Papers

For an oriented regular plane curve $\gamma$, define ${\cal T}\gamma=\gamma+\tau$, where $\tau$ is its unit tangent. We construct a noncircular curve $\Gamma_0$ such that every iterate ${\cal T}^n\Gamma_0$, $n\geq0$, is a smooth embedded closed curve with everywhere positive curvature. This answers a question of Tabachnikov. The construction starts with a noncompact convex curve $C$, asymptotic at its two ends to parallel lines, satisfying ${\cal T} C=C+(V,0)$ for some $V>0$. From $C$ we construct long closed convex curves. After matching perimeters, we compare each curve with a convex curve whose unit-tangent image is the next curve in the sequence. In suitable arclength coordinates, their curvature functions differ by an exponentially small amount in $L^1$. Uniform inverse estimates turn these approximate relations into an exact sequence $\Gamma_{n+1}={\cal T}\Gamma_n$. Each $\Gamma_n$ lies in a strip of width bounded independently of $n$, whereas the radii of iterated circles tend to infinity.

We study ranking models by population-average utility from pairwise comparisons when preferences vary across users and tasks. Prior work shows that a single comparison per user can be insufficient to identify the alternative with the highest average utility, even with arbitrarily many users (Golz et al., 2025). We investigate how many repeated comparisons within each user-task context are necessary and sufficient for ranking recovery. Under a heterogeneous Bradley-Terry model with fixed inverse temperature, we start with a naive MLE-based algorithm that requires $\Omega(1/\Delta^2)$ repeated comparisons per context to ensure ranking recovery. We then present two MLE-based variants and a randomized Russian Roulette-style algorithm that recover the ranking using $O(\log(1/\Delta))$ repeated comparisons per context, and we prove that this logarithmic dependence is optimal. Despite this worst-case requirement, our Russian Roulette algorithm uses only $O(1)$ comparisons per context in expectation. Synthetic experiments and semi-synthetic experiments based on Arena data compare the four algorithms in settings with varying levels of preference heterogeneity and under varying context distributions.

We investigate the relaxation dynamics and steady state of a qubit interacting with a coherent environment through an energy-conserving flip-flop interaction within the Markovian repeated-interaction framework. We derive an exact analytical solution for the evolving and stationary state, nonperturbative in the environmental coherence. We show that environmental coherence provides a resource for dissipative state preparation by expanding the set of accessible steady states. In particular, coherent ancillas can increase the system ground- state population beyond that of the bath, corresponding to an effective temperature below the bath temperature, and enhance its steady-state purity, with these effects controlled by the interplay between the system energy scale and the system-ancilla coupling. Nevertheless, we prove that the purity of the system can never exceed the purity of the ancilla. We further analyze the thermodynamics of the protocol and show that environmental coherence can modify and even reverse the natural direction of heat transfer, giving rise to anomalous heat flow. Remarkably, for fixed interaction parameters, the direction of the coherence-induced heat transfer is governed by the relative phase between the system and ancilla coherence, whereas their magnitudes determine the amount of heat exchanged. Our results establish environmental coherence as a resource for controlling steady-state preparation and energy transfer in repeated-interaction dynamics.

Distributionally robust optimization (DRO) protects decisions against distributional uncertainty by optimizing over an ambiguity set, but poorly aligned set geometry can require large radii and yield overly conservative decisions. We introduce diagnostic-transport DRO (DT-DRO), which uses held-out calibration data to adapt the ambiguity-set geometry to observed predictive errors. DT-DRO uses the conditional probability integral transform cumulative distribution function to diagnose systematic probability misallocation and translates this information into an outcome-level transport that jointly adjusts the ambiguity-set center and ground cost. The resulting formulation admits a computationally tractable dual reformulation. Theoretically, we derive valid ambiguity radii and decision-risk guarantees that tighten as estimation and approximation errors vanish, and show that DT-DRO can eliminate the nonvanishing robustness floor caused by model misspecification. Synthetic experiments and a power-outage application demonstrate improved decision quality, particularly under structural and tail misspecification.

