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1. Applying machine learning techniques to intermediate-length cascade decays

   UlHaq, Maaz; Kilic, Can; Lawrence-Sanderson, Benjamin; Sudha, Ram_Purandhar_Reddy (October 2023, Physical review D)

   In the collider phenomenology of extensions of the Standard Model with partner particles, cascade decays occur generically, and they can be challenging to discover when the spectrum of new particles is compressed and the signal cross section is low. Achieving discovery-level significance and measuring the properties of the new particles appearing as intermediate states in the cascade decays is a longstanding problem, with analysis techniques for some decay topologies already optimized. We focus our attention on a benchmark decay topology with four final state particles where there is room for improvement, and where multidimensional analysis techniques have been shown to be effective in the past. Using machine learning techniques, we identify the optimal kinematic observables for discovery, spin determination and mass measurement. In agreement with past work, we confirm that the kinematic observable Δ4 is highly effective. We quantify the achievable accuracy for spin determination and for the precision for mass measurements as a function of the signal size. 

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2. Probing topology in nonlinear topological materials using numerical K-theory

   https://doi.org/10.1103/PhysRevB.108.195142  

   Wong, Stephan; Loring, Terry A.; Cerjan, Alexander (November 2023, Physical Review B)

   Nonlinear topological insulators have garnered substantial recent attention as they have both enabled the discovery of new physics due to interparticle interactions, and may have applications in photonic devices such as topological lasers and frequency combs. However, due to the local nature of nonlinearities, previous attempts to classify the topology of nonlinear systems have required significant approximations that must be tailored to individual systems. Here, we develop a general framework for classifying the topology of nonlinear materials in any discrete symmetry class and any physical dimension. Our approach is rooted in a numerical K-theoretic method called the spectral localizer, which leverages a real-space perspective of a system to define local topological markers and a local measure of topological protection. Our nonlinear spectral localizer framework yields a quantitative definition of topologically non-trivial nonlinear modes that are distinguished by the appearance of a topological interface surrounding the mode. Moreover, we show how the nonlinear spectral localizer can be used to understand a system's topological dynamics, i.e., the time-evolution of nonlinearly induced topological domains within a system. We anticipate that this framework will enable the discovery and development of novel topological systems across a broad range of nonlinear materials 

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3. Robust convergence analysis of distributed optimization algorithms

   https://doi.org/10.1109/ALLERTON.2017.8262874  

   Sundararajan, Akhil; Hu, Bin; Lessard, Laurent (October 2017, Communication, Control, and Computing (Allerton), 2017 55th Annual Allerton Conference on)

   We present a unified framework for analyzing the convergence of distributed optimization algorithms by formulating a semidefinite program (SDP) which can be efficiently solved to bound the linear rate of convergence. Two different SDP formulations are considered. First, we formulate an SDP that depends explicitly on the gossip matrix of the network graph. This result provides bounds that depend explicitly on the graph topology, but the SDP dimension scales with the size of the graph. Second, we formulate an SDP that depends implicitly on the gossip matrix via its spectral gap. This result provides coarser bounds, but yields a small SDP that is independent of graph size. Our approach improves upon existing bounds for the algorithms we analyzed, and numerical simulations reveal that our bounds are likely tight. The efficient and automated nature of our analysis makes it a powerful tool for algorithm selection and tuning, and for the discovery of new algorithms as well. 

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4. Nonreciprocal and Topological Plasmonics

   https://doi.org/10.3390/photonics8040133  

   Shastri, Kunal; Abdelrahman, Mohamed; Monticone, Francesco (April 2021, Photonics)

   Metals, semiconductors, metamaterials, and various two-dimensional materials with plasmonic dispersion exhibit numerous exotic physical effects in the presence of an external bias, for example an external static magnetic field or electric current. These physical phenomena range from Faraday rotation of light propagating in the bulk to strong confinement and directionality of guided modes on the surface and are a consequence of the breaking of Lorentz reciprocity in these systems. The recent introduction of relevant concepts of topological physics, translated from condensed-matter systems to photonics, has not only given a new perspective on some of these topics by relating certain bulk properties of plasmonic media to the surface phenomena, but has also led to the discovery of new regimes of truly unidirectional, backscattering-immune, surface-wave propagation. In this article, we briefly review the concepts of nonreciprocity and topology and describe their manifestation in plasmonic materials. Furthermore, we use these concepts to classify and discuss the different classes of guided surface modes existing on the interfaces of various plasmonic systems. 

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5. Structure-Aware Image Segmentation with Homotopy Warping

   Hu, Xiaoling (December 2022, The Thirty-sixth Conference on Neural Information Processing Systems)

   Besides per-pixel accuracy, topological correctness is also crucial for the segmentation of images with fine-scale structures, e.g., satellite images and biomedical images. In this paper, by leveraging the theory of digital topology, we identify pixels in an image that are critical for topology. By focusing on these critical pixels, we propose a new homotopy warping loss to train deep image segmentation networks for better topological accuracy. To efficiently identify these topologically critical pixels, we propose a new algorithm exploiting the distance transform. The proposed algorithm, as well as the loss function, naturally generalize to different topological structures in both 2D and 3D settings. The proposed loss function helps deep nets achieve better performance in terms of topology-aware metrics, outperforming state-of-the-art structure/topology-aware segmentation methods. 

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