We develop a framework for comparing probability measures on finite posets via hockey-stick domination, an order relation defined through interval-counting test functions. The theory introduces poset integrals, derivatives, power functions and the associated moment functionals, all of which are invariant under poset isomorphisms. We prove that hockey-stick domination admits an exact quantitative characterization: whenever $μ$ is dominated by $ν$ in the hockey-stick order, the corresponding Zolotarev-type distance is equal to one half of the second-order poset moment of $ν-μ$. We further develop a constructive theory for generating such domination relations. In particular, we show that hockey-stick domination is preserved under direct products, disjoint unions, ordinal sums, and suitable ideal restrictions, yielding natural families of examples on chains, Boolean posets, rectangular lattices, rooted trees, and Young diagrams.

We propose a novel, intuitive measure of statistical performance: precision-weighted bias. Precision-weighted bias is defined as the unconditional bias of an estimator weighted by the degree of information (precision) it contains. Current guidelines, such as GRADE and CONSORT, often view the potential for increased bias in adaptive designs as a deterrent for the inclusion of such designs in systematic reviews. However, we demonstrate that the bias in a common-effect meta-analysis is approximately equal to the precision-weighted average of the precision-weighted biases of its constituent studies, rather than of their unweighted unconditional biases. Through simulation studies, we show that while adaptive designs may exhibit unweighted bias, they frequently have zero precision-weighted bias. Consequently, including these designs often results in a negligible change to the overall meta-analysis bias. These results suggest that precision-weighted bias is a superior indicator for determining whether to include an adaptive design in a meta-analysis. We recommend that precision-weighted bias be used as a standard complement to unweighted unconditional and conditional bias in simulation studies to support more inclusive and accurate evidence synthesis.

Let ${\mathcal C} ^{\rm rt}$ be the class of rooted trees and $\langle {\mathcal C} ^{\rm rt}\rangle _{\dot{\cup }Π}$ its minimal closure under isomorphism, finite direct products and finite disjoint unions. Posets from that closure are isomorphic to ${\mathbb X}= \dot{\bigcup} _{i<n}\prod _{j<m_i}{\mathbb X}_i^j$, where ${\mathbb X}_i^j$ are rooted trees. Defining ${\mathcal T}=\mathop{\rm Th} ({\mathbb X})$, ${\mathcal T} _i ^j=\mathop{\rm Th}({\mathbb X}_i^j)$, for $i<n$ and $j<m_i$, and $κ= \prod _{i<n}\prod _{j<m_i}I({\mathcal T} _i^j)$, we have (a) Vaught's conjecture is true for ${\mathcal T}$: $I({\mathcal T})=κ$, if $κ\in \{ 1,ω,{\mathfrak{c}}\}$, and, otherwise, $I({\mathcal T}) \in [3,ω)$; (b) ${\mathbb Y} \equiv {\mathbb X}$ iff $\;{\mathbb Y} \cong \dot{\bigcup}_{i<n}\prod _{j<m_i}{\mathbb Y} _i^j$, where ${\mathbb Y}_i^j\equiv {\mathbb X}_i^j$, for $i<n$ and $j<m_i$; (c) ${\mathbb E}\preccurlyeq {\mathbb X}$ iff $\;{\mathbb E} =\dot{\bigcup}_{i<n}\prod _{j<m_i}{\mathbb E}_i^j$, where ${\mathbb E}_i^j\preccurlyeq {\mathbb X}_i^j$, for $i<n$ and $j<m_i$; (d) ${\mathcal T}$ is atomic iff $\;{\mathcal T} _i^j$, for $i<n$ and $j<m_i$, are atomic; then $\dot{\bigcup}_{i<n}\prod _{j<m_i}{\mathbb A}_i^j$ is a countable atomic model of ${\mathcal T}$, where ${\mathbb A}_i^j$ is a countable atomic model of ${\mathcal T} _i^j$, for $i<n$ and $j<m_i$; (e) ${\mathcal T}$ is small iff $\;{\mathcal T} _i^j$, for $i<n$ and $j<m_i$, are small; then $\dot{\bigcup}_{i<n}\prod _{j<m_i}{\mathbb S}_i^j$ is a countably saturated model of ${\mathcal T}$, where ${\mathbb S}_i^j$ is a countably saturated model of ${\mathcal T}_i^j$, for $i<n$ and $j<m_i$.

