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A<sc>bstract</sc> In this paper we discuss gauging noninvertible zero-form symmetries in two dimensions, extending our previous work. Specifically, in this work we discuss more general gauged noninvertible symmetries in which the noninvertible symmetry is not multiplicity free, and discuss the case of Rep(A₄) in detail. We realize Rep(A₄) gaugings for thec= 1 CFT at the exceptional point in the moduli space and find new self-duality under gauging a certain non-group algebra object, leading to a larger noninvertible symmetry Rep(SL(2, ℤ₃)). We also discuss more general examples of decomposition in two-dimensional gauge theories with trivially-acting gauged noninvertible symmetries. 

Successful communication is thought to require members of a speech community to learn common mappings between words and their referents. But if one person’s concept of CAR is very different from another person’s, successful communication might fail despite the common mappings because different people would mean different things by the same word. Here we investigate the possibility that one source of representational alignment is language itself. We report a series of neural network simulations investigating how representational alignment changes as a function of agents having more or less similar visual experiences (overlap in “visual diet”) and how it changes with exposure to category names. We find that agents with more similar visual experiences have greater representational overlap. However, the presence of category labels not only increases representational overlap, but also greatly reduces the importance of having similar visual experiences. The results suggest that ensuring representational alignment may be one of language’s evolved functions. 

A<sc>bstract</sc> In this paper we discuss gauging noninvertible zero-form symmetries in two dimensions. We specialize to certain gaugeable cases, specifically, fusion categories of the form$$ \textrm{Rep}\left(\mathcal{H}\right) $$ $\mathrm{Rep}\left(H\right)$for$$ \mathcal{H} $$ $H$a suitable Hopf algebra (which includes the special case Rep(G) forGa finite group). We also specialize to the case that the fusion category is multiplicity-free. We discuss how to construct a modular-invariant partition function from a choice of Frobenius algebra structure on$$ {\mathcal{H}}^{\ast } $$ $H^{\ast }$. We discuss how ordinaryGorbifolds for finite groupsGare a special case of the construction, corresponding to the fusion category Vec(G) = Rep(ℂ[G]^*). For the cases Rep(S₃), Rep(D₄), and Rep(Q₈), we construct the crossing kernels for general intertwiner maps. We explicitly compute partition functions in the examples of Rep(S₃), Rep(D₄), Rep(Q₈), and$$ \textrm{Rep}\left({\mathcal{H}}_8\right) $$ $\mathrm{Rep}\left(H_8\right)$, and discuss applications inc= 1 CFTs. We also discuss decomposition in the special case that the entire noninvertible symmetry group acts trivially. 

Traditional systems for indoor pressure sensing and human activity recognition (HAR) rely on costly, high-resolution mats and computationally intensive neural network-based (NN-based) models that are prone to noise. In contrast, we design a cost-effective and noise-resilient pressure mat system for HAR, leveraging Velostat for intelligent pressure sensing and a novel hyperdimensional computing (HDC) classifier that is lightweight and highly noise resilient. To measure the performance of our system, we collected two datasets, capturing the static and continuous nature of human movements. Our HDC-based classification algorithm shows an accuracy of 93.19%, improving the accuracy by 9.47% over state-of-the-art CNNs, along with an 85% reduction in energy consumption. We propose a new HDC noise-resilient algorithm and analyze the performance of our proposed method in the presence of three different kinds of noise, including memory and communication, input, and sensor noise. Our system is more resilient across all three noise types. Specifically, in the presence of Gaussian noise, we achieve an accuracy of 92.15% (97.51% for static data), representing a 13.19% (8.77%) improvement compared to state-of-the-art CNNs. 

How young people navigate multiple roles and identities while rehearsing to teach younger students to program robot Finches