Refined elliptic tropical enumerative invariants

We suggest a new refined (i.e., depending on a parameter) tropical enumerative invariant of toric surfaces. This is the first known enumerative invariant that counts tropical curves of positive genus with marked vertices. Our invariant extends the refined rational broccoli invariant invented by L. Göttsche and the first author, though there is a serious difference between the invariants: our elliptic invariant counts weights assigned partly to individual tropical curves and partly to collections of tropical curves, and our invariant is not always multiplicative over the vertices of the counted tropical curves as was the case for other known tropical enumerative invariants of toric surfaces. As a consequence we define elliptic broccoli curves and elliptic broccoli invariants as well as elliptic tropical descendant invariants for any toric surface.     

Long-term characteristics of analogical processing in high-school students with high fluid intelligence: an fMRI study

Intelligence is known to predict scholastic achievement and enables high performance in cognitive tasks. Fluid intelligence is strongly related to analogical reasoning abilities, which are fundamental to mathematical thinking. Geometric analogical reasoning is a prototypical measure of fluid intelligence. However, the cerebral correlates of geometric analogical reasoning and their developmental modulation over time are still rarely investigated. We report a 1-year follow-up functional magnetic resonance imaging study of a geometric analogical reasoning task in high fluid intelligence high-school students. This study was designed to characterise the cerebral correlates of geometric analogical reasoning and to improve our knowledge about the impact of general cognitive development on behavioural performance and on cerebral mechanisms underlying geometric analogical reasoning in adolescents. Our data indicate that a fronto-parietal network comprising the left and right parietal lobes and the left middle frontal gyrus was equally modulated by task difficulty at both measuring time points. At the behavioural level, however, participants showed improvements in performance at the second measuring time point. The behavioural improvements point to a more efficient task processing. As this is not accompanied by differential recruitment of fronto-parietal brain regions, the data suggest an increase in neural efficiency for these brain regions.     

Broccoli curves and the tropical invariance of Welschinger numbers

In this paper we introduce broccoli curves, certain plane tropical curves of genus zero related to real algebraic curves. The numbers of these broccoli curves through given points are independent of the chosen points — for arbitrary choices of the directions of the ends of the curves, possibly with higher weights, and also if some of the ends are fixed. In the toric Del Pezzo case we show that these broccoli invariants are equal to the Welschinger invariants (with real and complex conjugate point conditions), thus providing a proof of the independence of Welschinger invariants of the point conditions within tropical geometry. The general case gives rise to a tropical Caporaso–Harris formula for broccoli curves which suffices to compute all Welschinger invariants of the plane.     

C−I‐Selective Cross‐Coupling Enabled by a Cationic Palladium Trimer

While there is a growing interest in harnessing synergistic effects of more than one metal in catalysis, relatively little is known beyond bimetallic systems. This report describes the straightforward access to an air‐stable Pd trimer and presents unambiguous reactivity data of its privileged capability to differentiate C?I over C?Br bonds in C?C bond formations (arylation and alkylation) of polyhalogenated arenes, which typical Pd⁰ and Pd^I‐Pd^I catalysts fail to deliver. Experimental and computational reactivity data, including the first location of a transition state for bond activation by the trimer, are presented, supporting direct trimer reactivity to be feasible.     

A General and Air‐tolerant Strategy to Conjugated Polymers within Seconds under Palladium(I) Dimer Catalysis

While current M⁰/M^II based polymerization strategies largely focus on fine‐tuning the catalyst, reagents and conditions for each and every monomer, this report discloses a single method that allows access to a variety of different conjugated polymers within seconds at room temperature. Key to this privileged reactivity is an air‐ and moisture stable dinuclear Pd^I catalyst. The method is operationally simple, robust and tolerant to air.     