Human behaviors, particularly non-pharmaceutical interventions (NPIs), are dynamically coupled with epidemic spreading. While prior studies mainly assume a linear interplay, real-world behavioral evolution is driven by nonlinear responses and social influence. Here, we incorporate these multifaceted mechanisms into a co-evolutionary model and analytically derive the critical thresholds. Notably, as the infection rate grows, NPI compliance initially rises but then abruptly drops to zero. This paradoxical decline indicates an emergent social dilemma: at high infection rates, abandoning NPIs is individually optimal but detrimentally triggers an explosive surge in epidemic prevalence. We further show that socially induced overestimation of the infection rate can counterintuitively prompt individuals to abandon NPIs. Moreover, the interplay with social influence induces periodic oscillations, reflecting a tragic cycle of recurrent epidemic waves. Furthermore, we validate the robustness of this NPI-abandonment dilemma in networked population. Our work illustrates rich emergent phenomena in the co-evolution of epidemic and behavior, challenging traditional views on this coupled dynamics.

Fault Injection Attacks (FIAs) are a significant threat to hardware security, capable of compromising systems by inducing malicious faults in computation or storage. Evaluating resilience against such attacks is challenging due to the high cost, complexity, and limited availability of physical fault experiments, particularly during pre-silicon development. Architectural-level simulation offers a developer-oriented, white-box perspective for systematic vulnerability assessment. This paper introduces InjectV, a fault injection attack framework for RISC-V platforms built on the gem5 simulator. InjectV enables precise, guided fault injection at security-critical execution points, such as control-flow decisions, counters, and comparisons, allowing systematic exploration of attack vectors. It currently supports transient fault attacks in registers and memory, broadening its ability to simulate diverse attack scenarios. Experimental results on security benchmarks from the FISSC suite, including hardened variants of the VerifyPIN application, demonstrate InjectV's ability to effectively identify fault-injection points, achieving a 95.8% time-saving advantage over traditional fault injection approaches.

The measurement of the spin-orbit obliquity, that is, the angle between the orbital axis of a planet and the stellar spin axis, provides crucial insights into how planets form and migrate. Observations of young transiting planets, which have not yet experienced significant tidal alterations, offer a unique opportunity to study their original obliquity configuration. We observed the warm Saturn-sized TOI-837 b (member of the 35 Myr old open cluster IC 2602) in-transit using ESPRESSO at VLT, collecting high-precision radial velocities to measure the Rossiter-McLaughlin effect. We found a sky-projected obliquity of $λ= 341.1^{+2.3}_{-2.5}$ deg. Using our knowledge of the stellar rotation period ($3.00 \pm 0.02$ d), we estimated a true obliquity of $ψ= 25.9^{+7.5}_{-6.3}$ deg, which indicates prograde motion and suggests a mildly misaligned orbit. This places TOI-837 b as the first planet younger than 100 Myr with accessible $ψ$ incompatible with an aligned orbit. Together with the primordial circular orbit of TOI-837 b and the presence of a bound stellar companion, this mild misalignment favours the possibility of a primordial obliquity excitation (secular torque on the protoplanetary disc) followed by disc-driven migration, rather than high-eccentricity migration after formation.

