Embeddings between partially commutative groups: two counterexamples

In this note we give two examples of partially commutative subgroups of partially commutative groups. Our examples are counterexamples to the Extension Graph Conjecture and to the Weakly Chordal Conjecture of Kim and Koberda, \cite{KK}. On the other hand we extend the class of partially commutative groups for which it is known that the Extension Graph Conjecture holds, to include those with commutation graph containing no induced $C_4$ or $P_3$. In the process, some new embeddings of surface groups into partially commutative groups emerge.Comment: 15 pages, 5 figures; to appear in Journal of Algebr

Limit groups over coherent right-angled Artin groups

A new class of groups $\mathcal{C}$, containing all coherent RAAGs and all toral relatively hyperbolic groups, is defined. It is shown that, for a group $G$ in the class $\mathcal{C}$, the $\mathbb{Z}[t]$-exponential group $G^{\mathbb{Z}[t]}$ may be constructed as an iterated centraliser extension. Using this fact, it is proved that $G^{\mathbb{Z}[t]}$ is fully residually $G$ (i.e. it has the same universal theory as $G$) and so its finitely generated subgroups are limit groups over $G$. If $\mathbb{G}$ is a coherent RAAG, then the converse also holds - any limit group over $\mathbb{G}$ embeds into $\mathbb{G}^{\mathbb{Z}[t]}$. Moreover, it is proved that limit groups over $\mathbb{G}$ are finitely presented, coherent and CAT$(0)$, so in particular have solvable word and conjugacy problems.Comment: 40 pages, 1 figur

D1S80 Single-Locus Discrimination Among African Populations

The highly polymorphic D1S80 locus has no known genetic function. However, this variable number of tandem repeats (VNTR) locus has been highly valuable in forensic identification. In this study we report the allele and genotype frequencies of five African populations (Benin, Cameroon, Egypt, Kenya, and Rwanda), which can be used as databases to help characterize populations and identify individuals. The allele frequencies were used to infer genetic associations through phylogenetic, principal component, and G test statistical analyses. Compliance with Hardy-Weinberg equilibrium expectations was determined as were FST estimates, theta p values, and power of discrimination assessment for each population. Our analyses of 28 additional populations demonstrate that the D1S80 locus alone can be used to discriminate geographic and ethnic groups. We have generated databases useful for human identification and phylogenetic studies

On the use of Machine Learning and Deep Learning for Text Similarity and Categorization and its Application to Troubleshooting Automation

Troubleshooting is a labor-intensive task that includes repetitive solutions to similar problems. This task can be partially or fully automated using text-similarity matching to find previous solutions, lowering the workload of technicians. We develop a systematic literature review to identify the best approaches to solve the problem of troubleshooting automation and classify incidents effectively. We identify promising approaches and point in the direction of a comprehensive set of solutions that could be employed in solving the troubleshooting automation problem

Visual Explanation for Identification of the Brain Bases for Developmental Dyslexia on fMRI Data

Peer reviewedPublisher PD

Disentangling Vacancy Oxidation on Metallicity-Sorted Carbon Nanotubes

Pristine single-walled carbon nanotubes (SWCNTs) are rather inert to O$_2$ and N$_2$, which for low doses chemisorb only on defect sites or vacancies of the SWCNTs at the ppm level. However, very low doping has a major effect on the electronic properties and conductivity of the SWCNTs. Already at low O$_2$ doses (80 L), the X-ray photoelectron spectroscopy (XPS) O 1s signal becomes saturated, indicating nearly all the SWCNT's vacancies have been oxidized. As a result, probing vacancy oxidation on SWCNTs via XPS yields spectra with rather low signal-to-noise ratios, even for metallicity-sorted SWCNTs. We show that, even under these conditions, the first principles density functional theory calculated Kohn-Sham O 1s binding energies may be used to assign the XPS O 1s spectra for oxidized vacancies on SWCNTs into its individual components. This allows one to determine the specific functional groups or bonding environments measured. We find the XPS O 1s signal is mostly due to three O-containing functional groups on SWCNT vacancies: epoxy (C$_2$$>$O), carbonyl (C$_2$$>$C$=$O), and ketene (C$=$C$=$O), as ordered by abundance. Upon oxidation of nearly all the SWCNT's vacancies, the central peak's intensity for the metallic SWCNT sample is 60\% greater than for the semiconducting SWCNT sample. This suggests a greater abundance of O-containing defect structures on the metallic SWCNT sample. For both metallic and semiconducting SWCNTs, we find O$_2$ does not contribute to the measured XPS O~1s spectra

What Do Studies of Insect Polyphenisms Tell Us about Nutritionally-Triggered Epigenomic Changes and Their Consequences?

Many insects are capable of remarkable changes in biology and form in response to their environment or diet. The most extreme example of these are polyphenisms, which are when two or more different phenotypes are produced from a single genotype in response to the environment. Polyphenisms provide a fascinating opportunity to study how the environment affects an animal’s genome, and how this produces changes in form. Here we review the current state of knowledge of the molecular basis of polyphenisms and what can be learnt from them to understand how nutrition may influence our own genomes