The general caloron correspondence

We outline in detail the general caloron correspondence for the group of automorphisms of an arbitrary principal $G$-bundle $Q$ over a manifold $X$, including the case of the gauge group of $Q$. These results are used to define characteristic classes of gauge group bundles. Explicit but complicated differential form representatives are computed in terms of a connection and Higgs field.Comment: 25 pages. New section added containing example

A Geometric Model for Odd Differential K-theory

Odd $K$-theory has the interesting property that it admits an infinite number of inequivalent differential refinements. In this paper we provide a bundle theoretic model for odd differential $K$-theory using the caloron correspondence and prove that this refinement is unique up to a unique natural isomorphism. We characterise the odd Chern character and its transgression form in terms of a connection and Higgs field and discuss some applications. Our model can be seen as the odd counterpart to the Simons-Sullivan construction of even differential $K$-theory. We use this model to prove a conjecture of Tradler-Wilson-Zeinalian regarding a related differential extension of odd $K$-theoryComment: 36 page

Characterization of the CBC2 readout ASIC for the CMS strip-tracker high-luminosity upgrade

The CMS Binary Chip 2 (CBC2) is a full-scale prototype ASIC developed for the front-end readout of the high-luminosity upgrade of the CMS silicon strip tracker. The 254-channel, 130 nm CMOS ASIC is designed for the binary readout of double-layer modules, and features cluster-width discrimination and coincidence logic for detecting high-PT track candidates. The chip was delivered in January 2013 and has since been bump-bonded to a dual-chip hybrid and extensively tested. The CBC2 is fully functional and working to specification: we present the result of electrical characterization of the chip, including gain, noise, threshold scan and power consumption, together with the performance of the stub finding logic. Finally we will outline the plan for future developments towards the production version

Circle actions, central extensions and string structures

The caloron correspondence can be understood as an equivalence of categories between $G$-bundles over circle bundles and $LG \rtimes_\rho S^1$-bundles where $LG$ is the group of smooth loops in $G$. We use it, and lifting bundle gerbes, to derive an explicit differential form based formula for the (real) string class of an $LG \rtimes_\rho S^1$-bundle.Comment: 25 page

Mixture-of-Linguistic-Experts Adapters for Improving and Interpreting Pre-trained Language Models

In this work, we propose a method that combines two popular research areas by injecting linguistic structures into pre-trained language models in the parameter-efficient fine-tuning (PEFT) setting. In our approach, parallel adapter modules encoding different linguistic structures are combined using a novel Mixture-of-Linguistic-Experts architecture, where Gumbel-Softmax gates are used to determine the importance of these modules at each layer of the model. To reduce the number of parameters, we first train the model for a fixed small number of steps before pruning the experts based on their importance scores. Our experiment results with three different pre-trained models show that our approach can outperform state-of-the-art PEFT methods with a comparable number of parameters. In addition, we provide additional analysis to examine the experts selected by each model at each layer to provide insights for future studies.Comment: 14 pages, 3 figures, Camera-Ready for EMNLP 2023 Findings (Long Paper