This manuscript investigates the spectral geometry of Riemannian submersions whose fibers have a basic mean curvature. By restricting the Laplace--Beltrami operator to the space of basic functions, we reduce the spectral problem on $M$ to the spectral problem for a weighted Laplacian on the base manifold, where the weight is determined by the fiber-volume function $S$. We derive a summation formula for the reciprocal of the basic Dirichlet eigenvalues (Basel-type series). Furthermore, using the framework of Supersymmetric Quantum Mechanics (SUSYQM), we establish a supersym\-me\-tric duality relating the basic Dirichlet and Neumann spectra under the trans\-for\-ma\-tion $S \mapsto 1/S$.

Thematic maps visually communicate statistical information about spatial units such as countries or states. They must balance the individual readability of those map elements that carry the statistical information and the overall cartographic context. Nowadays, most maps are not static images, but must flexibly respond to a range of device types and display sizes. Current approaches to responsive thematic mapping are limited: they are labor-intensive for practitioners and often rely on combining disjointed visual encodings to cover different device types. In this paper we introduce the first algorithmic framework to efficiently compute responsive thematic maps that smoothly adapt to different display sizes. A key component of our framework is the layout guide: a combinatorial structure which encodes the two essential aspects of a thematic map. The first aspect are the visual requirements of each statistical map element (at least their desired width and height), the second aspect is the cartographic context in the form of relative positions of map elements. Our main algorithmic contribution is the map arranger which takes a visual container as input and returns a suitable layout guide. The map arranger does so in a stable and consistent manner: if the container changes only a little, then so does the layout guide, and the same input container always results in the same layout guide. To use our framework, one needs three ingredients: $(1)$ a reference layout, which corresponds to the ``ideal'' thematic map, $(2)$ a total vertical and horizontal order for all map elements (the desired layouts for containers with extreme aspect ratios), and $(3)$ a thematic mapping algorithm that can construct a thematic map from a layout guide. We demonstrate our framework on two types of thematic maps, namely rectangular and Demers cartograms.

A model for predicting the residual stress gradient in a thin film segment is developed on the basis of the theory of dislocation pile-ups. The initial shear stress within the film is relaxed via the formation of a pile-up of screw dislocations against the impenetrable film-substrate interface. Plastic strain is related to the dislocation density, leading to a fundamental equation, which links the residual stress to this density. The distribution of dislocations within the pile-up for an arbitrary, non-uniform residual stress profile is derived analytically by applying the force balance condition. This results in a singular integro-differential equation for the residual stress profile. The equation is solved numerically by a collocation method for various initial stress distributions: constant, linear, parabolic, and exponential functions. The solutions demonstrate that the established residual stress profile strongly depends on the film segment's thickness-to-width ratio and the initial stress distribution. As this ratio increases, stress relaxation becomes more effective away from the film-substrate interface. In all cases, equilibrium requires a pile-up containing dislocations with both positive and negative Burgers vectors. The total number of dislocations and their density distribution vary significantly with the initial stress profile. This model provides a critical step towards more complex models of residual stress formation in constrained material systems, specifically, thin films.

Semantic communications enable AI-native wireless systems by mapping raw data into compressed task-oriented latent representations. However, independently trained agents often rely on heterogeneous latent spaces and background knowledge, leading to semantic mismatch that degrades mutual understanding and downstream task execution, especially in interferencelimited multi-user wireless networks. This paper investigates distributed latent-space alignment in multi-user semantic MIMO interference networks with cognitive radio constraints. We consider primary users and semantic-aware secondary users sharing the same wireless resources, where secondary agents must simultaneously mitigate interference and align heterogeneous semantic representations. To address this problem, we formulate semantic alignment as a non-cooperative game and derive a closed-form solution for the joint optimization of linear semantic MIMO transceivers under power and interference constraints. Exploiting the structure of the problem, we recast the original matrix valued optimization into a lower-dimensional power-allocation game, leading to an iterative semantic water-filling algorithm. We establish sufficient conditions for existence, uniqueness, and global convergence to a Nash equilibrium, explicitly relating semantic alignment properties and physical-channel interactions. Numerical results assess the performance of the proposed framework, revealing key trade-offs among semantic compression, task performance, and hierarchical spectrum access.

