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For $G$ a finite group and $T$ a $G$-Tambara functor, we construct the frame $\mathop{RadId}_G(T)$ of radical Tambara ideals and show that its points are the Nakaoka primes. We show that this frame is spatial and coherent, and deduce that the Nakaoka spectrum is a spectral space, recovering a recent result of Chan and Spitz.

Reinforcement learning (RL) has the potential to transform real-world decision-making systems by enabling autonomous agents to learn from experience. Deploying RL in real-world settings, especially in the context of human-robot interaction, requires defining state representations and reward functions, which are critical for learning efficiency and policy performance. Traditional RL approaches often rely on domain expertise and trial-and-error, necessitating extensive human involvement as well as direct interaction with the environment, which can be costly and impractical, especially in complex and safety-critical applications. This work proposes a novel RL framework that leverages off-policy evaluation (OPE) for state space and reward function selection, using only logged interaction data. This approach eliminates the need for real-time access to the environment or human-in-the-loop feedback, greatly reducing the dependency on costly real-time interactions. The proposed approach systematically evaluates multiple candidate state representations and reward functions by training offline RL agents and applying OPE to estimate policy performance. The optimal state space and reward funct

Human-robot interaction (HRI) evaluation relies almost exclusively on human-completed questionnaires, leaving the robot's perspective unexamined. We propose an \textit{inverted evaluation}, in which LLM-powered robots complete the same standardized instruments from their own perspective, and test whether these ratings agree with human ground truth. In Study~1, five LLMs completed HRI-CUES, Godspeed, and RoSAS questionnaires for 25~interactions ($N = 1{,}522$ evaluations) from the HRI-CUES dataset. LLMs achieved moderate-to-strong agreement on engagement dimensions (satisfaction $r$ up to $.65$ and enjoyment $r$ up to $.72$) with excellent test-retest reliability (ICC $\geq .82$), but \textit{systematically inverted} the comfort/strangeness dimension ($r = -.44$ to $-.67$, all $p < .05$), conflating engagement with comfort. In Study~2, a Nao robot running Claude~Sonnet~4.5 replicated these patterns in live interactions ($N = 4$), including real-time turn-by-turn assessment. The strangeness failure persisted across five models, synthetic controls, and embodied deployment for two participants. We argue that current LLM-based robots lack access to the internal affective states neede

To any essentially small tensor-triangulated category $\mathcal{K}$ and Thomason subset $Y \subseteq \mathrm{Spc}(\mathcal{K})$ we associate a ringed space $(\mathrm{Spf}(\mathcal{K},Y), \mathcal{O}_{\mathrm{Spf}(\mathcal{K},Y)}),$ called the formal spectrum of $(\mathcal{K},Y)$. We establish basic properties of this construction and compute it in several examples from algebraic geometry, chromatic homotopy theory, equivariant homotopy theory, and modular representation theory.

Demanding task environments (e.g., supervising a remotely piloted aircraft) require performing tasks quickly and accurately; however, periods of low and high operator workload can decrease task performance. Intelligent modulation of the system's demands and interaction modality in response to changes in operator workload state may increase performance by avoiding undesirable workload states. This system requires real-time estimation of each workload component (i.e., cognitive, physical, visual, speech, and auditory) to adapt the correct modality. Existing workload systems estimate multiple workload components post-hoc, but few estimate speech workload, or function in real-time. An algorithm to estimate speech workload and mitigate undesirable workload states in real-time is presented. An analysis of the algorithm's accuracy is presented, along with the results demonstrating the algorithm's generalizability across individuals and human-machine teaming paradigms. Real-time speech workload estimation is a crucial element towards developing adaptive human-machine systems.

We introduce a notion of stratification for rigidly-compactly generated tensor-triangulated categories relative to the homological spectrum and develop the fundamental features of this theory. In particular, we demonstrate that it exhibits excellent descent properties. In conjunction with Balmer's Nerves of Steel conjecture, we conclude that stratification admits a general form of descent. This gives a uniform treatment of several recent stratification results and provides a complete answer to the question: When does stratification descend? As a new application, we extend earlier work on the tensor triangular geometry of equivariant module spectra from finite groups to compact Lie groups.