Probabilistic programs provide a rigorous programming-language foundation for expressing rich probabilistic models and offer language-level support for solving challenging statistical inference problems. A key theoretical challenge that probabilistic programs inherit from probability theory is conditioning a probability distribution on an observation that has probability zero. Many languages address this challenge by using computational rules for conditioning that may work well for some problems but are statistically unsound for others. This article introduces a principled mathematical approach for conditioning probabilistic programs. We first show that existing techniques based on "soft conditioning" and "neighborhood limits" exhibit semantic issues from the perspective of measure theory and produce inference results that disagree with sound statistical reasoning. By leveraging tools from geometric measure theory, we construct a novel disintegration-based semantics for probabilistic program traces that enables sound conditioning. The theory delivers an explicit Bayes rule representation of the conditional distribution, which is directly compatible with widely used probabilistic inference algorithms that require access to unnormalized posterior densities. Our Bayes rule handles probabilistic models with loops, branches, discrete, continuous, and mixed-type distributions, observations on manifolds, differentiable structure, and additional modeling motifs that arise in practice.

Asymptotic Safety provides a promising framework for the quantization of Scalar-Tensor theories as non-perturbatively renormalizable quantum field theories. Over the past years, growing evidence has accumulated for the existence of non-trivial renormalization group fixed points in a variety of Scalar-Tensor models. In this work, we investigate the robustness of these fixed points under significant modifications of the computational setup. In particular, we employ a gauge condition that explicitly depends on the dynamical scalar field, going beyond a mere gauge-parameter deformation of the standard linear covariant gauges commonly used in the literature. Exploring different field parameterizations, we identify fixed points belonging to the Gaussian Matter class in four spacetime dimensions that are consistent with previous studies. The real part of the critical exponents associated with the scalar-field mass and the non-minimal scalar-curvature coupling turn out to have very small absolute value. We provide a comprehensive exploration of how the anomalous dimension of the scalar field and field parameterization impact those critical exponents showing that fixed-point candidates with two or four relevant directions emerge.

Under the assumption of integrability of the smooth Jacobi fields and a condition on the intersection pattern of the link, we prove uniqueness of special Lagrangian tangent cones in $\mathbb{C}^3$ whose links are compact immersed special Legendrian surfaces with transverse double points. The proof is based on a discrete Lojasiewicz type inequality, which comes from a gluing obstruction mechanism.

We give a direct and explicit construction of the homotopy span model of linear logic originally formulated by Melliès using abstract homotopy theory in the Quillen category Cat of small categories equipped with its natural model structure. Following the principles of homotopy theory, the formulas and proofs of linear logic are interpreted in the model as small categories up to categorical equivalence, the notion of weak homotopy equivalence underlying the natural Quillen model structure on Cat. Here, we explain how the original interpretation of proofs as fibrant spans can be replaced by a more liberal interpretation of proofs as separately fibrant spans. This relaxation from fibrant spans to separately fibrant spans enables us to give a simple and intuitive description of the homotopy span model, where the axiom and cut links are interpreted as identity spans, and where the symmetries of the exponential modality are captured by a shuffle structure on the interpretation of proofs.

Seismic data augmentation is critical for training robust deep learning (DL) models for fault detection and characterization, yet conventional approaches remain inadequate. Geometric transforms, e.g., flips or rotations, and noise injection fail to capture realistic seismic textures, while physics-based forward modeling is computationally expensive and often poorly aligned with the statistical characteristics of field data. We present a denoising diffusion probabilistic model (DDPM) framework that learns the high-dimensional distribution of seismic images directly from field data via iterative noise injection and learned denoising. We develop two variants: an unconditional model (U-DDPM) that generates realistic post-stack seismic patches and a fault-conditioned model (FC-DDPM) that produces diverse seismic realizations that honor user-specified fault geometries encoded as binary masks. Three open-source field datasets with differing amplitude scales and processing histories are jointly standardized for training, demonstrating cross-survey generalization. Generated images from U-DDPM reproduce the dominant textural patterns, amplitude distributions, and reflector continuity observed in real seismic data. FC-DDPM maintains structural fidelity to imposed fault masks while introducing realistic variability in surrounding seismic textures, enabling one-to-many realizations from a single structural template. Frequency-wavenumber spectral analysis confirms that synthetic samples preserve the spatiotemporal bandwidth and dip content of the training distribution. The proposed framework provides a practical, controllable augmentation mechanism for expanding limited fault-labeled training sets without computationally expensive forward modeling or survey-specific parameter tuning, directly addressing a key bottleneck in DL-based seismic interpretation.