We study spherical T-duality for iterated sphere bundles. We show that for a class of iterated sphere bundles the cohomological data contained in its Gysin sequences can be repackaged into data for a vanishing Massey product. We further show that if these bundles are endowed with an integral cohomology class of transgressive degree one, then they have a T-dual iterated sphere bundle, namely, the one associated to the same Massey product read backwards.

In this paper, we study the metalinear algebraic cobordism spectrum $\mathrm{MML}$ (also sometimes denoted $\mathrm{MSL}^c$), which is built from the structure groups of oriented vector bundles. We establish an interpolation between $\mathrm{MSL}$ and $\mathrm{MML}$ and deduce that the canonical morphism $\mathrm{MSL}\to \mathrm{MML}$ admits a retraction. We parametrize all such retractions in the category of $\mathrm{MSL}$-modules and, after fixing one of them, obtain an equivalence $\mathrm{MML}\cong\mathrm{MSL}\oplus Σ^{2,1}\mathrm{MGL}$. As an application of these results, we determine various invariants of the metalinear algebraic cobordism spectrum over a field (after inverting the exponential characteristic). More precisely, we determine the first few Milnor-Witt stems of $\mathrm{MML}$ in terms of the very effective algebraic and hermitian K-theory spectra, and the geometric diagonal of $\mathrm{MML}$ in terms of Stong's complex-spin cobordism ring. We also compute the slices and use them to describe the category of 2-inverted modules over the $\mathbb{E}_\infty$-ring spectrum $\mathrm{MML}$.

Accurate state of charge (SOC) estimation of lithium iron phosphate (LFP) batteries remains challenging because of their flat open-circuit-voltage (OCV)-SOC characteristics, temperature-dependent dynamics, and sensitivity to initialization errors. Here, we propose a physics-guided residual Kalman learning (PRKL) framework for electrochemical-model-based SOC estimation. PRKL combines a control-oriented single-particle-model-based extended Kalman filter (EKF), which provides recursive physical state propagation, with a gated recurrent unit (GRU) residual learner that compensates structured EKF errors using electrochemical states and measurement features. The framework is evaluated on a public graphite/LFP dataset covering three dynamic drive cycles, eight temperatures from -10 to 50 degrees C, and initialization offsets up to 20 percent. Using dynamic stress test (DST) and federal urban driving schedule (FUDS) cycles for training and the supplemental federal test procedure (US06) cycle for cross-profile testing within the same cell dataset, PRKL achieves a global average root mean square error (RMSE) of 1.19 percent, corresponding to a 77 percent reduction relative to the physics-only EKF. These results show that electrochemical state information can guide residual learning and improve recursive SOC estimation for LFP batteries. The present validation supports cross-profile robustness within the studied dataset and provides a basis for future cross-cell, ageing-aware, and embedded-platform validation.

We propose a zonotopic framework for synthesizing a single robust state feedback controller that is certified to stabilize every plant inside a matrix zonotope, describing linearly varying parameters or parametric uncertainty. Common robust design strategies rely on checking many vertex models or on complex gain-scheduling, leading to high offline computation and implementation complexity. Our approach finds a single gain that is provably valid across the entire parameter domain, which is simpler to implement and can reduce conservatism by exploiting the structure of the zonotope. We formulate the robust synthesis as a single convex program tailored to the zonotope representation and incorporate practical performance requirements (actuator constraints, decay rate, disturbance attenuation) into the same synthesis stage. In numerical experiments on a representative 4-state example, our controller provides larger stability coverage across the parameter domain, attains comparable transient performance and control effort to more complex designs, and significantly reduces the number and scale of offline synthesis problems required by other robust approaches, compared to common-vertex gain, $H_{\infty}$, and $μ$-synthesis baselines.

