Fundamental theories and models of many-body physics can be probed in experiments on ultracold atoms held in place by electromagnetic fields. In particular, of considerable interest are systems under curved confinement, since they can yield exotic states of matter which would be impossible to obtain in flat space. In this study we focus on relatively small samples, where curvature effects are stronger, and analyze by Monte Carlo simulations the peculiar structure arising in an assembly of soft-core bosons subject to a weak trapping potential with spherical symmetry. Upon suitable tuning of the parameters, a hundred particles or so group together in clusters arranged in a shell with icosahedral symmetry. As the number of particles increases, a second shell gradually develops, concentric to (and partly overlapping with) the original one, where clusters are in perfect registry with the first shell, thus forming a dodecahedral pattern. Cluster arrangements with the symmetry of other polyhedra are seen for different sets of parameters. At low temperature the superfluid density is non-uniform in the radial direction; heating the system progressively, superfluidity eventually vanishes while still clusters are present, a behavior resembling the transition from supersolid to normal solid on a plane. Two shells of clusters are also observed in systems of classical or distinguishable quantum particles, but in those cases the shells are more fragile to thermal fluctuations. All these behaviors can in principle be tested in systems of Rydberg-dressed atoms loaded into a bubble trap.

For compact sets in Euclidean space, Riesz energies whose exponents differ by $1$ are shown to arise as the endpoint cases of a one-parameter family of infinite-strip energies as the strip thickness increases from $0$ to $\infty$, under Neumann boundary conditions. An approach is suggested to a capacity conjecture of Pólya and Szegő.

We present HDLFORGE, a two-stage multi-agent framework for automated Verilog generation that optimizes the trade-off between generation speed and accuracy. The system uses a compact coder with a medium-sized LLM by default (Stage A) and escalates to a stronger coder with an ultra-large LLM (Stage B) only when needed, guided by a calibrated score from inexpensive diagnostics including compilation, lint, and smoke tests. A key innovation is a counterexample-guided formal agent that converts bounded-model-checking traces into reusable micro-tests, significantly reducing bug detection time and repair iterations. The portable escalation controller can wrap existing Verilog LLM pipelines without modifying their internals. Evaluated on VerilogEval Human, VerilogEval V2, and RTLLM benchmarks, HDLFORGE demonstrates improved accuracy-latency trade-offs compared to single-stage systems through comprehensive analysis of wall-clock time distributions, escalation thresholds, and agent ablations. On VerilogEval Human and VerilogEval V2, HDLFORGE-Qwen achieves 91.2% and 91.8% Pass@1 with roughly 50% lower median latency, dramatically improving accuracy over other medium-sized models, and 97.2% Pass@5 on RTLLM.

Fix $k \in \mathbb{N}$ and $0 < δ< 1$. We study how large $N$ must be so that every $δ$-dense subset $\mathcal{D} \subset \{0,1\}^N$ (meaning $|\mathcal{D}| \geq δ2^N$) contains the image of a metric embedding $f: \{0,1\}^k \to \mathcal{D}$. We study three variants. For a $(1+\varepsilon)$-bi-Lipschitz map $f$ with fixed $\varepsilon > 0$, we show $N = O(\varepsilon^{-2} \log(1/δ) k^3)$. For an isometric map with arbitrary rescaling (undistorted), we show $N = \log(1/δ) e^{Ω(k)}$ and conjecture $N = \log(1/δ) e^{O(k)}$. For an isometric map with bounded rescaling we show $N = \exp[\log(1/δ) e^{Θ(k)}]$. As a geometric application, we obtain a nonpositive Alexandrov curvature counterpart to the work of Bartal-Linial-Mendel-Naor on the nonlinear Dvoretzky problem. It is known that any subset of $\{0,1\}^N$ embedding with bi-Lipschitz distortion $< α$ into a metric space of nonnegative Alexandrov curvature must satisfy $|\mathcal{D}| \lesssim 2^{N(1-Ω(α^{-2}))}$. Work of Gromov and Kondo shows that this approach does not extend to CAT(0) targets. We prove that for every $N \gtrsim α^6 \geq 1$, any $\mathcal{D} \subset \{0,1\}^N$ embedding with distortion $< α$ into a CAT(0) space must satisfy $|\mathcal{D}| \lesssim 2^{N(1-Ω(α^{-4}))}$, via a completely different approach. Similar results hold for targets of nontrivial Enflo type. Finally, we prove the density analogue of a coloring theorem of Rodl-Sales: we give bounds for $(1+\varepsilon)$-bi-Lipschitz embeddings of the path $\{1,\ldots,k\}$ into dense subsets of $\{1,\ldots,N\}$ (improving a bound of Dumitrescu), and prove similar bounds for binary tree metrics.

