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Although recent advances in machine learning have shown its success to learn from independent and identically distributed (IID) data, it is vulnerable to out-of-distribution (OOD) data in an open world. Domain generalization (DG) deals with such an issue and it aims to learn a model from multiple source domains that can be generalized to unseen target domains. Existing studies on DG have largely focused on stationary settings with homogeneous source domains. However, in many applications, domains may evolve along a specific direction (e.g., time, space). Without accounting for such non-stationary patterns, models trained with existing methods may fail to generalize on OOD data. In this paper, we study domain generalization in non-stationary environment. We first examine the impact of environmental non-stationarity on model performance and establish the theoretical upper bounds for the model error at target domains. Then, we propose a novel algorithm based on adaptive invariant representation learning, which leverages the non-stationary pattern to train a model that attains good performance on target domains. Experiments on both synthetic and real data validate the proposed algorithm. 

This report presents a comprehensive collection of searches for new physics performed by the ATLAS Collaboration during the Run~2 period of data taking at the Large Hadron Collider, from 2015 to 2018, corresponding to about 140~$$^{-1}$$ of $$\sqrt{s}=13$$~TeV proton--proton collision data. These searches cover a variety of beyond-the-standard model topics such as dark matter candidates, new vector bosons, hidden-sector particles, leptoquarks, or vector-like quarks, among others. Searches for supersymmetric particles or extended Higgs sectors are explicitly excluded as these are the subject of separate reports by the Collaboration. For each topic, the most relevant searches are described, focusing on their importance and sensitivity and, when appropriate, highlighting the experimental techniques employed. In addition to the description of each analysis, complementary searches are compared, and the overall sensitivity of the ATLAS experiment to each type of new physics is discussed. Summary plots and statistical combinations of multiple searches are included whenever possible. 

A<sc>bstract</sc> A study of the Higgs boson decaying into bottom quarks (H→$$ b\overline{b} $$ $b\overline{b}$) and charm quarks (H→$$ c\overline{c} $$ $c\overline{c}$) is performed, in the associated production channel of the Higgs boson with aWorZboson, using 140 fb⁻¹of proton-proton collision data at$$ \sqrt{s} $$ $\sqrt{s}$= 13 TeV collected by the ATLAS detector. The individual production ofWHandZHwithH→$$ b\overline{b} $$ $b\overline{b}$is established with observed (expected) significances of 5.3 (5.5) and 4.9 (5.6) standard deviations, respectively. Differential cross-section measurements of the gauge boson transverse momentum within the simplified template cross-section framework are performed in a total of 13 kinematical fiducial regions. The search for theH→$$ c\overline{c} $$ $c\overline{c}$decay yields an observed (expected) upper limit at 95% confidence level of 11.5 (10.6) times the Standard Model prediction. The results are also used to set constraints on the charm coupling modifier, resulting in|κ_c| <4.2 at 95% confidence level. Combining theH→$$ b\overline{b} $$ $b\overline{b}$andH→$$ c\overline{c} $$ $c\overline{c}$measurements constrains the absolute value of the ratio of Higgs-charm and Higgs-bottom coupling modifiers (|κ_c/κ_b|) to be less than 3.6 at 95% confidence level. 

Abstract Recently proposed as a stable means of evaluating geometric compactness, theisoperimetric profileof a planar domain measures the minimum perimeter needed to inscribe a shape with prescribed area varying from 0 to the area of the domain. While this profile has proven valuable for evaluating properties of geographic partitions, existing algorithms for its computation rely on aggressive approximations and are still computationally expensive. In this paper, we propose a practical means of approximating the isoperimetric profile and show that for domains satisfying a“thick neck”condition, our approximation is exact. For more general domains, we show that our bound is still exact within a conservative regime and is otherwise an upper bound. Our method is based on a traversal of the medial axis which produces efficient and robust results. We compare our technique with the state‐of‐the‐art approximation to the isoperimetric profile on a variety of domains and show significantly tighter bounds than were previously achievable.