Finding any given 2‐factor in sparse pseudorandom graphs efficiently

Given an $n$‐vertex pseudorandom graph $G$ and an $n$‐vertex graph $H$ with maximum degree at most two, we wish to find a copy of $H$ in $G$, that is, an embedding $\phi :V\left(H\right)\to V\left(G\right)$ so that $\phi \left(u\right)\phi \left(v\right)\in E\left(G\right)$ for all $uv\in E\left(H\right)$. Particular instances of this problem include finding a triangle‐factor and finding a Hamilton cycle in $G$. Here, we provide a deterministic polynomial time algorithm that finds a given $H$ in any suitably pseudorandom graph $G$. The pseudorandom graphs we consider are $\left(p,\lambda \right)$‐bijumbled graphs of minimum degree which is a constant proportion of the average degree, that is, $\mathrm{\Omega }\left(pn\right)$. A $\left(p,\lambda \right)$‐bijumbled graph is characterised through the discrepancy property: $|e\left(A,B\right)?p|A||B||<\lambda \sqrt{|A||B|}$ for any two sets of vertices $A$ and $B$. Our condition $\lambda =O(p^{2}n/\log n)$ on bijumbledness is within a log factor from being tight and provides a positive answer to a recent question of Nenadov. We combine novel variants of the absorption‐reservoir method, a powerful tool from extremal graph theory and random graphs. Our approach builds on our previous work, incorporating the work of Nenadov, together with additional ideas and simplifications.     

Counting restricted orientations of random graphs

We count orientations of avoiding certain classes of oriented graphs. In particular, we study , the number of orientations of the binomial random graph in which every copy of is transitive, and , the number of orientations of containing no strongly connected copy of . We give the correct order of growth of and up to polylogarithmic factors; for orientations with no cyclic triangle, this significantly improves a result of Allen, Kohayakawa, Mota, and Parente. We also discuss the problem for a single forbidden oriented graph, and state a number of open problems and conjectures.     

Development of a Neutral Diketopyrrolopyrrole Phosphine Oxide for the Selective Bioimaging of Mitochondria at the Nanomolar Level

Development of novel bioimaging materials that exhibit organelle specific accumulation continues to be at the forefront of research interests and efforts. Among the various subcellular organelles, mitochondria, which are found in the cytoplasm of eukaryotic cells, are of particular interest in relation to their vital function. To date, most molecular probes that target mitochondria utilise delocalised lipophilic cations such as triphenylphosphonium and pyridinium. However, the use of such charged motifs is known to be detrimental to the working function of the mitochondrial transmembrane potential and there remains a strong case for development of neutral mitochondrial fluorescent probes. Herein, we demonstrate for the first time the exploitation of diketopyrrolopyrrole-based chemistries for the realisation of a neutral fluorescent probe that exhibits organelle specific accumulation within the mitochondria at the nanomolar level. The synthesised probe, which bears a neutral triphenylphosphine oxide moiety, exhibits a large Stokes shift and high fluorescence quantum yield in water, both highly sought-after properties in the development of bioimaging agents. In vitro studies reveal no interference with cell metabolism when tested for the human MCF7 breast cancer cell and nanomolar subcellular organelle colocalisation with commercially available mitochondrial staining agent Mitotracker Red. In light of its novelty, neutral structure and the preferential accumulation at nanomolar concentrations we anticipate this work to be of significant interest for the increasingly larger community devoted to the realisation of neutral mitochondrial selective systems and more widely to those engaged in the rational development of superior organic architectures in the biological field.     

Extending the Family of V4+ S=${{ 1/2 }}$ Kagome Antiferromagnets

The ionothermal synthesis, structure, and magnetic susceptibility of a novel inorganic–organic hybrid material, imidazolium vanadium(III,IV) oxyfluoride [C₃H₅N₂][V₉O₆F₂₄(H₂O)₂] (ImVOF) are presented. The structure consists of inorganic vanadium oxyfluoride slabs with kagome layers of V⁴⁺ S=${{ 1/2 }}$ ions separated by a mixed valence layer. These inorganic slabs are intercalated with imidazolium cations. Quinuclidinium (Q) and pyrazinium (Pyz) cations can also be incorporated into the hybrid structure type to give QVOF and PyzVOF analogues, respectively. The highly frustrated topology of the inorganic slabs, along with the quantum nature of the magnetism associated with V⁴⁺, means that these materials are excellent candidates to host exotic magnetic ground states, such as the highly sought quantum spin liquid. Magnetic susceptibility measurements of all samples suggest an absence of conventional long‐range magnetic order down to 2 K despite considerable antiferromagnetic exchange.     