Decision Support Systems (DSS) play a crucial role in enabling non-expert designers to explore complex, performance-driven design spaces. This paper presents a gamified decision-making framework that integrates game engines with real-time performance feedback. Performance criteria include structural behavior, environmental parameters, fabrication, material, and cost considerations. The developed design framework was tested with architecture students and non-expert designers on the design of an exoskeleton facade to retrofit an existing building. Participants (N=24) were able to iteratively modify façade geometries while receiving real-time feedback across the three key criteria: 1) structural behavior, including deflection, mass, and stress/strength ratio; 2) environmental parameters, such as solar gain and heating/cooling energy demands; and 3) fabrication considerations, including fabrication and material costs, robotic machining, and material setup. The evaluation of participant interactions reveals that gamified feedback mechanisms significantly enhance user comprehension and informed decision-making across the criteria. Further, participants' understanding of structural, material, and fabrication performance in relation to the iterative design task suggests that curated design spaces and structured guidance improve efficiency compared to open-ended generative tools. This research contributes to pre-occupancy evaluations, demonstrating how gamified environments enable stakeholder participation in the design process through informed decisionmaking and customized negotiation of performance criteria. .

Chiral nematic liquid crystals are one-dimensional photonic band-gap materials whose reflection wavelength can be well tuned by temperature, but only limited and irreversible tuning can be achieved by electric fields. In contrast, oblique heliconical chiral nematic materials blueshift with <1kV/mm fields applied along the helix axis, whereas chiral ferroelectric nematic liquid crystals can be redshifted by <0.1kV/mm fields applied perpendicular to the helix axis. Here we demonstrate that in ferroelectric nematic liquid crystals, the reflection color can be reversibly tuned also by electric fields applied along the helix axis. In sandwich cells assembled with bare conducting indium tin oxide (ITO) substrates, the reflectivity peak wavelength increases by up to 200 nm under fields up to 0.4 kV/mm. When the ITO substrates are treated with an electrically insulating polymer layer, the reflectivity shift is suppressed. We propose a theoretical model assuming helical deformation of the helix axis under electric field. This model accounts for all observations and also yields an estimate of the splay elastic constant which is challenging to determine by other methods. Our findings expand understanding of ferroelectric nematic liquid crystals and suggest potential applications in both tunable reflectors and energy-efficient smart windows.

Liouville quantum gravity (LQG) is, heuristically, a theory of random Riemannian geometry with Riemannian metric tensor $e^{γh} (\mathrm{d} x^2 + \mathrm{d} y^2)$, where $h$ is a variant of the Gaussian free field and $γ> 0$ is a parameter. If $U \subset \mathbb{C}$ is an open set, $ϕ\colon U \to ϕ(U)$ is a conformal map, and $h^ϕ = h \circ ϕ^{-1} + Q \log|(ϕ^{-1})'|$ (where $Q = Q(γ)$ is a parameter), then the LQG surface on $U$ defined with field $h$ is equivalent to the LQG surface on $ϕ(U)$ with field $h^ϕ$. This equivalence is meant in the sense that the area measures and distance functions on these surfaces are almost surely equivalent. It is known for the area measure that, in fact, this equivalence holds almost surely for all conformal maps $ϕ$ simultaneously (Sheffield-Wang 2016). We prove the corresponding result for the distance function. This makes precise the frequently used heuristic definition that a quantum surface is a random equivalence class of domains equipped with the LQG area measure and LQG distance function.

