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Homotopy theory of net representations

The homotopy theory of representations of nets of algebras over a (small) category with values in a closed symmetric monoidal model category is developed. We illustrate how each morphism of nets of algebras determines a change-of-net Quillen adjunction between the model categories of net representations, which is furthermore, a Quillen equivalence when the morphism is a weak equivalence. These techniques are applied in the context of homotopy algebraic quantum field theory with values in coch...

The time is out of joint. Teacher subjectivity during COVID-19

In this study, we address the issue of mathematics teachers’ personal and professional responsiveness to changing circumstances, such as the shift in external demands made on teacher practice due to the COVID-19 pandemic. For investigating a such delicate issue, we take a theoretical approach, which is quite novel in the feld of mathematics education: Lacan’s psychoanalytical lens. Specifically, we will use this psychoanalytical lens to analyze a case study focusing on a primary school teac...

Market areas in general equilibrium

This paper proposes a spatial model with a realistic geography where a continuous distribution of agents (e.g., farmers) engages in economic interactions with one location from a finite set (e.g., cities). The spatial structure of the equilibrium consists of a tessellation, i.e., a partition of space into a collection of mutually exclusive market areas. After proving the existence of a unique equilibrium, we characterize how the location of borders and, in the case with mobile labor, the set ...

Exact completion and constructive theories of sets

In the present paper we use the theory of exact completions to study categorical properties of small setoids in Martin-Löf type theory and, more generally, of models of the Constructive Elementary Theory of the Category of Sets, in terms of properties of their subcategories of choice objects (i.e., objects satisfying the axiom of choice). Because of these intended applications, we deal with categories that lack equalisers and just have weak ones, but whose objects can be regarded as collectio...

Short Communication: Localized Adversarial Artifacts for Compressed Sensing MRI

As interest in deep neural networks (DNNs) for image reconstruction tasks grows, their reliability has been called into question [V. Antun, F. Renna, C. Poon, B. Adcock, and A. C. Hansen, Proc. Natl. Acad. Sci. USA, 117 (2020), pp. 30088–30095; N. M. Gottschling, V. Antun, B. Adcock, and A. C. Hansen, The Troublesome Kernel: Why Deep Learning for Inverse Problems Is Typically Unstable, preprint, arXiv:2001.01258, 2020]. However, recent work has shown that, compared to total variation (TV) min...

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