ electrochemical reduction to CO, but with current densities significantly below those obtained with solid-state materials. By depositing a simple Fe porphyrin mixed with carbon black onto a carbon paper support, it was possible to obtain a catalytic material that could be used in a flow cell for fast and selective conversion of CO₂ to CO. At neutral pH (7.3) a current density as high as 83.7 mA cm⁻² was obtained with a CO selectivity close to 98 %. In basic solution (pH 14), a current density of 27 mA cm⁻² was maintained for 24 h with 99.7 % selectivity for CO at only 50 mV overpotential, leading to a record energy efficiency of 71 %. In addition, a current density for CO production as high as 152 mA cm⁻² (>98 % selectivity) was obtained at a low overpotential of 470 mV, outperforming state-of-the-art noble metal based catalysts.     

Topology‐Matching Design of an Influenza‐Neutralizing Spiky Nanoparticle‐Based Inhibitor with a Dual Mode of Action

In this study, we demonstrate the concept of “topology‐matching design” for virus inhibitors. With the current knowledge of influenza A virus (IAV), we designed a nanoparticle‐based inhibitor (nano‐inhibitor) that has a matched nanotopology to IAV virions and shows heteromultivalent inhibitory effects on hemagglutinin and neuraminidase. The synthesized nano‐inhibitor can neutralize the viral particle extracellularly and block its attachment and entry to the host cells. The virus replication was significantly reduced by 6 orders of magnitude in the presence of the reverse designed nano‐inhibitors. Even when used 24 hours after the infection, more than 99.999 % inhibition is still achieved, which indicates such a nano‐inhibitor might be a potent antiviral for the treatment of influenza infection.     

A new approach for the total synthesis of spilanthol and analogue with improved anesthetic activity

A 5-step synthesis of spilanthol (affinin) is reported, where the route features complete control of alkene geometry during the assembling of the double bonds, with the use of a Sonogashira cross-coupling reaction, a Z-selective alkyne semi-reduction and a HWE olefination reaction as the key steps. A simplified analogue was also prepared in 4 steps. Both compounds were found to permeate dermatomed pig ear skin through an in vitro Franz-type diffusion cell. The simplified analogue presented a superior anesthetic effect in vivo, using the tail flick model, when compared to spilanthol and to the commercial standard EMLA^®. These results suggest that both spilanthol and its analogue could be useful as a topical anesthetic in clinical practice.     

Glass transition temperature of colloidal polystyrene dispersed in various liquids

Recently, there has been significant interest in measuring the glass transition temperature (T_g) of thin polymer films floated atop liquid substrates. However, such films still have intrinsically asymmetric interfaces, that is, a free surface and a liquid–polymer interface. In an effort to analyze the influence of different liquids on the T_g of confined polymers in which there is no interfacial asymmetry, a colloidal suspension of polystyrene (PS) nanoparticles (NPs) was employed. The T_gs of PS NPs suspended in either glycerol or an ionic liquid were characterized using differential scanning calorimetry. Nanoparticles suspended in an ionic liquid showed an invariance of T_g with confinement, that is, decreasing diameter. In contrast, nanoparticles suspended in glycerol showed a slight decrease in T_g with confinement. The dependence of NP T_g on the nature of the surrounding liquid exhibited a positive correlation with the interfacial energy of the liquid–PS interface and no correlation with interfacial softness, as measured by viscosity. A comparison of the results with thin films supported by liquid or solid substrates revealed a nontrivial interplay between interfacial softness and interfacial interactions on the T_g of confined PS. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1776–1783     

An Approximate Probabilistic Model for Structured Gaussian Elimination

Many of the fast methods for factoring integers and computing discrete logarithms require the solution of large sparse linear systems of equations over finite fields. Structured Gaussian elimination has been proposed as a first step in solving such sparse systems. It is a method for selecting pivots in an attempt to preserve the sparseness of the coefficient matrix. Eventually it terminates with a (smaller) residual linear system which must be solved by some other method. In many cases, the original column density is roughly proportional to the reciprocal of the of the column index. We discuss the asymptotic behavior of structured Gaussian elimination for this situation. One result is the observation that, for the column density just mentioned, the size of the residual system grows linearly with the size of the problem. This makes it possible to extrapolate the results of Monte Carlo simulation to much larger problems.     

Photocrosslinking of thin polymer films – materials for sensors and actuators

Polymers with temperature dependent degrees of swelling, especially polymers which exhibit lower critical solution temperature (LCST) behaviour in aqueous solutions, are of interest for applications in microsystems. For these applications it is necessary to form and pattern thin films in the μm-range. This has been achieved through photocrosslinking of linear prepolymers. Copolymers based on N-isopropylacrylamide (NIPAAm) were modified with a stilbazolium salt chromophore to yield photocrosslinkable temperature sensitive polymers. The chromophore reacts via a [2+2]-cycloaddition under irradiation, this can be used to crosslink the polymer. The photocrosslinking properties were studied by UV irradiation of thin films and measuring the changes in UV absorption spectra. Through irradiation of thin films through a mask it was possible to obtain patterned networks in the μm-range (20 μm space width and > 50 μm line width). The polymers exhibited LCST behaviour, which was measured using DSC. The resulting patterned networks had temperature dependent swelling properties in aqueous media.