We revisit the classical integrals introduced by Coxeter, not to recalculate their well-known exact values, but to use them as a tool to derive elliptic integral identities. By embedding Coxeter's first integral into a one-parameter family $$ I(λ)=\int_{0}^{π/2} \arccos\!\left(\frac{\cosθ}{1+λ\cosθ}\right)\,dθ, $$ and differentiating with respect to the parameter \(λ\), we show that the derivative $I'(λ)$ can be expressed as an elliptic-type integral. Integrating $I'(λ)$ between 0 and 2 yields the identity $$ \int_0^2 \int_0^{π/2} \frac{\cos^2θ} {(1+s\cosθ)\sqrt{(1+s\cosθ)^2-\cos^2θ}} \,dθ\, ds=A-B=\frac{π^2}{12}, $$ where $A$ and $B$ are the first two so-called Coxeter integrals $$ A = \int_0^{π/2} \arccos\!\left(\frac{\cosθ}{1+2\cosθ}\right) dθ, $$ and $$ B = \int_0^{π/2} \arccos\!\left(\frac{1}{1+2\cosθ}\right) dθ. $$ The derivative $I'(λ)$ can be expressed in terms of incomplete elliptic integrals of the first kind $F$ and of the third kind $Π$. This approach establishes a direct connection between classical Coxeter integrals and elliptic functions. The method highlights how well-known trigonometric integrals can serve as a bridge to explore properties and relations of elliptic integrals, offering new analytic insights beyond the original Coxeter evaluations.

In this article, we establish the Drinfeld correspondence between Poisson Lie groups and their infinitesimal counterparts, Lie bialgebras, in the infinite-dimensional setting. Specifically, we extend this correspondence to regular Lie groups modeled on convenient vector spaces, with a particular focus on those modeled on nuclear Fréchet and nuclear Silva spaces. Important examples of interest include the smooth loop group $C^{\infty}(\mathbb{S}^{1}, G)$ and the analytic loop group $C^ω(\mathbb{S}^{1}, G)$ of a 1-connected real Lie group $G$, as well as $\widetilde{\mathrm{Diff}^{\infty}(M)_0}$ and $\widetilde{\mathrm{Diff}^ω(M)_0}$ -- the universal covering groups of the identity components of the groups of smooth and real-analytic diffeomorphisms of a compact manifold $M$.

Accurate and efficient reconstruction techniques are essential in multiresolution analysis and image compression, particularly when the data are represented as cell averages. In this work, we present a non-separable progressive multivariate Weighted Essentially Non-Oscillatory (WENO) scheme specifically designed for cell-average data, with applications to digital image processing. The proposed method extends Harten's multiresolution framework through a non-linear WENO reconstruction adapted to the cell-average context, achieving high-order accuracy in smooth regions and stable, non-oscillatory behavior near discontinuities. We also establish theoretical results regarding the consistency and approximation properties of the method. Finally, several numerical experiments on piecewise smooth functions and digital images are presented to demonstrate its performance and validate its effectiveness against the linear Lagrange reconstruction of the same order of accuracy.

Regression is the workhorse of statistics, and is often faced with real data that contain outliers. When these are casewise outliers, that is, cases that are entirely wrong or belong to a different population, the issue can be remedied by existing casewise robust regression methods. It is another matter when cellwise outliers occur, that is, suspicious individual entries in the data matrix containing the regressors and the response. We propose a new regression method that is robust to both casewise and cellwise outliers, and handles missing values as well. Its construction allows for skewed distributions. We show that it obeys the first breakdown result for cellwise robust regression. It is also the first such method that is geared to making robust out-of-sample predictions. Its performance is studied by simulation, and it is illustrated on a substantial real dataset.