Quantum systems face a fundamental trade-off: they must remain decoupled from the environment to maintain long coherence times, yet they require interactions with the environment to be accessible for measurement. As a prime example, emitter arrays coupled to waveguides facilitate collective modes that, owing to interference, can suppress radiation into the waveguide. While complete destructive interference creates perfectly dark states with infinite lifetimes, their inherent decoupling makes them unmeasurable in standard waveguide quantum electrodynamics. Consequently, current approaches must rely on system non-idealities that permit measurement but limit the coherence times. In this work, we lift this limitation by proposing the use of weakly squeezed light generated in \{chi}(2) nonlinear waveguides for the spectroscopy of completely dark states. We show that the fluorescence spectrum probes transitions between the dressed dark states of the emitter array. This work paves the way towards the measurement and control of dark states, with applications for robust quantum memories, computation, and communication.

In this work, we apply deformed light-cone null reduction method to a complex Maxwell theory in a manifestly gauge-invariant formulation. We show that the local U(1) gauge structure degenerates in the $c\to 0$ limit: the Gauss law constraint reduces from a restriction on initial data to a conservation law, releasing the longitudinal gauge mode as an independent degree of freedom (d.o.f). This raises the physical field count from $2(d-1)$ to $2d$. We prove a no-go theorem: under the single-mode Kaluza-Klein(KK)-like ansatz, no scaling of the field components can simultaneously preserve nontrivial dynamics and a first-class Gauss law, due to an inherent mismatch between velocity-type and constraint-type contributions in the parent action. Rather than representing the Carrollian electrodynamics derived via group contraction, the free complex scalar theory that emerges is merely an artifact of the truncation procedure at $c\to0$.

Agricultural crops are a type of cultural trait and the way farmers of US counties select them can itself result in county-level cultural traits. Using real-world data from 1997 to 2022, we have developed a systematic framework to study the selective mechanisms behind these traits. Our findings indicate that environmental payoff-biased selection has driven counties to adopt traits that maximize their adaptability and yield within their specific environments. These empirical results align with existing theoretical literature [3,16]. Additionally, a clear long-term selective trend is evident, showing that US counties are gradually developing a specific set of more complex combinatorial traits, which provide greater payoffs by enhancing the farmers' environmental adaptability. This study serves as a strong case for empirically modeling the cultural evolutionary processes among US farmers.

Fractional Wiener--Weierstrass bridges are a class of Gaussian processes obtained by replacing trigonometric functions in the construction of classical Weierstrass functions by fractional Brownian bridges. A number of their sample path properties were derived in Schied--Zhang (2024,2026). The analysis in these papers left several open questions, most of which are addressed here. Specifically, we prove that, in the regime in which the Weierstrass mechanism dominates the underlying fractional Brownian bridge, the limiting $b$-adic variation coefficient has an absolutely continuous distribution and is therefore genuinely random. At the critical point between the two roughness regimes, we establish the power-variation formula and the critical $Φ$-variation limit conjectured in Schied--Zhang (2024). Finally, we derive the Hausdorff dimension for the graphs of the sample paths by proving a conjecture from Schied--Zhang (2026) for the missing high-Hurst case.

We introduce a rank measure for first-order logic and prove a "rank-preserving'" version of Gaifman's theorem. Compared to earlier "rank-preserving locality theorems'" (in particular, [Grohe, Kreutzer, Siebertz, JACM 2017]), our theorem is not only much simpler, but also yields formulas in exactly the same normal form as Gaifman's original theorem. As an application of this theorem, we give a simplified proof of the main result of [Grohe, Kreutzer, Siebertz, JACM 2017] that first-order properties of nowhere-dense structures can be decided in almost linear time.