Geometry‐Related Children's Literature Improves the Geometry Achievement and Attitudes of Second‐Grade Students

Use of mathematics‐related literature can engage students' interest and increase their understanding of mathematical concepts. A quasi‐experimental study of two second‐grade classrooms assessed whether daily inclusion of geometry‐related literature in the classroom improved attitudes toward geometry and achievement in geometry. Consistent with the hypothesis, only the students in the classroom with a strong emphasis on geometry‐related children's literature showed a significant improvement in their attitudes about geometry over time. While both classes improved their geometry performance over the 4 weeks of the study, the class with a strong emphasis on geometry‐related literature improved significantly more (51.2%) than the control class (33.47%). Children's literature can provide a useful and interesting context in which students can develop their understanding of geometry.     

Protonation and Proton‐Coupled Electron Transfer at S‐Ligated [4Fe‐4S] Clusters

Biological [Fe‐S] clusters are increasingly recognized to undergo proton‐coupled electron transfer (PCET), but the site of protonation, mechanism, and role for PCET remains largely unknown. Here we explore this reactivity with synthetic model clusters. Protonation of the arylthiolate‐ligated [4Fe‐4S] cluster [Fe₄S₄(SAr)₄]^2? ( 1 , SAr=S‐2,4‐6‐(iPr)₃C₆H₂) leads to thiol dissociation, reversibly forming [Fe₄S₄(SAr)₃L]^1? ( 2 ) and ArSH (L=solvent, and/or conjugate base). Solutions of 2 +ArSH react with the nitroxyl radical TEMPO to give [Fe₄S₄(SAr)₄]^1? ( 1_ox ) and TEMPOH. This reaction involves PCET coupled to thiolate association and may proceed via the unobserved protonated cluster [Fe₄S₄(SAr)₃(HSAr)]^1? ( 1‐H ). Similar reactions with this and related clusters proceed comparably. An understanding of the PCET thermochemistry of this cluster system has been developed, encompassing three different redox levels and two protonation states.     

Raman spectroscopy monitors adverse bone sequelae of cancer radiotherapy

Raman spectroscopy provides information on bone chemical composition and structure via widely used metrics including mineral to matrix ratio, mineral crystallinity and carbonate content, collagen crosslinking ratio and depolarization ratios. These metrics are correlated with bone material properties, such as hardness, plasticity and Young''s modulus. We review application of Raman spectroscopy to two important irradiated animalmodels: the mouse tibia, amodel for damage to cortical bone sites including the rib (breast cancer) and to healthy tissue adjacent to extremity sarcomas, and the rat mandible, a model for radiation damage in head and neck cancer radiotherapy. Longitudinal studies of irradiated mouse tibia demonstrate that radiation-induced matrix abnormalities can persist even 26 weeks postradiation. Polarized Raman spectroscopy shows formation of more ordered orientation of both mineral and collagen. At 8 weeks post-radiation, irradiated rat hemimandible exhibits transient hypermineralization, increased collagen cross-linking and decreased depolarization ratios of mineral and collagen. A standard radioprotectant, amifostine, mitigates rat mandible radiation damage, with none remaining detectable 18 weeks post-radiation. Already a powerful tool to monitor radiation damage, Raman spectroscopy may be important in development of new radiotherapy protocols and radioprotective agents. Further in vivo studies of radiation effects on the rodent models are underway, as are development of methodologies for eventual use in human subjects.     

Surface‐Specific Functionalization of Nanoscale Metal–Organic Frameworks

A method for modifying the external surfaces of a series of nanoscale metal–organic frameworks (MOFs) with 1,2‐dioleoyl‐sn‐glycero‐3‐phosphate (DOPA) is presented. A series of zirconium‐based nanoMOFs of the same topology (UiO‐66, UiO‐67, and BUT‐30) were synthesized, isolated as aggregates, and then conjugated with DOPA to create stably dispersed colloids. BET surface area analysis revealed that these structures maintain their porosity after surface functionalization, providing evidence that DOPA functionalization only occurs on the external surface. Additionally, dye‐labeled ligand loading studies revealed that the density of DOPA on the surface of the nanoscale MOF correlates to the density of metal nodes on the surface of each MOF. Importantly, the surface modification strategy described will allow for the general and divergent synthesis and study of a wide variety of nanoscale MOFs as stable colloidal materials.     

A photomechanics material for elastoplastic stress analysis

The object of this investigation was to develop a technique or method for elastoplastic stress analysis using the optical effects of transparent materials. Of paramount importance was the selection and characterization of a suitable model material. In particular, it was desirable that the material be able to undergo large plastic strains while, at the same time, exhibiting a suitable level of optical response. A mixture of flexible and rigid polyester resins was found suitable, i.e., the mixture exhibited large strains and good optical response. It was found that unload birefringence (fringe order immediately upon removal of load) could be used to determine strain for a uniaxial-stress field. In particular, it provided a means for evaluating stress- and strain-concentration factors. Comparisons with other methods showed that the proposed method was reliable and gave results that are similar to those by other means. The usefulness of the material and method for two- and three-dimensional problems awaits further study.