Vertex Representations for Yangians of Kac-Moody algebras

30 pagesUsing vertex operators, we build representations of the Yangian of a simply laced Kac-Moody algebra and of its double. As a corollary, we prove the PBW property for simply laced affine Yangians.Peer reviewe

Factors Influencing the Surprising Instability of Word Embeddings

Despite the recent popularity of word embedding methods, there is only a small body of work exploring the limitations of these representations. In this paper, we consider one aspect of embedding spaces, namely their stability. We show that even relatively high frequency words (100-200 occurrences) are often unstable. We provide empirical evidence for how various factors contribute to the stability of word embeddings, and we analyze the effects of stability on downstream tasks.Comment: NAACL HLT 201

The formal shift operator on the Yangian double

Let $\mathfrak{g}$ be a symmetrizable Kac-Moody algebra with associated Yangian $Y_\hbar\mathfrak{g}$ and Yangian double $\mathrm{D}Y_\hbar\mathfrak{g}$. An elementary result of fundamental importance to the theory of Yangians is that, for each $c\in \mathbb{C}$, there is an automorphism $\tau_c$ of $Y_\hbar\mathfrak{g}$ corresponding to the translation $t\mapsto t+c$ of the complex plane. Replacing $c$ by a formal parameter $z$ yields the so-called formal shift homomorphism $\tau_z$ from $Y_\hbar\mathfrak{g}$ to the polynomial algebra $Y_\hbar\mathfrak{g}[z]$. We prove that $\tau_z$ uniquely extends to an algebra homomorphism $\Phi_z$ from the Yangian double $\mathrm{D}Y_\hbar\mathfrak{g}$ into the $\hbar$-adic closure of the algebra of Laurent series in $z^{-1}$ with coefficients in the Yangian $Y_\hbar\mathfrak{g}$. This induces, via evaluation at any point $c\in \mathbb{C}^\times$, a homomorphism from $\mathrm{D}Y_\hbar\mathfrak{g}$ into the completion of the Yangian with respect to its grading. We show that each such homomorphism gives rise to an isomorphism between completions of $\mathrm{D}Y_\hbar\mathfrak{g}$ and $Y_\hbar\mathfrak{g}$ and, as a corollary, we find that the Yangian $Y_\hbar\mathfrak{g}$ can be realized as a degeneration of the Yangian double $\mathrm{D}Y_\hbar\mathfrak{g}$. Using these results, we obtain a Poincar\'{e}-Birkhoff-Witt theorem for $\mathrm{D}Y_\hbar\mathfrak{g}$ applicable when $\mathfrak{g}$ is of finite type or of simply-laced affine type.Comment: 40 page

Examination of the Association Between Intimate Partner Violence and STI/HIV Risk in African American Women in High Risk Areas of Atlanta, GA: A Mixed Methods Analysis

In March 2012, President Obama issued a Presidential Memorandum creating an interagency Federal Working Group to explore the intersection of HIV/AIDS, violence against women and girls, and gender-related health disparities. Intimate partner violence (IPV) and HIV constitute major public health issues for women, particularly African American women who are disproportionately affected by HIV/AIDS. In 2012, the rate of HIV for African American women was four to 20 times higher than rates for females of other races. This study explores the complex relationship between IPV and STI/HIV risk in African American females. In an attempt to examine the intersection of IPV and STI/HIV risk this study used cross-sectional survey data to quantitatively examine the differences between women who had experienced IPV in the previous 12 months (cases) and women who had not experienced IPV in the previous 12 months (controls) in: 1) previous STI diagnosis, 2) accessing HIV testing and 3) mean scores of fear of condom negotiation due to physical violence. Chi-square analyses were completed to determine if the populations were statistically significant in terms of previous STI diagnosis and accessing HIV testing. An independent-samples t-test was conducted to compare the fear of condom negotiation scores for cases and controls. In addition, qualitative analysis was conducted to further elucidate the mechanisms from experiencing IPV to an increased risk of HIV infection. The quantitative analysis suggests a significant difference between fear of condom negotiation due to fear of physical violence. The qualitative analysis suggests that women who experience IPV are often forced to have sex with their partners, experience physical violence in response to condom negotiation and use drugs and/or alcohol to cope with the abuse. HIV prevention interventions need to address IPV as a possible risk factor. In addition, an enhancement of IPV screening in healthcare settings is needed. Future prospective studies are critical to address the issues of temporality and causality

Experimental investigations concerning the limits of detonation in gaseous mixtures. Part I

It is the purpose of this investigation to determine quantitatively the limits of detonation in gaseous mixtures for the conditions imposed and for a number of given gaseous explosive mixtures