Let $\varepsilon\in (0,1/2]$ and let $G$ be a balanced bipartite graph on $2n$ vertices with minimum degree at least $(1/2 + \varepsilon)n$. Then, whp, the hitting time for minimum degree 2 coincides with the hitting time for Hamiltonicity. This extends Bollobás--Kohayakawa and gives a bipartite analogue of Johansson's theorem. As an immediate corollary, we deduce a sharp threshold result for Hamiltonicity in such graphs.

Quantum integrability in a system is characterized by a large number of conserved charges. However, finding the conserved charges in a generic quantum system is highly challenging. The integrable matrix theory provides a unified framework to obtain the conserved charges in a certain class of systems. We demonstrate this framework in case of a single-particle system on a 1D finite-sized lattice with inhomogeneous nearest neighbor hopping to study the statistical properties of the system across its chaotic--integrable crossover from the perspective of the conserved charges. The eigenspectrum of our random matrix model is studied first. We then estimate the conserved charges and find their properties throughout the chaotic to integrable transition of the system. We calculate the number of conserved charges across this crossover and observe that it is nearly equal to the size of the system at its integrable limit. Our result suggests that the number of conserved charges, estimated using the integrable matrix theory, can be a measure of quantum integrability.

Lifted product codes are an important family of quantum low-density parity-check (QLDPC) codes, as they were the first QLDPC code family shown to be asymptotically good. Understanding the structure of their parity-check matrices $H_{\mathsf{X}}$ and $H_{\mathsf{Z}}$, as well as the associated Tanner graphs, is essential for analyzing their decoding behavior and error-floor performance. In this work, we show that the Tanner graphs of $H_{\mathsf{X}}$ and $H_{\mathsf{Z}}$ are indeed isomorphic, and investigate their graph-theoretical structure. We establish conditions ensuring the connectivity of these graphs and provide bounds on their minimal absorbing sets, providing new insight into the combinatorial structures influencing decoding performance.

Traditional HCI interaction models assume a single monolithic interface and a stable sensorimotor loop. These models fit poorly with cross-device (XVA) and ubiquitous analytics (UA), where interactive data sensemaking unfolds across multiple devices, artifacts, and people in disparate settings from the office to the factory floor. In this paper, we show how interaction in ubiquitous analytics can be modeled using distributed cognition as propagation of representational state across substrates -- minds, speech, bodies, artifacts, and devices -- rather than as traffic through a single interface. On this basis we introduce input and output channels as generalizations of the visual channels from data visualization: just as visual channels carry data through properties of the visual substrate, input and output channels carry representational state through substrates whose availability, suitability, and preferability depend on context. We demonstrate the channels and substrates framework by reanalyzing several ubiquitous, immersive, and situated analytics systems.

Hybrid manganese halides enable the coexistence of molecular chirality, polar order, and magnetic exchange within a single lattice. Here, we combine first-principles calculations with spin-space-group analysis to investigate the synthesized enantiomeric pair [(R)/(S)-MPA]2[MnCl4(H2O)] (MPA = beta-methylphenethylammonium). We predict that its compensated magnetic state hosts altermagnetic spin splitting in the nonrelativistic limit, and that the coupled chiral, polar, and magnetic degrees of freedom define a symmetry-related manifold. From this manifold, we derive simple sign rules for the electronic and magneto-optical response: reversing both chirality and polarity, or reversing the magnetic domain alone, inverts the spin splitting throughout the Brillouin zone, whereas reversing chirality alone or polarity alone changes the spin-splitting sign only in symmetry-selected regions. With spin-orbit coupling, reversing chirality or magnetic order flips the Kerr rotation angle, while changing the polar variant leaves it unchanged. These results reveal a chemically accessible route to translate molecular handedness into symmetry-controlled spin splitting and magneto-optical readout in hybrid manganese halides. Critically, we show that the sign and momentum pattern of the splitting are governed by the interplay of the chiral, polar, and magnetic degrees of freedom. This interplay opens the possibility to control the spin splitting through a judicious design of the organic cations, by modulating their chirality and polarity.

