A Lagrangian relaxation approach to the edge-weighted clique problem

The $b$-clique polytope $CP^n_b$ is the convex hull of the node and edge incidence vectors of all subcliques of size at most $b$ of a complete graph on $n$ nodes. Including the Boolean quadric polytope $QP^n$ as a special case and being closely related to the quadratic knapsack polytope, it has received considerable attention in the literature. In particular, the max-cut problem is equivalent with optimizing a linear function over $QP^n_n$. The problem of optimizing linear functions over $CP^n_b$ has so far been approached via heuristic combinatorial algorithms and cutting-plane methods. We study the structure of $CP^n_b$ in further detail and present a new computational approach to the linear optimization problem based on Lucena's suggestion of integrating cutting planes into a Lagrangian relaxation of an integer programming problem. In particular, we show that the separation problem for tree inequalities becomes polynomial in our Lagrangian framework. Finally, computational results are presented. \u

Natural and anthropogenic changes in a lake-forest system in Bukovina (Romania) since 1340 AD documented by sedimentary organic geochemistry (C, N and n-alkanes)

Lake Bolatau-Feredeu is a small (surface: 0.3 ha; catchment area: 31 ha) landslide-dammed lake in Bukovina (Eastern Carpathians, Romania). Elemental concentration, stable isotope composition of carbon and nitrogen, and n-alkane composition of the saturated hydrocarbon fraction of the organic material were analyzed along the sediment profile from Lake Bolatau-Feredeu covering the past 700 years. The ranges of delta C-13 values (- 30.5 to - 26.6 parts per thousand) and C/N atomic ratios (10.5 and 15.4) placed the organic material of the recent Bolatau-Feredeu sediment between the C3 Land Plants and the lacustrine algae. The n-alkane proxies provide better distinction between organic matter inputs. Detected major shifts in the n-alkane composition and the C and N concentrations along with the stable isotope compositions pointed towards three distinct stages in the environmental history of the lake-catchment system. The proxy information indicate a substantial landscape change characterized by deforestation and an increase in open pastureland with herbaceous vegetation from similar to 1820. The C/N, delta N-15, and delta C-13 values showed the highest variability probably linked to a variable lacustrine environment and decreased productivity in the catchment between similar to 1640 and 1760. It can be assumed that the extended periods of lake ice cover during the cold decades experienced at the turn of the 17th -18th centuries resulted in diminished biological productivity both in the lake and its catchment. Finally, afforestation and the decline in lake productivity have been reconstructed for the period of - 1470-1560

Electric-field-driven direct desulfurization

The ability to elucidate the elementary steps of a chemical reaction at the atomic scale is important for the detailed understanding of the processes involved, which is key to uncover avenues for improved reaction paths. Here, we track the chemical pathway of an irreversible direct desulfurization reaction of tetracenothiophene adsorbed on the Cu(111) closed-packed surface at the submolecular level. Using the precise control of the tip position in a scanning tunneling microscope and the electric field applied across the tunnel junction, the two carbon–sulfur bonds of a thiophene unit are successively cleaved. Comparison of spatially mapped molecular states close to the Fermi level of the metallic substrate acquired at each reaction step with density functional theory calculations reveals the two elementary steps of this reaction mechanism. The first reaction step is activated by an electric field larger than 2 V nm–1, practically in absence of tunneling electrons, opening the thiophene ring and leading to a transient intermediate. Subsequently, at the same threshold electric field and with simultaneous injection of electrons into the molecule, the exergonic detachment of the sulfur atom is triggered. Thus, a stable molecule with a bifurcated end is obtained, which is covalently bound to the metallic surface. The sulfur atom is expelled from the vicinity of the molecule.PostprintPeer reviewe

Magmatic PGE Sulphide Mineralization in Clinopyroxenite from the Platreef, Bushveld Complex, South Africa

