Adults with intellectual disabilities (ID) face systemic social exclusion that narrows autonomy and life opportunities. While social virtual reality (VR) offers a powerful medium for identity expression and community belonging, research often adopts a remedial paradigm, focusing on training functional skills in scripted environments. This paper challenges this deficit-based model by treating social VR as an open world for participation. Following 11 adults with ID across multi-session engagements with VRChat, we employed an adaptive, relational method to scaffold participant leadership. Findings reveal that participants used the platform for interest-driven discovery, sustained through interdependent care webs. Crucially, the study demonstrates how social VR supports transferable confidence and emerging digital citizenship, enabling some users to transition from novices to community leaders. We contribute six Disability Justice-aligned design principles articulating world-making paradigm that reorients Human-Computer Interaction toward supporting personhood and self-determination in mainstream digital publics.

We study quantum advantage in the 1-step graph domination game on cycle graphs numerically, analytically and through the use of Noisy intermediate scale quantum (NISQ) processors. We find explicit strategies that realise the recently found upper bounds for small graphs and generalise them to larger cycles. We demonstrate that NISQ computers realise the predicted quantum advantages with high accuracy.

The key information of a model category structure on a poset is encoded in a transfer system, which is a combinatorial gadget, originally introduced to investigate homotopy coherence structures in equivariant homotopy theory. We describe how a transfer system associated with in a model structure on a lattice is affected by left and right Bousfield localization and provide a minimal generating system of morphisms which are responsible for the change in model structure. This leads to new concrete insights into the behavior of model categories on posets in general.

Transfer systems on finite posets have recently been gaining traction as a key ingredient in equivariant homotopy theory. Additionally, they also naturally occur in the data of a model structure. We give a complete characterization of all model category structures on a finite lattice, using transfer systems as our main tool, resulting in new connections between abstract homotopy theory and equivariant methods.

Light curves of young stars exhibit photometric variability over hours to decades and across a wide range of amplitudes. On time scales beyond a few rotation periods, these light curves are typically stochastic. The variability arises from a combination of accretion rate changes, line-of-sight extinction variations, and evolving spotted stellar surfaces. We aim to develop a methodology to quantitatively compare the full variability statistics of these inhomogeneously sampled light curves with model calculations. To achieve this, we converted the light curves into variability fingerprints. They map the probability of variation by a given amount over a given timescale. Applying principal component analysis to these fingerprints produces a stable distribution of the first two principal components. We show that this distribution is a continuum without clusters. Adding a model-generated fingerprint to an observational sample does not significantly alter the distribution of the sample, allowing a robust comparison between the model and observed light curves to assess statistical realism. We show that photometric uncertainties, timing, and observing cadence have a minimal impact on model placement within the observational distribution. The main source of variance among highly variable light curves of young stars is the timescale of the onset of significant variability (above 0.3mag), with 1-3month timescales being the most critical. The secondary cause of variance are long-term (above 1.5yr) dimming or rising trends.

We study the rigidity of maps between bounded symmetric domains that preserve the Carathéodory/Kobayashi distance. We show that such maps are only possible when the rank of the co-domain is at least as great as that of the domain. When the ranks are equal, and the domain is irreducible, we prove that the map is either holomorphic or antiholomorphic. In the holomorphic case, we show that the map is in fact a triple homomorphism, under the additional assumption that the origin is mapped to the origin. We exploit the large-scale geometry of the Carathéodory distance and use the horocompactification and Gromov product to obtain these results without requiring any smoothness assumptions on the maps.

The increasing demand for high-purity postconsumer plastics for recycling highlights the importance of efficient material identification. Near-Infrared (NIR) spectroscopy is widely used to capture unique spectral fingerprints of materials for identification purposes. However, developing efficient and lightweight machine learning models with NIR spectral data for accurate and real-time classification of plastic materials is still in high demand. This paper presents a new hybrid approach combining the k-nearest neighbours (KNN) model with the filter-based correlation feature selection (CFS) technique for plastic identification. Experiments were conducted to test six key recyclable plastic polymers consisting of Polyethylene Terephthalate (PET), High-Density Polyethylene (HDPE), Low-Density Polyethylene (LDPE), Polyvinyl Chloride (PVC), Polypropylene (PP), and Polystyrene (PS). Feature selection techniques - CFS and principal component analysis (PCA) are applied to extract the essential discriminative features of each type of plastic. With the extracted features, KNN and support vector machine (SVM) models are developed respectively for plastic identification. Experimental results demonstrate that the CFS-KNN model achieves a success rate of 100% with a computational time of 40ms under laboratory conditions, outperforming the PCA-SVM, PCA-KNN and CFS-SVM models in terms of accuracy and computational efficiency.

The plethysm product of Schur functions corresponds to composing polynomial representations of infinite general linear groups. Finding the plethysm coefficients $\langle s_\nu \circ s_\mu, s_\lambda\rangle$ that express an arbitrary plethysm $s_\nu \circ s_\mu$ as a sum $\sum_\lambda \langle s_\nu \circ s_\mu, s_\lambda \rangle s_\lambda$ of Schur functions is a fundamental open problem in algebraic combinatorics. We prove two stability theorems for plethysm coefficients under the operations of adding and/or joining an arbitrary partition to either $\mu$ or $\nu$. In both theorems $\mu$ may be replaced with an arbitrary skew partition. As special cases we obtain all stability results on the plethysm product of two Schur functions in the literature to date. The proofs are entirely combinatorial using plethystic semistandard tableaux with positive and negative entries.

We analyse the dimension spectrum of continued fractions expansions with coefficients restricted to infinite subsets of $ \mathbb{N}$. We prove that the set of powers $P_q=\{q^n\colon n\in \mathbb{N}\}$ has full dimension spectrum for each integer $q\geq 2$, answering a question by Chousionis, Leykekhman and Urbański. On the other hand, we show that the dimension spectrum for $P^*_q=\{q^n\colon n\in \mathbb{N}\}\cup\{1\}$ has many gaps and regions where it is nowhere dense. We also investigate the case where $A$ is generated by a monomial, $M_q=\{n^q\colon n\in\mathbb{N}\}$. For $M_q$ we prove that the dimension spectrum is full for $q\in\{1,2,3,4,5\}$, and it has a gap for each $q\geq 6$. Furthermore we show for $q\in\{6,7,8\}$ that the dimension spectrum of $M_q$ is the disjoint union of two nontrivial closed intervals, and it is the disjoint union of three nontrivial closed intervals for $q \in\{9,10\}$. For $q\geq 11$ we show that the dimension spectrum of $M_q$ consists of finitely many disjoint nontrivial closed intervals. The results concerning $M_q$ extend existing results for $q=1$ and $q=2$. In our analysis we employ Perron-Frobenius (transfer) operators, and numerical tools developed by Falk and Nussbaum that give rigorous estimates for the Hausdorff dimension for continued fractions expansions.

The famous Koecher-Vinberg theorem characterises the finite dimensional formally real Jordan algebras among the finite dimensional order unit spaces as the ones that have a symmetric cone. An alternative characterisation of symmetric cones was obtained by Walsh who showed that the symmetric cones correspond exactly to the finite dimensional order unit spaces for which there exists a gauge-reversing map from the interior of the cone to itself. In this paper we prove an infinite dimensional version of this characterisation of symmetric cones.