From the very beginning, Quantum Mechanics has been accompanied by crucial foundational questions: the possibility of visualizing physical processes, the limits of measurement epitomized by the Heisenberg uncertainty principle, the existence of a deeper underlying reality with additional degrees of freedom, the role of measurements, and the status of locality. Long regarded as philosophical speculations, these issues were progressively reformulated into precise mathematical statements and ultimately subjected to experimental verification. The trajectory proved unpredictable: questions once dismissed as metaphysical gave rise to experimental platforms, which in turn matured into devices and technologies powering quantum computation, communication, and sensing. Yet this development is not unidirectional: advances in technology also feed back into foundations, enabling tests of principles that were previously out of reach, for example, whether quantum superposition persists at larger and larger scales and whether reality, gravity included, is fundamentally quantum. In this way, the dialogue between foundational inquiry and technological progress continues to shape both our theoretical understanding and the practical realization of quantum phenomena.

This paper studies the structure and properties of a rearrangement-invariant quasi-Banach space $QA_{φ,ψ}$ which generalizes the classical space $QA$ introduced by Arias-de-Reyna in connection with the study of the pointwise almost everywhere convergence of Fourier series. We present basic properties of $QA_{φ,ψ}$ and explore the relationship between $QA_{φ,ψ}$ and other rearrangement-invariant Banach spaces.

Strategic interaction in congested systems is commonly modelled using Stackelberg games, where competing leaders anticipate the behaviour of self-interested followers. A key limitation of existing models is that they typically ignore agents who do not directly participate in market competition, yet both contribute to and adapt to congestion. Although such non-follower agents do not generate revenue or respond to market incentives, their behaviour reshapes congestion patterns, which in turn affects the decisions of leaders and followers through shared resources. We argue that overlooking non-followers leads to systematically distorted equilibrium predictions in congestion-coupled markets. To address this, we introduce a three-level Stackelberg framework with heterogeneous leaders differing in decision horizons and feasible actions, strategic followers, and non-follower agents that captures bidirectional coupling between infrastructure decisions, competition, and equilibrium congestion. We instantiate the framework in the context of electric vehicle (EV) charging infrastructure, where charging providers compete with rivals, while EV and non-EV traffic jointly shape congestion. The model illustrates how explicitly accounting for non-followers and heterogeneous competitors qualitatively alters strategic incentives and equilibrium outcomes. Beyond EV charging, the framework applies to a broad class of congestion-coupled multi-agent systems in mobility, energy, and computing markets.

Completeness for a (topological) space is often based on the existence of special structures (such as metrics, uniformities, proximities, convergences, etc) that explicitly induce the topology, making the completeness induction-dependent. However, in any given space $X=(X,τ)$, suppose we fix a base $\mathcal{B}$ of $τ$ that is \emph{graded}, in the sense it is partitioned as $\mathcal{B}=\bigcup_{\varepsilon\in \mathcal{E}}\mathcal{B}_\varepsilon$ into open covers $\mathcal{B}_\varepsilon$ of $X$, making $X=(X,τ,\mathcal{B})$ a \emph{(graded) base space}. If we now relax the notion of \emph{convergence of nets} to a notion of \emph{approach between nets} in $X$, then we obtain a more natural \emph{induction-free} notion of a \emph{cauchy net} in a base space, hence a corresponding \emph{induction-free} notion of \emph{completeness} for base spaces. We find that many classical concepts and results on completeness for uniform spaces carry over to completeness for a certain class of base spaces (named \emph{locally symmetric base spaces} or \emph{$lsb$-spaces}) that properly contains uniform spaces. The said classical results include characterization of compactness, Baire's theorem, existence of a completion, and completeness results for product and function $lsb$-spaces.