Witten recently proposed a background-independent algebraic framework for quantum gravity, wherein an observer endowed with a Hamiltonian defines a diffeomorphism invariant worldline algebra manifested by the modified Hamiltonian constraint. In the semiclassical limit, this construction admits a lift to a von Neumann algebra acting on a Hilbert space defined by geodesic in a fixed background. Motivated by this, we revisit quantization of certain class of deformed CFT Hamiltonian on a cylinder to capture non-perturbative aspects of black holes. We construct a type-I Von-Neuman algebra by imposing conformal boundary conditions on cut-offs near fixed points of Hamiltonian flow, acting on a GNS Hilbert space built from highest-weight representation of `emergent modular Virasoro algebra'. Upon identifying the Hamiltonian with the modular Hamiltonian of a sharp subregion associated to a fixed reference KMS (vacuum) state, the algebra changes to type-III$_{1}$ factor. We also discuss the structure of emergent Hilbert spaces using `open-closed string' duality after incorporating an emergent non-trivial center made out of scalars at fixed points. We further employ this modular quantization of a single holographic CFT to demonstrate how the boundary limit of exact Hartle-Hawking correlator of smooth BTZ background emerge in the strict semiclassical limit in an alternative dual description, while at finite $G_{N}$, the corresponding description is intrinsically non-smooth, featuring both a stretched horizon and a boundary cutoff. The exact correlator has also been precisely reproduced from the vacuum correlators in modular quantization. We further discuss the effect of incorporating gravity by including the center via AdS/CFT on boundary correlators, for which the description of a smooth horizon is replaced by a (stretched) horizon containing explicit microstructures embedded within it.

We quantify an unusual flux-dependent systematic which is periodic in raw counts in flight data from the James Webb Space Telescope's Near Infrared Imager and Slitless Spectrograph (JWST/NIRISS), used extensively for exoplanet imaging and spectroscopy. Originally discovered in the aperture masking interferometry (AMI) mode, it also manifests in the Single Object Slitless Spectroscopy (SOSS) mode with the same dominant period of 1024 in raw analog-to-digital units (ADU). The likely cause of the signal is an analog-to-digital converter (ADC) integral nonlinearity (INL) in which case it will apply to all observations taken with the NIRISS instrument. Fortunately, it is straightforward to correct the data in postprocessing. The periodic INL is shown to be flux-dependent, increasing in amplitude with higher pixel counts on the detector. We derive a model of this periodic INL by fitting a combination of a polynomial and sinusoid multiplied with the residuals of ramp fits to the uncalibrated data and find an amplitude of 125ppm, up to a 2.5-count shift for a pixel with 20,000ADU. We apply this model to correct the well-studied NIRISS SOSS Program ERS1366 dataset of WASP-39b and reduce the data into a transmission spectrum. We find that our corrected transmission spectrum removes the INL systematic from the uncorrected spectrum at the 30ppm level across both orders, and also corrects a 55ppm offset between Order 1 and Order 2. We recommend a larger scale data-driven calibration of the periodic INL and the adoption of the outcome into NIRISS data pipelines.

Community detection in complex networks is frequently challenged by incomplete or noisy adjacency matrices. Traditional symmetric nonnegative matrix factorization methods typically rely on zero-imputation for unobserved entries, which compromises clustering reliability. This paper proposes a Masked Symmetric Nonnegative Matrix Factorization (Masked SymNMF) framework designed to factorize partially observed networks directly. By defining a masking operator over the observed entries, the proposed model restricts the objective evaluation exclusively to valid data. To overcome the severe non-convexity inherent in the symmetric factorization, we formulate an asymmetric relaxation penalized by a regularization term. We prove the exact penalty property of this reformulated model, establishing its theoretical equivalence to the original symmetric problem under sufficient regularization. Furthermore, an alternating nonnegative least squares framework is developed, yielding tailored update rules for Multiplicative Updates, Hierarchical Alternating Least Squares, and Projected Gradient Descent algorithms. Extensive numerical experiments on synthetic datasets and real-world networks demonstrate that the proposed Masked SymNMF outperforms baseline imputation methods across varying observation densities, providing a theoretically sound and practically efficient approach for community detection in incomplete networks.