We present the development of a new astrochemical research tool HILTRAC, the Highly Instrumented Low Temperature ReAction Chamber. The instrument is based on a pulsed form of the CRESU (Cinétique de Réaction en Écoulement Supersonique Uniforme, meaning reaction kinetics in a uniform supersonic flow) apparatus, with the aim of collecting kinetics and spectroscopic information on gas phase chemical reactions important in interstellar space or planetary atmospheres. We discuss the apparatus design and its flexibility, the implementation of pulsed laser photolysis followed by laser induced fluorescence (PLP-LIF), and the first implementation of direct infrared frequency comb spectroscopy (DFCS) coupled to the uniform supersonic flow. Achievable flow temperatures range from 32(3) - 111(9) K, characterising a total of five Laval nozzles for use with N2 and Ar buffer gases by pressure impact measurements. These results were further validated using LIF and DFCS measurements of the CH radical and OCS, respectively. Spectroscopic constants and linelists for OCS are reported for the 1001 band near $2890 - 2940 cm^{-1}$ for both $OC^{32}S$ and $OC^{34}S$, measured using DFCS. Additional peaks

We prove a thick subcategory theorem for the category of $d$-excisive functors from finite spectra to spectra. This generalizes the Hopkins-Smith thick subcategory theorem (the $d=1$ case) and the $C_2$-equivariant thick subcategory theorem (the $d=2$ case). We obtain our classification theorem by completely computing the Balmer spectrum of compact $d$-excisive functors. A key ingredient is a non-abelian blueshift theorem for the generalized Tate construction associated to the family of non-transitive subgroups of products of symmetric groups. Also important are the techniques of tensor triangular geometry and striking analogies between functor calculus and equivariant homotopy theory. In particular, we introduce a functor calculus analogue of the Burnside ring and describe its Zariski spectrum à la Dress. The analogy with equivariant homotopy theory is strengthened further through two applications: We explain the effect of changing coefficients from spectra to ${\mathrm{H}\mathbb{Z}}$-modules and we establish a functor calculus analogue of transchromatic Smith-Floyd theory as developed by Kuhn-Lloyd. Our work offers a new perspective on functor calculus which builds upon the previ

We prove a version of Quillen's stratification theorem in equivariant homotopy theory for a finite group $G$, generalizing the classical theorem in two directions. Firstly, we work with arbitrary commutative equivariant ring spectra as coefficients, and secondly, we categorify it to a result about equivariant modules. Our general stratification theorem is formulated in the language of equivariant tensor-triangular geometry, which we show to be tightly controlled by the non-equivariant tensor-triangular geometry of the geometric fixed points. We then apply our methods to the case of Borel-equivariant Lubin--Tate $E$-theory $\underline{E_n}$, for any finite height $n$ and any finite group $G$, where we obtain a sharper theorem in the form of cohomological stratification. In particular, this provides a computation of the Balmer spectrum as well as a cohomological parametrization of all localizing $\otimes$-ideals of the category of equivariant modules over $\underline{E_n}$, thereby establishing a finite height analogue of the work of Benson, Iyengar, and Krause in modular representation theory.

We investigate to what extent we can descend the classification of localizing, smashing and thick ideals in a presentably symmetric monoidal stable $\infty$-category $\mathscr{C}$ along a descendable commutative algebra $A$. We establish equalizer diagrams relating the lattices of localizing and smashing ideals of $\mathscr{C}$ to those of $\mathrm{Mod}_{A}(\mathscr{C})$ and $\mathrm{Mod}_{A\otimes A}(\mathscr{C})$. If $A$ is compact, we obtain a similar equalizer for the lattices of thick ideals which, via Stone duality, yields a coequalizer diagram of Balmer spectra in the category of spectral spaces. We then give conditions under which the telescope conjecture and stratification descend from $\mathrm{Mod}_{A}(\mathscr{C})$ to $\mathscr{C}$. The utility of these results is demonstrated in the case of faithful Galois extensions in tensor triangular geometry.

We prove that a jointly conservative family of geometric functors between rigidly-compactly generated tensor triangulated categories induces a surjective map on Balmer spectra. From this we deduce a fiberwise criterion for Balmer's comparison map to be a continuous bijection. This gives short alternative proofs of the Hopkins--Neeman theorem and its generalization, due to Lau, to the case of a finite group acting trivially on an affine scheme.

Fluent human-robot collaboration requires a robot teammate to understand, learn, and adapt to the human's psycho-physiological state. Such collaborations require a computing system that monitors human physiological signals during human-robot collaboration (HRC) to quantitatively estimate a human's level of comfort, which we have termed in this research as comfortability index (CI) and uncomfortability index (unCI). Subjective metrics (surprise, anxiety, boredom, calmness, and comfortability) and physiological signals were collected during a human-robot collaboration experiment that varied robot behavior. The emotion circumplex model is adapted to calculate the CI from the participant's quantitative data as well as physiological data. To estimate CI/unCI from physiological signals, time features were extracted from electrocardiogram (ECG), galvanic skin response (GSR), and pupillometry signals. In this research, we successfully adapt the circumplex model to find the location (axis) of 'comfortability' and 'uncomfortability' on the circumplex model, and its location match with the closest emotions on the circumplex model. Finally, the study showed that the proposed approach can estim