The rapid growth of the Internet of Things (IoT) devices in the sixth-generation (6G) wireless networks raises significant generality and scalability challenges due to energy consumption, deployment complexity, and environmental impact. Ambient IoT (A-IoT), leveraging ambient energy harvesting (EH) for batteryless device operation, has emerged as a promising solution to address these challenges.Among various EH and communication techniques, visible light communication (VLC) integrated with ambient backscatter communication (AmBC) offers remarkable advantages, including energy neutrality, high reliability, and enhanced security. In this paper, we propose a joint VLC-AmBC architecture, emphasizing fundamental concepts, system designs, and practical implementations. We explore potential applications in environmental monitoring, healthcare, smart logistics, and secure communications. We present proof-of-concept demonstrations for three distinct types of ambient backscatter devices (AmBDs): EH-Only, VLC-Relay, and VLC-Control. Experimental results demonstrate the feasibility of implementing joint VLC-AmBC systems, highlighting their practical viability across various deployment scenarios. Finally, we outline future research directions, including integrated sensing and communication, as well as optimized energy-efficient deployment. Open issues, such as large-scale deployment challenges, are also discussed, thereby providing a clear roadmap for future developments in joint VLC-AmBC-enabled A-IoT ecosystems.

Techniques from topological data analysis (TDA) have proven effective in studying time-dependent data arising in dynamic systems, such as animal swarming behavior and spatiotemporal patterns in neuroscience. While early algorithms leveraged efficient updates to persistence diagrams for dynamic data, they struggled to distinguish behaviors that are isometric at each fixed time but differ qualitatively. This limitation was addressed by Kim and Mémoli, who introduced a spatiotemporal persistence framework for dynamic metric spaces, resulting in multiparameter persistence modules. However, these modules pose computational challenges. To address this, we build on insights from Gómez and Mémoli, who observed that the homology of Rips complexes over size $(2k+2)$ point subsets of a metric space--termed principal curvature sets--is both tractable and informative. We extend this idea to dynamic settings by introducing dynamic curvature-set persistent homology, applying the spatiotemporal framework of Kim and Mémoli to curvature sets. We prove that the resulting multiparameter persistence modules are interval-decomposable: in fact, they possess a stronger property we term antichain-decomposable. Utilizing this property, we present a new algorithm to efficiently compute the erosion distance $d_E$ (due to Patel) between arbitrary antichain-decomposable modules (including, but not limited to modules produced by our construction). Additionally, our construction is stable with respect to a generalized Gromov-Hausdorff distance between time-dependent datasets proposed by Kim and Mémoli. This enables a robust computational pipeline for distinguishing dynamic data, as demonstrated in experiments with the Boids model, where we successfully detect parameter changes.

2D materials and their monolayers have attracted widespread interest by virtue of their unique electronic and optical properties. In addition to their remarkable physical characteristics, their atomically thin nature enables their integration in ultra-compact photonic and electronic devices, with potential for dynamic tunability via strain, charge carrier modulation or heterostructure engineering. While early research relied on micrometer-scale mechanically exfoliated flakes, recent advances, particularly gold-assisted exfoliation of transition metal dichalcogenides (TMDCs), have enabled the preparation of high-quality, large-area monolayers, opening new opportunities for scalable device integration. For the field of nanophotonics in particular, the ability to transfer large-area 2D materials onto both flat and patterned substrates is essential for the development of functional devices. However, existing transfer techniques are often limited in scalability, and compatibility with structured surfaces. Here, we present a versatile and reliable transfer method of large-area monolayers and hBN/monolayer heterostructures onto both flat and nanostructured substrates. Our approach, based on the physical properties of low-density polyethylene, preserves the intrinsic optical quality of the materials and is compatible with a variety of device architectures. We demonstrate its applicability by fabricating devices that modulate the photoluminescence of TMDC monolayers through the manipulation of the photonic environment, strain or electrical gating. We further demonstrate the fabrication of van der Waals heterostructures using the same method. By enabling clean transfer of a wide range of monolayers and heterostructures, this technique offers a practical pathway for the development of next-generation optoelectronic platforms with improved functionality, scalability, and tunability.

