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  1. We construct two types of unital separable simple 𝐶∗-algebras: 𝐴𝐶1 𝑧 and 𝐴𝐶2 𝑧 , one exact but not amenable, the other nonexact. Both have the same Elliott invariant as the Jiang–Su algebra – namely, 𝐴𝐶𝑖 𝑧 has a unique tracial state,  𝐾0  𝐴𝐶𝑖 𝑧  , 𝐾0  𝐴𝐶𝑖 𝑧  + ,  1 𝐴𝐶𝑖 𝑧  = (Z, Z+, 1), and 𝐾1  𝐴𝐶𝑖 𝑧  = {0} (𝑖 = 1, 2). We show that 𝐴𝐶𝑖 𝑧 (𝑖 = 1, 2) is essentially tracially in the class of separable 𝒵-stable 𝐶∗-algebras of nuclear dimension 1.more »𝐴𝐶𝑖 𝑧 has stable rank one, strict comparison for positive elements and no 2-quasitrace other than the unique tracial state. We also produce models of unital separable simple nonexact (exact but not nuclear) 𝐶∗-algebras which are essentially tracially in the class of simple separable nuclear𝒵-stable 𝐶∗-algebras, and the models exhaust all possible weakly unperforated Elliott invariants.We also discuss some basic properties of essential tracial approximation. 1.« less
    Free, publicly-accessible full text available January 1, 2023
  2. Free, publicly-accessible full text available February 1, 2023
  3. We revisit the notion of tracial approximation for unital simple C*-algebras. We show that a unital simple separable in nite dimensional C*-algebra A is asymptotically tracially in the class of C-algebras with nite nuclear dimension if and only if A is asymptotically tracially in the class of nuclear Z-stable C-algebras. 1
  4. This paper focuses on a core task in computational sustainability and statistical ecology: species distribution modeling (SDM). In SDM, the occurrence pattern of a species on a landscape is predicted by environmental features based on observations at a set of locations. At first, SDM may appear to be a binary classification problem, and one might be inclined to employ classic tools (e.g., logistic regression, support vector machines, neural networks) to tackle it. However, wildlife surveys introduce structured noise (especially under-counting) in the species observations. If unaccounted for, these observation errors systematically bias SDMs. To address the unique challenges of SDM,more »this paper proposes a framework called StatEcoNet. Specifically, this work employs a graphical generative model in statistical ecology to serve as the skeleton of the proposed computational framework and carefully integrates neural networks under the framework. The advantages of StatEcoNet over related approaches are demonstrated on simulated datasets as well as bird species data. Since SDMs are critical tools for ecological science and natural resource management, StatEcoNet may offer boosted computational and analytical powers to a wide range of applications that have significant social impacts, e.g., the study and conservation of threatened species.« less