Dualization and deformations of the Bar-Natan—Russell skein module

This thesis studies the Bar-Natan skein module of the solid torus with a particular boundary curve system, and in particular a diagrammatic presentation of it due to Russell. This module has deep connections to topology and categorification: it is isomorphic to both the total homology of the (n,n)-Springer variety and the 0th Hochschild homology of the Khovanov arc ring H^n. We can also view the Bar-Natan--Russell skein module from a representation-theoretic viewpoint as an extension of the Frenkel--Khovanov graphical description of the Lusztig dual canonical basis of the nth tensor power of the fundamental U_q(sl_2)-representation. One of our primary results is to extend a dualization construction of Khovanov using Jones--Wenzl projectors from the Lusztig basis to the Russell basis. We also construct and explore several deformations of the Russell skein module. One deformation is a quantum deformation that arises from embedding the Russell skein module in a space that obeys Kauffman--Lins diagrammatic relations. Our quantum version recovers the original Russell space when q is specialized to -1 and carries a natural braid group action that recovers the symmetric group action of Russell and Tymoczko. We also present an equivariant deformation that arises from replacing the TQFT algebra A used in the construction of the rings H^n by the equivariant homology of the two-sphere with the standard action of U(2) and taking the 0th Hochschild homology of the resulting deformed arc rings. We show that the equivariant deformation has the expected rank. Finally, we consider the Khovanov two-functor F from the category of tangles. We show that it induces a surjection from the space of cobordisms of planar (2m, 2n)-tangles to the space of (H^m, H^n)-bimodule homomorphisms and give an explicit description of the kernel. We use our result to introduce a new quotient of the Russell skein module

adSformers: Personalization from Short-Term Sequences and Diversity of Representations in Etsy Ads

In this article, we present a general approach to personalizing ads through encoding and learning from variable-length sequences of recent user actions and diverse representations. To this end we introduce a three-component module called the adSformer diversifiable personalization module (ADPM) that learns a dynamic user representation. We illustrate the module's effectiveness and flexibility by personalizing the Click-Through Rate (CTR) and Post-Click Conversion Rate (PCCVR) models used in sponsored search. The first component of the ADPM, the adSformer encoder, includes a novel adSformer block which learns the most salient sequence signals. ADPM's second component enriches the learned signal through visual, multimodal, and other pretrained representations. Lastly, the third ADPM "learned on the fly" component further diversifies the signal encoded in the dynamic user representation. The ADPM-personalized CTR and PCCVR models, henceforth referred to as adSformer CTR and adSformer PCCVR, outperform the CTR and PCCVR production baselines by $+2.66\%$ and $+2.42\%$, respectively, in offline Area Under the Receiver Operating Characteristic Curve (ROC-AUC). Following the robust online gains in A/B tests, Etsy Ads deployed the ADPM-personalized sponsored search system to $100\%$ of traffic as of February 2023

Folksonomies and clustering in the collaborative system CiteULike

We analyze CiteULike, an online collaborative tagging system where users bookmark and annotate scientific papers. Such a system can be naturally represented as a tripartite graph whose nodes represent papers, users and tags connected by individual tag assignments. The semantics of tags is studied here, in order to uncover the hidden relationships between tags. We find that the clustering coefficient reflects the semantical patterns among tags, providing useful ideas for the designing of more efficient methods of data classification and spam detection.Comment: 9 pages, 5 figures, iop style; corrected typo

Impact of body mass index on relapse in children with acute lymphoblastic leukemia treated according to Nordic treatment protocols

Objectives High body mass index (BMI) is associated with poorer survival in childhood acute lymphoblastic leukemia (ALL), but the actual impact on the risk of relapse still needs to be clarified. We evaluated the impact of BMI at diagnosis on the risk of relapse in children with ALL treated according to Nordic Society of Paediatric Haematology and Oncology (NOPHO) protocols. Method In a multicenter study, we collected data on BMI at diagnosis and outcome of 2558 children aged 2.0-17.9 years diagnosed between 1992 and 2016. Patients were divided into four groups according to International Obesity Task Force (IOTF) childhood BMI cut-offs: underweight, = 30 kg/m(2). Results In Cox multivariate regression analyses, an increased risk of relapse was observed in children aged 10-17.9 years with unhealthy BMI at diagnosis (underweight hazard ratio HR: 2.90 [95% confidence interval: 1.24-6.78],P = .01; overweight, HR: 1.95 [1.11-3.43],P = .02, and obese HR: 4.32 [95% 2.08-8.97],P <.001), compared to children with healthy weight. BMI had no impact on relapse in children under 10 years of age. Conclusion High BMI, and especially obesity at diagnosis, is an independent adverse prognostic factor for relapse in older children with ALL.Peer reviewe