Neurons encode information about the environment through their activity. As animals explore the environment, neurons rapidly acquire selectivity for distinct features of the external world; characterizing how these selectivity patterns emerge, reorganize, and overlap is key to linking neural activity to behavior and cognition. Calcium imaging in freely behaving animals can record large neuronal populations, but quantifying neuron-behavior selectivity directly from continuous fluorescence is challenging because both signals are temporally autocorrelated and calcium kinetics introduce time lags. Here we present INTENSE (INformation-Theoretic Evaluation of Neuronal SElectivity), an open-source framework that uses mutual information to detect neuron-behavior associations from raw calcium fluorescence data. INTENSE controls false discoveries using circular-shift permutation testing that preserves temporal structure and optimizes temporal delays to account for indicator kinetics and prospective/retrospective encoding. To separate genuine mixed selectivity from associations driven by behavioral covariance, INTENSE applies conditional mutual information-based disentanglement. We validated INTENSE on synthetic datasets, demonstrating robust detection across diverse signal-to-noise ratios and reliability conditions, whereas methods lacking temporal controls show poor performance. Applied to CA1 miniscope recordings in mice freely exploring an open field, INTENSE reveals robust selectivity to multiple variables (place, head direction, object interaction, locomotion) and refines mixed-selectivity estimates by distinguishing redundant from genuinely multi-variable encoding. Together, INTENSE enables high-throughput, information-theoretic selectivity mapping with principled control of temporal structure and behavioral covariance, bridging large-scale recordings to circuit-level hypotheses.

Large-scale linear programs (LPs) arise in many decision systems, including ranking, allocation, and matching problems that must be solved repeatedly at massive scale. Prior work such as ECLIPSE and LinkedIn's open-source DuaLip showed that ridge-regularized dual ascent with first-order methods can scale to these settings. However, the original implementation was tightly coupled to a small number of schemas and built on a CPU-centric Scala/Spark stack, limiting extensibility and preventing effective use of modern accelerators. We present a redesigned solver architecture that decouples problem specification from the optimization engine and targets GPU execution. The system uses an operator-centric programming model in which LP formulations are expressed through composable primitives for dual objective evaluation and blockwise projection operators for decomposable constraint families. This design allows new formulations to be added locally while reusing a shared optimization loop, diagnostics, and distributed infrastructure. To realize the available parallelism, we develop GPU execution techniques tailored to sparse matching constraints, including constraint-aligned sparse layouts, batched projection kernels, and a distributed design that communicates only dual variables. Further, we improve the underlying ridge-regularized dual ascent method with Jacobi-style row normalization, primal scaling, and a continuation scheme for the regularization parameter. On extreme-scale matching workloads, the GPU implementation achieves at least a 10x wall-clock speedup over the prior distributed CPU DuaLip solver under matched stopping criteria, while maintaining convergence guarantees.

Topological magnetism, characterized by topologically protected spin textures, offers rich physics and transformative prospects for spintronics. However, its stabilization typically demands external magnetic fields, preventing straightforward implementation. Here, we report a universal field-free approach for engineering 2D topologically-trivial spin spirals into topological magnetisms. This approach leverages twisted antiferromagnetic bilayers, where locked spin spirals in the two sublayers form spatially alternating ferromagnetic and antiferromagnetic domains upon twisting. These domains frustrate the uniform antiferromagnetic interlayer exchange, spontaneously stabilizing moire topological magnetisms without external fields. Using first-principles and atomistic spin-model simulations, we validate this approach using bilayers NiCl2 and NiBr2, as representative examples. For twisted NiCl2, we predict topological spin states tunable by the twist angle, including isolated and high-order antiferromagnetic bimerons. For twisted NiBr2, strong frustration yields trivial triple-q spin spirals, which transform into moire topological magnetism with the application of vertical compressive strain. Our findings demonstrate that topologically non-trivial spin textures can be engineered from their trivial counterparts, thus providing a new paradigm for topological spintronics

The method of resurgent continuation of transseries reveals a new correspondence between the $q$-series for enumerating degeneracies of quarter-BPS states in supersymmetric black holes and $\hat{Z}$ invariants of Chern-Simons theory on a class of 3 dimensional orientation-reversed manifolds.