Spatial computing, generative AI, and open web standards are converging. Three spatial operating systems -- Android XR, Meta Horizon OS, and Apple visionOS -- now ship with platform-level scene understanding. Wearable displays span the range from full headsets to slim smartglasses. Agentic AI operates on the same spatial substrates as the human user. This convergence enables new opportunities for \textit{ubiquitous analytics} (UA): the use of many, physically distributed, networked devices to support data sensemaking anytime and anywhere. But proprietary platforms are settling design conventions that will calcify without evidence-based alternatives. UA has now matured to the point where its intellectual history can be read as a structured genealogy of foundations, contributions, and lineages. We trace this genealogy and organize it into clusters spanning cognition, context, interaction, platforms, visualization, collaboration, and evaluation. Finally, we cross these clusters with each other, yielding a total of 42 future research challenges.

We study compatibility-constrained combinatorial chemical assembly through the lens of commutative algebra. Given a finite set $F$ of chemical families, a finite set $H$ of handle types, and a compatibility relation $Pairs(f) \subseteq H \times H$ for each $f \in F$, we construct an assembly ideal $I = J_{bool} + J_{sel} + K_{compat}$ in a polynomial ring $R = k[F,H,H']$ whose variety $V(I) \subseteq \{0,1\}^n$ encodes the set of feasible reaction triples. We prove that $I$ is zero-dimensional and radical, whence $R/I \cong k^{|V(I)|}$. Elimination ideals characterise handle diagnosticity (whether a handle determines its family), the toric ideal of the log-linear model on $V(I)$ measures redundancy in the compatibility relation, and a multi-step ideal $I^{(k)}$ encodes orthogonality constraints among simultaneous assembly plans; the clique number $ω(G_\perp)$ of the associated orthogonality graph gives the maximum number of mutually compatible plans. We derive a necessary and sufficient criterion for a new family to raise $ω$. The framework is instantiated on the bioorthogonal click-chemistry landscape ($|F|=8$, $|H|=17$), yielding $|V(I)|=30$, a toric ideal with 2 generators, ML degree 1, and $ω(G_\perp)=4$. All computations are verified over $\mathbb{Q}$ in SymPy.

The mechanism of a pressure-induced quantum critical point in the heavy fermion ferromagnet CeRh$_6$Ge$_4$ has attracted interest, as ferromagnetic quantum criticality in a clean itinerant Ce compound is typically avoided. The localized versus itinerant character of the 4\textit{f} electrons is a key aspect for understanding this behavior. We investigated the electronic structure of the 4\textit{f} shell in CeRh$_6$Ge$_4$ using core-level photoelectron and x-ray absorption spectroscopy, demonstrating the hybridization of Ce 4\textit{f} with the conduction electrons. Linearly polarized x-ray absorption reveals a temperature-dependent linear dichroism consistent with the crystal-electric-field (CEF) sequence as inferred from the static susceptibility. This dichroism cannot be described by an ionic full-multiplet model alone, but is reproduced by including the Kondo effect within a single-impurity Anderson model in the non crossing approximation (SIAM/NCA). The Kondo effect mixes higher lying crystal-field states into a resulting multiorbital ground state with 4\textit{f} occupancy \textit{n}$_f$\,$\sim$\,0.9. Deviations at low temperatures between the measured linear dichroism and calculated dichroism suggest an orbital-dependent Kondo effect. A scenario in which there is a multiorbital ground state and orbital-dependent Kondo hybridization should be a starting point for a model of pressure-induced criticality in CeRh$_6$Ge$_4$.