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1. Topological superfluid defects with discrete point group symmetries

   https://doi.org/10.1038/s41467-022-32362-5  

   Xiao, Y.; Borgh, M. O.; Blinova, A.; Ollikainen, T.; Ruostekoski, J.; Hall, D. S. (August 2022, Nature Communications)

   Abstract Discrete symmetries are spatially ubiquitous but are often hidden in internal states of systems where they can have especially profound consequences. In this work we create and verify exotic magnetic phases of atomic spinor Bose–Einstein condensates that, despite their continuous character and intrinsic spatial isotropy, exhibit complex discrete polytope symmetries in their topological defects. Using carefully tailored spinor rotations and microwave transitions, we engineer singular line defects whose quantization conditions, exchange statistics, and dynamics are fundamentally determined by these underlying symmetries. We show how filling the vortex line singularities with atoms in a variety of different phases leads to core structures that possess magnetic interfaces with rich combinations of discrete and continuous symmetries. Such defects, with their non-commutative properties, could provide unconventional realizations of quantum information and interferometry. 

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2. Free quotients of favorable Calabi-Yau manifolds

   https://doi.org/10.1007/JHEP07(2022)116  

   Gray, James; Wang, Juntao (July 2022, Journal of High Energy Physics)

   A bstract Non-simply connected Calabi-Yau threefolds play a central role in the study of string compactifications. Such manifolds are usually described by quotienting a simply connected Calabi-Yau variety by a freely acting discrete symmetry. For the Calabi-Yau threefolds described as complete intersections in products of projective spaces, a classification of such symmetries descending from linear actions on the ambient spaces of the varieties has been given in [16]. However, which symmetries can be described in this manner depends upon the description that is being used to represent the manifold. In [24] new, favorable, descriptions were given of this data set of Calabi-Yau threefolds. In this paper, we perform a classification of cyclic symmetries that descend from linear actions on the ambient spaces of these new favorable descriptions. We present a list of 129 symmetries/non-simply connected Calabi-Yau threefolds. Of these, at least 33, and potentially many more, are topologically new varieties. 

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3. A note on the predictions of models with modular flavor symmetries

   https://doi.org/j.physletb.2019.135153  

   Chen, M.-C.; Ramos-Sánchez. S.; Ratz, M. (February 2020, Physics letters)

   Models with modular flavor symmetries have been thought to be highly predictive. We point out that these predictions are subject to corrections from non–holomorphic terms in the Lagrangean. Specifically, in the models discussed in the literature, the Kähler potential is not fixed by the symmetries, for instance. The most general Kähler potential consistent with the symmetries of the model contains additional terms with additional parameters, which reduce the predictive power of these constructions. We also comment on potential ways of how one may conceivably retain the predictivity. 

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4. Lifted Hybrid Variational Inference

   https://doi.org/10.24963/ijcai.2020/585  

   Chen, Yuqiao; Yang, Yibo; Natarajan, Sriraam; Ruozzi, Nicholas (July 2020, IJCAI 2020)

   Lifted inference algorithms exploit model symmetry to reduce computational cost in probabilistic inference. However, most existing lifted inference algorithms operate only over discrete domains or continuous domains with restricted potential functions. We investigate two approximate lifted variational approaches that apply to domains with general hybrid potentials, and are expressive enough to capture multi-modality. We demonstrate that the proposed variational methods are highly scalable and can exploit approximate model symmetries even in the presence of a large amount of continuous evidence, outperforming existing message-passing-based approaches in a variety of settings. Additionally, we present a sufficient condition for the Bethe variational approximation to yield a non-trivial estimate over the marginal polytope. 

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5. Symphony in the Latent Space: Provably Integrating High-dimensional Techniques with Non-linear Machine Learning Models

   https://doi.org/10.1609/aaai.v37i9.26233  

   Wu, Qiong; Li, Jian; Liu, Zhenming; Li, Yanhua; Cucuringu, Mihai (February 2023, AAAI)

   This paper revisits building machine learning algorithms that involve interactions between entities, such as those between financial assets in an actively managed portfolio, or interactions between users in a social network. Our goal is to forecast the future evolution of ensembles of multivariate time series in such applications (e.g., the future return of a financial asset or the future popularity of a Twitter account). Designing ML algorithms for such systems requires addressing the challenges of high-dimensional interactions and non-linearity. Existing approaches usually adopt an ad-hoc approach to integrating high-dimensional techniques into non-linear models and re- cent studies have shown these approaches have questionable efficacy in time-evolving interacting systems. To this end, we propose a novel framework, which we dub as the additive influence model. Under our modeling assump- tion, we show that it is possible to decouple the learning of high-dimensional interactions from the learning of non-linear feature interactions. To learn the high-dimensional interac- tions, we leverage kernel-based techniques, with provable guarantees, to embed the entities in a low-dimensional latent space. To learn the non-linear feature-response interactions, we generalize prominent machine learning techniques, includ- ing designing a new statistically sound non-parametric method and an ensemble learning algorithm optimized for vector re- gressions. Extensive experiments on two common applica- tions demonstrate that our new algorithms deliver significantly stronger forecasting power compared to standard and recently proposed methods. 

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