The short term debt vs. long term debt puzzle: a model for the optimal mix

This paper argues that the existing finance literature is inadequate with respect to its coverage of capital structure of small and medium sized enterprises (SMEs). In particular it is argued that the cost of equity (being both conceptually ill defined and empirically non quantifiable) is not applicable to the capital structure decisions for a large proportion of SMEs and the optimal capital structure depends only on the mix of short and long term debt. The paper then presents a model, developed by practitioners for optimising the debt mix and demonstrates its practical application using an Italian firm's debt structure as a case study

Clinical precursors of tics: an EMTICS study

Background: Children with Tourette syndrome (TS) often have comorbid disorders, particularly attention-deficit/ hyperactivity disorder (ADHD) and obsessive-compulsive disorder (OCD). While subtle premorbid symptoms have been described in various psychiatric disorders, the presence of clinical precursors that may exist before the onset of tics is unknown. This longitudinal study aimed to find clinical precursors of tics by assessing a range of clinical characteristics prior to tic onset in comparison with children without onset of tics. Methods: A sample of 187 3- to 10-year-old first-degree unaffected relatives of children with TS were followed up to 7 years in the European Multicentre Tics in Children Study (EMTICS). We investigated whether clinical characteristics assessed at baseline predicted tic onset, comparing 126 children without tic onset to 61 children who developed tics. We used the least absolute shrinkage and selection operator (LASSO) method, a penalised logistic regression approach. We also explored sex differences and repeated our analyses in an age- and sex-matched subsample. Results: Children with tic onset were more frequently male (b = 0.36), had higher baseline severity of conduct problems (b = 0.23), autism spectrum disorder symptoms (ASD; b = 0.08), compulsions (b = 0.02) and emotional problems (b = 0.03) compared to children without tic onset. Conduct and ASD problems were male-specific predictors, whereas severity of compulsions and oppositional (b = 0.39) and emotional problems were female-specific predictors. Conclusion: This study supports the presence of clinical precursors prior to tic onset and highlights the need of sex-specific monitoring of children at risk of developing tics. This may aid in the earlier detection of tics, particularly in females. We moreover found that tics most often persisted one year after tic onset, in contrast to the common belief that tics are mostly transient

Lack of Association of Group A Streptococcal Infections and Onset of Tics: European Multicenter Tics in Children Study

Background and objectives: The goal of this work was to investigate the association between group A streptococcal (GAS) infections and tic incidence among unaffected children with a family history of chronic tic disorders (CTDs). Methods: In a prospective cohort study, children with no history for tics who were 3 to 10 years of age with a first-degree relative with a CTD were recruited from the European Multicentre Tics in Children Study (EMTICS) across 16 European centers. Presence of GAS infection was assessed with throat swabs, serum anti-streptolysin O titers, and anti-DNAse titers blinded to clinical status. GAS exposure was defined with 4 different definitions based on these parameters. Cox regression analyses with time-varying GAS exposure were conducted to examine the association of onset of tics and GAS exposure during follow-up. Sensitivity analyses were conducted with Cox regression and logistic regression analyses. Results: A total of 259 children were recruited; 1 child was found to have tic onset before study entry and therefore was excluded. Sixty-one children (23.6%) developed tics over an average follow-up period of 1 (SD 0.7) year. There was a strong association of sex and onset of tics, with girls having an ≈60% lower risk of developing tics compared to boys (hazard ratio [HR] 0.4, 95% confidence interval [CI] 0.2-0.7). However, there was no statistical evidence to suggest an association of any of the 4 GAS exposure definitions with tic onset (GAS exposure definition 1: HR 0.310, 95% CI 0.037-2.590; definition 2: HR 0.561, 95% CI 0.219-1.436; definition 3: HR 0.853, 95% CI 0.466-1.561; definition 4: HR 0.725, 95% CI 0.384-1.370). Discussion: These results do not suggest an association between GAS exposure and development of tics. Classification of evidence: This study provides Class I evidence that group A streptococcal exposure does not associate with the development of tics in children with first-degree relatives with chronic tic disorder