Covalent‐Allosteric Inhibitors to Achieve Akt Isoform‐Selectivity

Isoforms of protein kinase Akt are involved in essential processes including cell proliferation, survival, and metabolism. However, their individual roles in health and disease have not been thoroughly evaluated. Thus, there is an urgent need for perturbation studies, preferably mediated by highly selective bioactive small molecules. Herein, we present a structure‐guided approach for the design of structurally diverse and pharmacologically beneficial covalent‐allosteric modifiers, which enabled an investigation of the isoform‐specific preferences and the important residues within the allosteric site of the different isoforms. The biochemical, cellular, and structural evaluations revealed interactions responsible for the selective binding profiles. The isoform‐selective covalent‐allosteric Akt inhibitors that emerged from this approach showed a conclusive structure–activity relationship and broke ground in the development of selective probes to delineate the isoform‐specific functions of Akt kinases.     

Sequence‐Defined Introduction of Hydrophobic Motifs and Effects in Lectin Binding of Precision Glycomacromolecules

This study investigates the influence of an increasingly hydrophobic backbone of multivalent glycomimetics based on sequence‐defined oligo(amidoamines) on their resulting affinity toward bacterial lectins. Glycomacromolecules are obtained by stepwise assembly of tailor‐made building blocks on solid support, using both hydrophobic aliphatic and aromatic building blocks to enable a gradual change in hydrophobicity of the backbone. Their binding behavior toward model lectin Concanavalin A (ConA) is evaluated using isothermal titration calorimetry (ITC) and surface plasmon resonance (SPR) showing higher affinities for glycomacromolecules with higher content of hydrophobic and aromatic moieties in the backbone. Finally, glycomacromolecules are tested in a bacterial adhesion inhibition study against Escherichia coli where more hydrophobic backbones yield higher inhibitory potentials most likely due to additional secondary interactions with hydrophobic regions of the protein receptor as well as a change in conformation exposing carbohydrate ligands for increased binding. Overall, the results highlight the influence and thereby importance of the polymer backbone itself on the resulting properties of polymeric biomimetics.     

Annelated Cyclobutanes by Fe‐Catalyzed Cycloisomerization of Enyne Acetates

Cationic Fe complexes of the general type [(Ph₃P)₂Fe(CO)(NO)]X (X=BF₄, BAr^F₄) catalyze the redox‐neutral cycloisomerization of 1,6‐ and 1,7‐enyneacetates to afford bicyclic cyclobutanes under mild conditions in good yields and diastereoselectivities.     

Multivariate Analysis of MALDI Imaging Mass Spectrometry Data of Mixtures of Single Pollen Grains

Mixtures of pollen grains of three different species (Corylus avellana, Alnus cordata, and Pinus sylvestris) were investigated by matrix-assisted laser desorption/ionization time-of-flight imaging mass spectrometry (MALDI-TOF imaging MS). The amount of pollen grains was reduced stepwise from >?10 to single pollen grains. For sample pretreatment, we modified a previously applied approach, where any additional extraction steps were omitted. Our results show that characteristic pollen MALDI mass spectra can be obtained from a single pollen grain, which is the prerequisite for a reliable pollen classification in practical applications. MALDI imaging of laterally resolved pollen grains provides additional information by reducing the complexity of the MS spectra of mixtures, where frequently peak discrimination is observed. Combined with multivariate statistical analyses, such as principal component analysis (PCA), our approach offers the chance for a fast and reliable identification of individual pollen grains by mass spectrometry.

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In Situ Investigations of Mechanochemical One‐Pot Syntheses

We present an in situ triple coupling of synchrotron X‐ray diffraction with Raman spectroscopy, and thermography to study milling reactions in real time. This combination of methods allows a correlation of the structural evolution with temperature information. The temperature information is crucial for understanding both the thermodynamics and reaction kinetics. The reaction mechanisms of three prototypical mechanochemical syntheses, a cocrystal formation, a C?C bond formation (Knoevenagel condensation), and the formation of a manganese‐phosphonate, were elucidated. Trends in the temperature development during milling are identified. The heat of reaction and latent heat of crystallization of the product contribute to the overall temperature increase. A decrease in temperature occurs via release of, for example, water as a by‐product. Solid and liquid intermediates are detected. The influence of the mechanical impact could be separated from temperature effects caused by the reaction.