Understanding whether uniquely quantum features can provide concrete advantages in thermodynamic processes is a central objective of quantum thermodynamics. A key challenge is quantifying how different forms of non-classicality can be systematically harnessed to enhance thermodynamic tasks. In light of this, we prove that any form of non-classicality can serve as a thermodynamic resource. In particular, any system that possesses quantum magic, coherence, or non-classical correlations can be leveraged to extract higher amounts of work than if the system does not possess such resources. The quantum thermodynamic advantages--quantified by the ratio between work extractable from a resource state and work extractable in its absence--increase with the resource robustness. We show that for any convex quantum resource theory, any resourceful state can yield a work-extraction advantage over all free states via a cyclic quench/thermalization protocol whose Hamiltonian is engineered from an optimal robustness witness. We illustrate concrete examples in which the robustness measures increase with the system's dimension, yielding quantum thermodynamic advantages that scale with it. In contrast, we also show that preparing a resource state (e.g., one with magic, coherence, or non-classical correlations) can be significantly more thermodynamically costly than preparing any state without such a resource. Concretely, there always exists a protocol that can prepare any non-resourceful state at significantly less work than it takes to prepare a resourceful state. Overall, our results provide operational meaning to robustness measures of quantum resources in terms of their thermodynamic costs and advantages.

In this paper, we prove two-sided heat kernel estimates on what we call "book-like" graphs. These are graphs consisting of pieces that satisfy the parabolic Harnack inequality that are glued together in a sufficiently nice way over a possibly infinite set of vertices. The prototypical example is gluing a copy of the square four-dimensional lattice $\mathbb{Z}^4,$ a copy of $\mathbb{Z}^5$, and a copy of $\mathbb{Z}^6$ by identifying their $x_1$-axes and taking the lazy simple random walk on this glued graph. Our results are flexible enough to handle perturbations of this example, for instance by adding diagonals to one of the lattices or a few extra vertices/edges.

This study applies Computational Grounded Theory (CGT) to analyze student misconceptions using interaction data from an AI-powered chatbot deployed in a university-level Modern Physics course. The chatbot - the UTA Study Buddy Bot - engaged students in peer-like problem-solving conversations throughout the semester, generating a rich dataset of over 10 million tokens. To explore patterns in student reasoning and identify recurring conceptual difficulties, we implemented a CGT pipeline that combined natural language processing, unsupervised clustering of sentence-level vector embeddings, human interpretation of emergent themes, and supervised learning to evaluate the generalizability of identified categories. Preliminary results revealed persistent misconceptions in areas such as relativistic momentum and quantum energy levels, along with distinctive trends in how students phrased their questions and expressed uncertainty. These findings underscore the potential of CGT as a scalable, theory-aligned approach for extracting insights from chatbot dialogues and guiding the development of more adaptive, AI-driven educational tools in physics instruction.

Anthropomorphizing conversational technology is a natural human tendency. Today, the anthropomorphic metaphor is overly reinforced across intelligent tools. Large Language Models (LLMs) are particularly anthropomorphized through interface design. While metaphors are inherently partial, anthropomorphic interfaces highlight similarities between LLMs and humans, but mask crucial differences. As a result, the metaphor is often taken literally; users treat LLMs as if they are truly human. With few safeguards in place, this extreme anthropomorphism drives users to delusion and harm. Users also experience dissonance between the ethics of using LLMs, their growing ubiquity, and limited interface alternatives. We propose repositioning anthropomorphism as a design variable, developing opposing extremes as a theoretical framework for how interface metaphors shape and can disrupt the default metaphor. We introduce a spectrum of metaphors from transparency-driven ''anti-anthropomorphism'' to uncanny ''hyper-anthropomorphism''. These metaphors introduce materiality to interface metaphors, exposing LLMs as sociotechnical systems shaped by human labor, infrastructure, and data. This spectrum shifts interface design away from optimizing usability and toward encouraging critical engagement.

