A note on the computational complexity of the moment-SOS hierarchy for polynomial optimization

The moment-sum-of-squares (moment-SOS) hierarchy is one of the most celebrated and widely applied methods for approximating the minimum of an n-variate polynomial over a feasible region defined by polynomial (in)equalities. A key feature of the hierarchy is that, at a fixed level, it can be formulated as a semidefinite program of size polynomial in the number of variables n. Although this suggests that it may therefore be computed in polynomial time, this is not necessarily the case. Indeed, as O'Donnell (2017) and later Raghavendra & Weitz (2017) show, there exist examples where the sos-representations used in the hierarchy have exponential bit-complexity. We study the computational complexity of the moment-SOS hierarchy, complementing and expanding upon earlier work of Raghavendra & Weitz (2017). In particular, we establish algebraic and geometric conditions under which polynomial-time computation is guaranteed to be possible.Comment: 10 page

Про періодичні розв'язки системи сингулярно збурених диференціальних рівнянь з періодичними коефіцієнтами

Запропоновано алгоритм побудови періодичних розв'язків сингулярно збуреної системи диференціальних рівнянь з періодичними коефіцієнтами у некритичному випадку.Предложен алгоритм построения периодических решений сингулярно возмущенной системы дифференциальных уравнений с периодическими коэффициентами в некритическом случае.An algorithm of constructing the periodic solutions of a singularly perturbed system of differential equations with periodic coefficients in the uncritical case is proposed

Phosphocholine-Modified Lipooligosaccharides of Haemophilus influenzae Inhibit ATP-Induced IL-1beta Release by Pulmonary Epithelial Cells

Phosphocholine-modified bacterial cell wall components are virulence factors enabling immune evasion and permanent colonization of the mammalian host, by mechanisms that are poorly understood. Recently, we demonstrated that free phosphocholine (PC) and PC-modified lipooligosaccharides (PC-LOS) from Haemophilus influenzae, an opportunistic pathogen of the upper and lower airways, function as unconventional nicotinic agonists and efficiently inhibit the ATP-induced release of monocytic IL-1beta. We hypothesize that H. influenzae PC-LOS exert similar effects on pulmonary epithelial cells and on the complex lung tissue. The human lung carcinoma-derived epithelial cell lines A549 and Calu-3 were primed with lipopolysaccharide from Escherichia coli followed by stimulation with ATP in the presence or absence of PC or PC-LOS or LOS devoid of PC. The involvement of nicotinic acetylcholine receptors was tested using specific antagonists. We demonstrate that PC and PC-LOS efficiently inhibit ATP-mediated IL-1beta release by A549 and Calu-3 cells via nicotinic acetylcholine receptors containing subunits alpha7, alpha9, and/or alpha10. Primed precision-cut lung slices behaved similarly. We conclude that H. influenzae hijacked an endogenous anti-inflammatory cholinergic control mechanism of the lung to evade innate immune responses of the host. These findings may pave the way towards a host-centered antibiotic treatment of chronic airway infections with H. influenzae

Association mapping in Scandinavian winter wheat for yield, plant height and traits important for second-generation bioethanol production

A collection of 100 wheat varieties representing more than 100 years of wheat-breeding history in Scandinavia was established in order to identify marker-trait associations for plant height, grain yield and biomass potential for bioethanol production. The field-grown material showed variations in plant height from 54 to 122 cm and in grain yield from 2 to 6.61 t ha-1. The release of monomeric sugars was determined by high-throughput enzymatic treatment of ligno-cellulosic material and varied between 0.169 and 0.312 g/g dm for glucose and 0.146 and 0.283 g/g dm for xylose. As expected, plant height and grain yield showed to be highly influenced by genetic factors with repeatability (R) equal to 0.75 and 0.53 respectively, while this was reduced for glucose and xylose (R=0.09 for both) . The study of trait correlations showed how old, low-yielding, tall varieties released higher amounts of monomeric sugars after straw enzymatic hydrolysis, showing reduced recalcitrance to bioconversion compared to modern varieties. 93 lines from the collection were genotyped with the DArTseq® genotypic platform and 5525 markers were used for genome-wide association mapping. Six QTLs for grain yield, plant height and glucose released from straw were mapped. One QTL for plant height was previously reported, while the remaining QTLs constituted new genomic regions linked to trait variation. This paper is one of the first studies in wheat to identify QTLs that are important for bioethanol production based on a genome-wide association approach

