Solution to the Henckell--Rhodes problem: finite FF-inverse covers do exist

For a finite connected graph $\mathcal{E}$ with set of edges $E$, a finite $E$-generated group $G$ is constructed such that the set of relations $p=1$ satisfied by $G$ (with $p$ a word over $E\cup E^{-1}$) is closed under deletion of generators (i.e.~edges). As a consequence, every element $g\in G$ admits a unique minimal set $\mathrm{C}(g)$ of edges (the \emph{content} of $g$) needed to represent $g$ as a word over $\mathrm{C}(g)\cup\mathrm{C}(g)^{-1}$. The crucial property of the group $G$ is that connectivity in the graph $\mathcal{E}$ is encoded in $G$ in the following sense: if a word $p$ forms a path $u\longrightarrow v$ in $\mathcal{E}$ then there exists a $G$-equivalent word $q$ which also forms a path $u\longrightarrow v$ and uses only edges from their content; in particular, the content of the corresponding group element $[p]_G=[q]_G$ spans a connected subgraph of $\mathcal{E}$ containing the vertices $u$ and $v$. As an application it is shown that every finite inverse monoid admits a finite $F$-inverse cover. This solves a long-standing problem of Henckell and Rhodes.Comment: 46 pages, 14 figures, new result Cor. 2.7 included, several inaccuracies removed, more details include

Electrochemical Estimations of the Gold Nanoparticle Size Effect on Cysteine-Gold Oxidation,

Gold nanoparticles are interesting for nanobiomedical applications, such as for drug delivery and as diagnostic imaging contrast agents. However, their stability and reactivity in-vivo are influenced by their surface properties and size. Here, we investigate the electrochemical oxidation of differently sized citrate-coated gold nanoparticles in the presence and absence of L-cysteine, a thiol-containing amino acid with high binding affinity to gold. We found that smaller sized (5, 10 nm) gold nanoparticles were significantly more susceptible to electrochemical L-cysteine interactions and/or L-cysteine-facilitated gold oxidation than larger (20, 50 nm) sized gold nanoparticles, both for the same mass and nominal surface area, under the conditions investigated (pH 7.4, room temperature, stagnant solutions, and scan rates of 0.5 to 450 mV s−1). The electrochemical measurements of drop-casted gold nanoparticle suspensions on paraffin-impregnated graphite electrodes were susceptible to the quality of the electrode. Increased cycling resulted in irreversible oxidation and detachment/oxidation of gold into solution. Our results suggest that L-cysteine-gold interactions are stronger for smaller nanoparticles

Effect of surface roughness on optical heating of metals

Heating by absorption of light is a commonly used technique to ensure a fast temperature increase of metallic samples. The rate of heating when using optical heating depends critically on the absorption of light by a sample. Here, the reflection and scattering of light from UV to IR by surfaces with different roughness of iron-based alloy samples (Fe, 1 wt-% Cr) is investigated. A combination of ellipsometric and optical scattering measurements is used to derive a simplified parametrisation which can be used to obtain the absorption of light from random rough metal surfaces, as prepared through conventional grinding and polishing techniques. By modelling the ellipsometric data of the flattest sample, the pseudodielectric function of the base material is derived. Describing an increased roughness by a Maxwell-Garnett model does not yield a reflectivity which follows the experimentally observed sum of scattered and reflected intensities. Therefore, a simple approach is introduced, based on multiple reflections, where the number of reflections depends on the surface roughness. This approach describes the data well, and is subsequently used to estimate the fraction of absorbed energy. Using numerical modelling, the effect on the heating rate is investigated. A numerical example is analysed, which shows that slight changes in roughness may result in big differences of the energy input into a metallic sample, with consequences on the achieved temperatures. Though the model oversimplifies reality, it provides a physically intuitive approach to estimate trends

The algebra of adjacency patterns: Rees matrix semigroups with reversion

We establish a surprisingly close relationship between universal Horn classes of directed graphs and varieties generated by so-called adjacency semigroups which are Rees matrix semigroups over the trivial group with the unary operation of reversion. In particular, the lattice of subvarieties of the variety generated by adjacency semigroups that are regular unary semigroups is essentially the same as the lattice of universal Horn classes of reflexive directed graphs. A number of examples follow, including a limit variety of regular unary semigroups and finite unary semigroups with NP-hard variety membership problems.Comment: 30 pages, 9 figure

Association of Pyrethroid Pesticide Exposure With Attention-Deficit/Hyperactivity Disorder in a Nationally Representative Sample of U.S. Children

Background Pyrethroid pesticides cause abnormalities in the dopamine system and produce an ADHD phenotype in animal models, with effects accentuated in males versus females. However, data regarding behavioral effects of pyrethroid exposure in children is limited. We examined the association between pyrethroid pesticide exposure and ADHD in a nationally representative sample of US children, and tested whether this association differs by sex. Methods Data are from 8–15 year old participants (N = 687) in the 2001–2002 National Health and Nutrition Examination Survey. Exposure was assessed using concurrent urinary levels of the pyrethroid metabolite 3-phenoxybenzoic acid (3-PBA). ADHD was defined by either meeting Diagnostic and Statistical Manual of Mental Disorders-Fourth Edition criteria on the Diagnostic Interview Schedule for Children (DISC) or caregiver report of a prior diagnosis. ADHD symptom counts were determined via the DISC. Multivariable logistic regression examined the link between pyrethroid exposure and ADHD, and poisson regression investigated the link between exposure and ADHD symptom counts. Results Children with urinary 3-PBA above the limit of detection (LOD) were twice as likely to have ADHD compared with those below the LOD (adjusted odds ratio [aOR] 2.42; 95 % confidence interval [CI] 1.06, 5.57). Hyperactive-impulsive symptoms increased by 50 % for every 10-fold increase in 3-PBA levels (adjusted count ratio 1.50; 95 % CI 1.03, 2.19); effects on inattention were not significant. We observed possible sex-specific effects: pyrethroid biomarkers were associated with increased odds of an ADHD diagnosis and number of ADHD symptoms for boys but not girls. Conclusions We found an association between increasing pyrethroid pesticide exposure and ADHD which may be stronger for hyperactive-impulsive symptoms compared to inattention and in boys compared to girls. Given the growing use of pyrethroid pesticides, these results may be of considerable public health import

The finite basis problem for Kauffman monoids

We prove a sufficient condition under which a semigroup admits no finite identity basis. As an application, it is shown that the identities of the Kauffman monoid Kn are nonfinitely based for each n≥3. This result holds also for the case when Kn is considered as an involution semigroup under either of its natural involutions. © 2015, Springer Basel