The complement of the Bowditch space in the SL(2,C) character variety

Let ${\mathcal X}$ be the space of type-preserving \SL(2,C) characters of the punctured torus $T$. The Bowditch space ${\mathcal X}_{BQ}$ is the largest open subset of ${\mathcal X}$ on which the mapping class group acts properly discontinuously, this is characterized by two simple conditions called the $BQ$-conditions. In this note, we show that $[\rho]$ is in the interior of the complement of ${\mathcal X}_{BQ}$ if there exists an essential simple closed curve $X$ on $T$ such that $|{\rm tr} \rho(X)|<0.5$.Comment: 6 page

Latent variable language models

There has been a renewed interest in generative modeling/unsupervised learning for language for downstream natural language understanding tasks. In this thesis, we explore the augmentation of standard language models with latent variables. In the first chapter, we provide a brief introduction of language models, the classical n-gram treatment and the more common Neural Language Models in use today. We also briefly introduce variational autoencoders and the recent work improving upon them. In Chapter 2, we review work that explores the space where latent variable models and language models intersect. We then empirically analyse the effectiveness of a couple of these methods. In particular, we re-implement the models from Bowman et al. (2015) and Yang et al. (2017), and benchmark them against the Penn Treebank dataset with some experiments of our own. In Chapter 3, we discuss an ICML submission: Generating Contradictions, Entailments and Neutral Sentences. In this work, we encode source sentences to a latent distribution space and attempt to manipulate it from there to generate sentences corresponding to the given logical entailment. While our efforts are unsuccessful, we believe that enabling controllable latent variable distributions is an interesting direction to pursue. In Chapter 4, we conclude with a review of the content covered in the thesis, and a higher-level discussion of what possible avenues of future work could resemble.Dernièrement, il y a eu un renouvellement d'intérêts dans l'application de modèles génératifs en compréhension de la langue. Dans ce mémoire, nous explorons l'ajout de variables latentes dans les modèles de langues traditionnels. Dans le chapitre 1, nous introduisons brièvement les modèles de langues, notamment les modèles n-gram et les modèles de langue neuronaux, couramment utilisés de nos jours. Nous présentons également les auto-encodeurs variationnels ainsi que différents moyens d'améliorer leur performance. Dans le chapitre 2, nous passons en revue les travaux ou des modèles à variables latentes sont appliqués en modélisation de la langue. Nous analysons également l'efficacité de plusieurs de ces méthodes. En particulier, nous analysons les modèles de cite bowman2015generating et cite yang2017improved, et les évaluons entre autres sur Penn Treebank. Dans le chapitre 3, nous présentons un article encore non publié: Generating Contradictions, Entailments and Neutral Sentences. Dans ce travail, nous encodons des phrases sources dans une distribution latente. Nous manipulons par la suite cet espace afin de générer des phrases correspondant à certaines implications logiques. Malgré nos efforts infructueux, nous croyons que l'utilisation de variables latentes contrôlables est une direction intéressante à suivre. Dans le chapitre 4, nous concluons avec un bref survol du mémoire et discutons des travaux futurs possibles

Protein folding and the robustness of cells

The intricate intracellular infrastructure of all known life forms is based on proteins. The folded shape of a protein determines both the protein’s function and the set of molecules it will bind to. This tight coupling between a protein’s function and its interconnections in the molecular interaction network has consequences for the molecular course of evolution. It is also counter to human engineering approaches. Here we report on a simulation study investigating the impact of random errors in an abstract metabolic network of 500 enzymes. Tight coupling between function and interconnectivity of nodes is compared to the case where these two properties are independent. Our results show that the model system under consideration is more robust if function and interconnection are intertwined. These findings are discussed in the context of nanosystems engineering

mGlu5: A double-edged sword for aversive learning related therapeutics

Aversive memories underlie many types of anxiety disorders. One area of research to more effectively treat anxiety disorders has therefore been identifying pharmacological targets to affect memory processes. Among these targets, the metabotropic glutamate 5 receptor (mGlu5) has received attention due to the availability of drugs to utilize its role in learning and memory. In this review, we highlight preclinical studies examining the role of mGlu5 at various stages of aversive learning and its inhibition via extinction in order to gain a better understanding of its therapeutic potential. We suggest that mGlu5 has distinct roles at different stages of memory that not only makes it a tricky target, but a double-edged sword as a therapeutic. However, the selective involvement of mGlu5 in different memory stages allows for certain precision that could be harnessed clinically. We therefore suggest potential applications, limitations, and pitfalls when considering use of mGlu5 modulators as therapeutics. In addition, we recommend future studies to address important gaps in this literature, such as sex and age factors in light of anxiety disorders being more prevalent in those demographics

Microsatellite markers uncover cryptic species of Odontotermes (Termitoidae: Termitidae) from Peninsular Malaysia

Termites from the genus Odontotermes are known to contain numerous species complexes that are difficult to tell apart morphologically or with mitochondrial DNA sequences. We developed markers for one such cryptic species complex, that is, Odontotermes srinakarinensis sp. nov. from Maxwell Hill Forest Reserve (Perak, Malaysia), and characterised them using a sample of 41 termite workers from three voucher samples from the same area. We then genotyped 150 termite individuals from 23 voucher samples/colonies of this species complex from several sites in Peninsular Malaysia. We analysed their population by constructing dendograms from the proportion of shared-alleles between individuals and genetic distances between colonies; additionally, we examined the Bayesian clustering pattern of their genotype data. All methods of analysis indicated that there were two distinct clusters within our data set. After the morphologies of specimens from each cluster were reexamined, we were able to separate the two species morphologically and found that a single diagnostic character found on the mandibles of its soldiers could be used to separate the two species quite accurately. The additional species in the clade was identified as Odontotermes denticulatus after it was matched to type specimens at the NHM London and Cambridge Museum of Zoology