The Platreef, at the base of the northern limb of the Bushveld Complex in South Africa, hosts platinum-group element (PGE) mineralization in association with base-metal sulphides (BMS) and platinum-group minerals (PGM). However, whilst a magmatic origin of the stratiform mineralization of the upper Platreef has been widely confirmed, the processes responsible for the PGE and BMS mineralization and metasomatism of the host rocks in the Platreef are still under discussion. In order to contribute to the present discussion, we present an integrated petrographical, mineral-chemical, whole-rock trace- and major-element, sulphur- and neodymium-isotope, study of Platreef footwall clinopyroxenite drill core samples from Overysel, which is located in the northern sector of the northern Bushveld limb. A metasomatic transformation of magmatic pyroxenite units to non-magmatic clinopyroxenite is in accordance with the petrography and whole-rock chemical analysis. The whole-rock data display lower SiO2, FeO, Na2O and Cr (<1700 ppm), and higher CaO, concentrations in the here-studied footwall Platreef clinopyroxenite samples than primary magmatic Platreef pyroxenite and norite. The presence of capped globular sulphides in some samples, which display differentiation into pyrrhotite and pentlandite in the lower, and chalcopyrite in the upper part, is attributed to the fractional crystallization of a sulphide liquid, and a downward transport of the blebs. In situ sulphur (V-CDT) isotope BMS data show isotopic signatures (δ34S = 0.9 to 3.1 ‰; Δ33S = 0.09 to 0.32‰) close to or within the pristine magmatic range. Elevated (non-zero) Δ33S values are common for Bushveld magmas, indicating contamination by older, presumably crustal sulphur in an early stage chamber, whereas magmatic δ34S values suggest the absence of local crustal contamination during emplacement. This is in accordance with the εNd (2.06 Ga) (chondritic uniform reservoir (CHUR)) values, of −6.16 to −6.94, which are similar to those of the magmatic pyroxenite and norite of the Main Zone and the Platreef in the northern sector of the northern Bushveld limb. Base-metal sulphide textures and S–Se-ratios give evidence for a secondary S-loss during late- to post-magmatic hydrothermal alteration. The textural evidence, as well as the bulk S/Se ratios and sulphide S isotopes studies, suggest that the mineralization in both the less and the pervasively hydrothermally altered clinopyroxenite samples of Overysel are of magmatic origin. This is further supported by the PPGE (Rh, Pt, Pd) concentrations in the BMS and mass-balance calculations, in both of which large proportions of the whole-rock Pd and Rh are hosted by pentlandite, whereas Pt and the IPGE (Os, Ir, Ru) were interpreted to mainly occur in discrete PGM. However, the presence of pentlandite with variable PGE concentrations on the thin section scale may be related to variations in the S content, already at S-saturation during magmatic formation, and/or post-solidification mobilization and redistribution

Controlling single molecule conductance by a locally induced chemical reaction on individual thiophene units

The authors acknowledge the Emmy-Noether-Program of the Deutsche Forschungsgemeinschaft, the SFB 767, Core Program PN19-03 (contract number 21 N/08.02.2019) founded by the Romanian Ministry of Research and Innovation, Basque Departamento de Universidades e Investigación (grant no. IT-756-13), the Spanish Ministerio de Economía y Competitividad (grant no. FIS2013-48286-C2-8752-P and FIS2016-75862-P) andthe Operational Programme Research, Development and Education financed by European Structural and Investment Funds and the Czech Ministry of Education, Youth and Sports (Project No. SOLID21 CZ.02.1.01/0.0/0.0/16_019/0000760).Among the prerequisites for the progress of single‐molecule‐based electronic devices are a better understanding of the electronic properties at the individual molecular level and the development of methods to tune the charge transport through molecular junctions. Scanning tunneling microscopy (STM) is an ideal tool not only for the characterization, but also for the manipulation of single atoms and molecules on surfaces. The conductance through a single molecule can be measured by contacting the molecule with atomic precision and forming a molecular bridge between the metallic STM tip electrode and the metallic surface electrode. The parameters affecting the conductance are mainly related to their electronic structure and to the coupling to the metallic electrodes. Here, the experimental and theoretical analyses are focused on single tetracenothiophene molecules and demonstrate that an in situ‐induced direct desulfurization reaction of the thiophene moiety strongly improves the molecular anchoring by forming covalent bonds between molecular carbon and copper surface atoms. This bond formation leads to an increase of the conductance by about 50 % compared to the initial state.Publisher PDFPeer reviewe

Multiorbital exciton formation in an organic semiconductor

Harnessing the optoelectronic response of organic semiconductors requires a thorough understanding of the fundamental light-matter interaction that is dominated by the excitation of correlated electron-hole pairs, i.e. excitons. The nature of these excitons would be fully captured by knowing the quantum-mechanical wavefunction, which, however, is difficult to access both theoretically and experimentally. Here, we use femtosecond photoemission orbital tomography in combination with many-body perturbation theory to gain access to exciton wavefunctions in organic semiconductors. We find that the coherent sum of multiple electron-hole pair contributions that typically make up a single exciton can be experimentally evidenced by photoelectron spectroscopy. For the prototypical organic semiconductor buckminsterfullerene (C$_{60}$), we show how to disentangle such multiorbital contributions and thereby access key properties of the exciton wavefunctions including localization, charge-transfer character, and ultrafast exciton formation and relaxation dynamics

Gaze Strategy in the Free Flying Zebra Finch (Taeniopygia guttata)

Fast moving animals depend on cues derived from the optic flow on their retina. Optic flow from translational locomotion includes information about the three-dimensional composition of the environment, while optic flow experienced during a rotational self motion does not. Thus, a saccadic gaze strategy that segregates rotations from translational movements during locomotion will facilitate extraction of spatial information from the visual input. We analysed whether birds use such a strategy by highspeed video recording zebra finches from two directions during an obstacle avoidance task. Each frame of the recording was examined to derive position and orientation of the beak in three-dimensional space. The data show that in all flights the head orientation was shifted in a saccadic fashion and was kept straight between saccades. Therefore, birds use a gaze strategy that actively stabilizes their gaze during translation to simplify optic flow based navigation. This is the first evidence of birds actively optimizing optic flow during flight