Quantifying the likelihood of structural models through a dynamically enhanced powder X-ray diffraction protocol

Structurally characterizing new materials is tremendously challenging, especially when single crystal structures are hardly available which is often the case for covalent organic frameworks. Yet, knowledge of the atomic structure is key to establish structure-function relations and enable functional material design. Herein, a new protocol is proposed to unambiguously predict the structure of poorly crystalline materials through a likelihood ordering based on the X-ray diffraction (XRD) pattern. Key of the procedure is the broad set of structures generated from a limited number of building blocks and topologies, which is submitted to operando structural characterization. The dynamic averaging in the latter accounts for the operando conditions and inherent temporal character of experimental measurements, yielding unparalleled agreement with experimental powder XRD patterns. The proposed concept can hence unquestionably identify the structure of experimentally synthesized materials, a crucial step to design next generation functional materials

Characterizing the turbulent drag properties of rough surfaces with a Taylor--Couette setup

Wall-roughness induces extra drag in wall-bounded turbulent flows. Mapping any given roughness geometry to its fluid dynamic behaviour has been hampered by the lack of accurate and direct measurements of skin-friction drag. Here the Taylor-Couette (TC) system provides an opportunity as it is a closed system and allows to directly and reliably measure the skin-friction. However, the wall-curvature potentially complicates the connection between the wall friction and the wall roughness characteristics. Here we investigate the effects of a hydrodynamically fully rough surface on highly turbulent, inner cylinder rotating, TC flow. We find that the effects of a hydrodynamically fully rough surface on TC turbulence, where the roughness height k is three orders of magnitude smaller than the Obukhov curvature length Lc (which characterizes the effects of curvature on the turbulent flow, see Berghout et al. arXiv: 2003.03294, 2020), are similar to those effects of a fully rough surface on a flat plate turbulent boundary layer (BL). Hence, the value of the equivalent sand grain height ks, that characterizes the drag properties of a rough surface, is similar to those found for comparable sandpaper surfaces in a flat plate BL. Next, we obtain the dependence of the torque (skin-friction drag) on the Reynolds number for given wall roughness, characterized by ks, and find agreement with the experimental results within 5 percent. Our findings demonstrate that global torque measurements in the TC facility are well suited to reliably deduce wall drag properties for any rough surface.Comment: 18 pages, 13 figure

Gallium Arsenide (GaAs) Quantum Photonic Waveguide Circuits

Integrated quantum photonics is a promising approach for future practical and large-scale quantum information processing technologies, with the prospect of on-chip generation, manipulation and measurement of complex quantum states of light. The gallium arsenide (GaAs) material system is a promising technology platform, and has already successfully demonstrated key components including waveguide integrated single-photon sources and integrated single-photon detectors. However, quantum circuits capable of manipulating quantum states of light have so far not been investigated in this material system. Here, we report GaAs photonic circuits for the manipulation of single-photon and two-photon states. Two-photon quantum interference with a visibility of 94.9 +/- 1.3% was observed in GaAs directional couplers. Classical and quantum interference fringes with visibilities of 98.6 +/- 1.3% and 84.4 +/- 1.5% respectively were demonstrated in Mach-Zehnder interferometers exploiting the electro-optic Pockels effect. This work paves the way for a fully integrated quantum technology platform based on the GaAs material system.Comment: 10 pages, 4 figure