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We describe a multidisciplinary collaboration to iteratively design an interactive exhibit for a public science center on paleoclimate, the study of past climates. We created a data physicalisation of mountains and ice sheets that can be tangibly manipulated by visitors to interact with a wind simulation visualisation that demonstrates how the climate of North America differed dramatically between now and the peak of the last ice age. We detail the system for interaction and visualisation plus design choices to appeal to an audience that ranges from children to scientists and responds to site requirements. 

We introduce a variant of stable logarithmic maps, which we call punctured logarith- mic maps. They allow an extension of logarithmic Gromov–Witten theory in which marked points have a negative order of tangency with boundary divisors. As a main application we develop a gluing formalism which reconstructs stable logarithmic maps and their virtual cycles without expansions of the target, with trop- ical geometry providing the underlying combinatorics. Punctured Gromov–Witten invariants also play a pivotal role in the intrinsic con- struction of mirror partners by the last two authors, conjecturally relating to symplec- tic cohomology, and in the logarithmic gauged linear sigma model in work of Qile Chen, Felix Janda and Yongbin Ruan. 

In-person human interaction relies on our spatial perception of each other and our surroundings. Current remote communication tools partially address each of these aspects. Video calls convey real user representations but without spatial interactions. Augmented and Virtual Reality (AR/VR) experiences are immersive and spatial but often use virtual environments and characters instead of real-life representations. Bridging these gaps, we introduce DualStream, a system for synchronous mobile AR remote communication that captures, streams, and displays spatial representations of users and their surroundings. DualStream supports transitions between user and environment representations with different levels of visuospatial fidelity, as well as the creation of persistent shared spaces using environment snapshots. We demonstrate how DualStream can enable spatial communication in real-world contexts, and support the creation of blended spaces for collaboration. A formative evaluation of DualStream revealed that users valued the ability to interact spatially and move between representations, and could see DualStream fitting into their own remote communication practices in the near future. Drawing from these findings, we discuss new opportunities for designing more widely accessible spatial communication tools, centered around the mobile phone. 

Abstract As announced in Gross and Siebert (in Algebraic geometry: Salt Lake City 2015, Proceedings of Symposia in Pure Mathematics, vol 97, no 2. AMS, Providence, pp 199–230, 2018) in 2016, we construct and prove consistency of the canonical wall structure . This construction starts with a log Calabi–Yau pair ( X ,  D ) and produces a wall structure, as defined in Gross et al. (Mem. Amer. Math. Soc. 278(1376), 1376, 1–103, 2022). Roughly put, the canonical wall structure is a data structure which encodes an algebro-geometric analogue of counts of Maslov index zero disks. These enumerative invariants are defined in terms of the punctured invariants of Abramovich et al. (Punctured Gromov–Witten invariants, 2020. arXiv:2009.07720v2 [math.AG]). There are then two main theorems of the paper. First, we prove consistency of the canonical wall structure, so that, using the setup of Gross et al. (Mem. Amer. Math. Soc. 278(1376), 1376, 1–103, 2022), the canonical wall structure gives rise to a mirror family. Second, we prove that this mirror family coincides with the intrinsic mirror constructed in Gross and Siebert (Intrinsic mirror symmetry, 2019. arXiv:1909.07649v2 [math.AG]). While the setup of this paper is narrower than that of Gross and Siebert (Intrinsic mirror symmetry, 2019. arXiv:1909.07649v2 [math.AG]), it gives a more detailed description of the mirror. 

E-textiles, which embed circuitry into textile fabrics, blend art and creative expression with engineering, making it a popular choice for STEAM classrooms [6, 12]. Currently, e-textile development relies on tools intended for traditional embedded systems, which utilize printed circuit boards and insulated wires. These tools do not translate well to e-textiles, which utilize fabric and uninsulated conductive thread. This mismatch of tools and materials can lead to an overly complicated development process for novices. In particular, rapid prototyping tools for traditional embedded systems are poorly matched for e-textile prototyping. This paper presents the ThreadBoard, a tool that supports rapid prototyping of e-textile circuits. With rapid prototyping, students can test circuit designs and identify circuitry errors prior to their sewn project. We present the design process used to iteratively create the ThreadBoard’s layout, with the goal of improving its usability for e-textile creators. 

We prove a decomposition formula of logarithmic Gromov–Witten invariants in a degeneration setting. A one-parameter log smooth family $$X \longrightarrow B$$ with singular fibre over $$b_0\in B$$ yields a family $$\mathscr {M}(X/B,\beta ) \longrightarrow B$$ of moduli stacks of stable logarithmic maps. We give a virtual decomposition of the fibre of this family over $$b_0$$ in terms of rigid tropical maps to the tropicalization of $X/B$ . This generalizes one aspect of known results in the case that the fibre $$X_{b_0}$$ is a normal crossings union of two divisors. We exhibit our formulas in explicit examples. 

Creative iterative development over the past several years has generated an extensive set of computational tools, learning resources, and materials in the realm of paper mechatronics - an educational craft and design approach that weaves computational and mechanical elements into established traditions of children's construction with paper. Here, we both reflect upon our past and recent work of paper mechatronics, then look to the near- to medium-term future to speculate upon both the emerging trends in technology design and expanding learning potential of this medium for children along material, spatial, and temporal dimensions. We summarize lessons learned through various children's workshops with our materials; and we use these lessons as a foundation upon which to create a wide variety of novel tools and activities in educational papercrafting. We speculate upon the frontiers of this work based on current convergences and shifts in tangible creative computational media. 

We present FoldMecha, a computer-aided design (CAD) system for exploratory construction of mechanical papercraft. FoldMecha enables students to (a) design their own movements with simple mechanisms by modifying parameters and (b) build physical prototypes. This paper describes the system, as well as associated prototyping methods that make the construction process easier and more adaptable to widely different creations. The paper also discusses a week-long workshop that we held with six teenagers using FoldMecha. The teens successfully designed and built their own mechanisms, and adapted them to a variety of creations. Throughout the workshop, they progressively achieved an advanced level of skill and understanding about mechanical movements.