We establish combinatorial characterizations of virtually torsion-free and virtually free groups using the canonical graph decomposition theory in \cite{DJKK22}. Our main results show that a finitely presented, residually finite group $Γ$ is virtually torsion-free if and only if there exists a locality parameter $r>0$ such that its $r$-local cover admits a canonical tree-decomposition with finite quotient and finite adhesion, every finite subgroup of $Γ$ fixes a vertex of this decomposition, and the finite subgroups in each bag have uniformly bounded order. Moreover, a finitely generated group $Γ$ is virtually free if and only if for some $r>0$ its $r$-global decomposition has a finite model graph with finite bags and the tree-decomposition of the $r$-local cover is $Γ$-equivariantly isomorphic to the Bass--Serre tree arising from a splitting of $Γ$ as a finite graph of finite groups.

We construct new families of solutions for General Relativity coupled to a general class of non-linear sigma models, some of which can be embedded in supergravity. The solutions include neutral, charged and magnetized black holes with bumpy horizons, bumpy stars, and anisotropic cosmologies in $d\geq 4$ dimensions, as well as black strings and black $p$-branes. We also present a family of time-dependent solutions in $2+1$-dimensions. The construction relies on a set of first-order Bogomol'nyi-Prasad-Sommerfield relations for the coset scalars, that were recently exploited for the construction of bumpy black holes on the non-linear sigma model with homogenous target $SU(2)/U(1)$ in 2601.22914 [hep-th].

Using floor vibrations to accurately predict occupants' footstep locations is essential for smart building operation and privacy-preserving indoor sensing. However, existing approaches are dominated by either physics-based models that rely on simplified wave propagation assumptions and careful calibration, or data-driven methods that require large labeled datasets and often lack robustness to subject and environmental variability. This work introduces a new approach by treating an instrumented building floor as a physical reservoir computer, whose intrinsic structural dynamics can perform nonlinear spatio-temporal computation and information extraction directly. Specifically, foot strike-induced floor vibrations recorded by a distributed accelerometer network are processed using a lightweight physical reservoir computing (PRC) pipeline consisting of short waveform extraction, root-mean-square (RMS) normalization, principal component analysis (PCA), and a weighted linear readout. Results of this study, involving 2 participants and 12 accelerometers, showed that RMS normalization and PCA projection successfully extracted occupant-invariant features from floor-vibration waveform data, enabling a single linear readout to predict foot-strike location across repeated traversals and participants. Sub-meter accuracy is achieved along the hallway direction with moderate sensing coverage, while cross-participant tests achieved meter-scale accuracy without subject-specific recalibration or retraining. These findings demonstrate that building-scale structures can function as capable physical reservoir computers for intelligent monitoring.

When multiple datasets describe complementary information about the same set of entities, for example, brain scans of an individual over time, global trade network across years, or user information across social media platforms, integrating these snapshots allows us to see a more holistic picture. A common way of identifying structure in data is through clustering, but while clustering may be applied to each dataset separately, we learn more in the multi-view setting by identifying joint clusters. We consider a clustering problem where each view conflates some of these joint clusters, only revealing partial information, and seek to recover the true joint cluster structure. We introduce this multi-view clustering model and a method for recovering it: the transposed Khatri-RAo Framework for joinT cluster recoverY (KRAFTY). The model is flexible and can accommodate a variety of data-generating processes, including latent positions in random dot product graphs and Gaussian mixtures. A key advantage of KRAFTY is that it represents joint clusters in a space with sufficient dimension so that each joint cluster occupies an orthogonal subspace in the transposed Khatri-Rao matrix, which results in a sharp drop in the scree plot at the true number of joint clusters, enabling easy model selection. Our simulations show that when the number of joint clusters exceeds the sum of the numbers of clusters in each individual view, our method outperforms existing methods in both joint clustering accuracy and estimation of the number of joint clusters.