Language models trained with long-horizon agentic reinforcement learning can generalize knowledge through reasoning, express precise actions, and pursue goals over many steps, raising the ceiling on what an embodied agent can understand and decide. Physical interaction, however, remains the domain of action policies, which provide dense, low-latency control. We present NavGPT-3, a harness that connects the two models, with an OS-like runtime built above it: reasoning, acting, and monitoring run as threads with their own context, tools, and permissions, while the runtime schedules them and decides which thread controls the robot's motion, so that the robot can react to sudden real-world events through interruption and thread switching. Beneath it, our action policy NavGPT VLA, trained on 19.28M examples, allocates visual tokens using codec allocation, in proportion to scene change; its 8B model alone reaches 76.94 SR on R2R-CE and leads RxR-CE with 82.39 SR. With the complete harness, NavGPT-3 sets the state of the art on R2R-CE (81.51 SR) and, for the first time, brings an autonomous agent to human level: on RxR-CE it matches human followers in success (90.43 vs. 90.4 SR) and path fidelity (78.47 vs. 77.7 nDTW) at 1 min 22 s per episode, versus roughly 3 min for a human. We comprehensively ablate the harness design and the interaction between the two models, showing how tools and the action policy shape the path from language-model reasoning to physical control: when NavGPT VLA executes the route, the reasoning loop shortens and the system's minimum reaction time falls from 3-19 s per language-model decision to 0.5-1 s per action-policy step (1-2 Hz). These results show that designing this embodied interface is central to connecting frontier language-model intelligence with low-level physical control. We will release all models, code, and evaluation records.

Planning is increasingly important for long-horizon agents, where successful execution requires coordinating subgoals, tool use, and intermediate outcomes over many steps. Yet assumptions made during planning may be invalidated by the environment, tools may return unexpected results, or actions may fail. Effective agents must therefore not only generate plans, but also revise them. Such revisions often affect only part of a plan, leaving the preceding and subsequent structure intact. Rather than regenerate the entire plan and risk unnecessary changes, repair can regenerate the affected region conditioned on the preserved prefix and suffix. We introduce Plan-and-Patch, a plan-and-act framework in which a diffusion language model (dLLM) generates a structured, program-like plan through parallel unmasking and repairs it by filling in selected regions while keeping the surrounding steps fixed. We compare DreamReasoner-8B and Qwen3-8B as diffusion and autoregressive (AR) planners. On Natural Plan without task-specific training, diffusion (53.7%) achieves nearly twice the plan repair success rate of AR (27.0%). After task-specific training on agentic benchmarks, ALFWorld and TextCraft, the planners achieve similar observed success in plan generation, while diffusion reduces mean plan-generation latency by 39-46% relative to AR. Our results show that Plan-and-Patch provides a framework for faster plan generation and effective plan repair in long-horizon agents.

Intracluster Light (ICL) is a diffuse stellar component of galaxy groups and clusters, bound to the structure's potential rather than to individual galaxies and primarily formed through the stripping and mergers of intermediate-mass galaxies. Its formation and evolution is strongly linked to the central galaxies of groups and clusters, typically the Brightest Cluster Galaxies (BCGs) in clusters. To determine the properties of the progenitor galaxies of the ICL of clusters and groups at redshift z = 0 and compare them with the progenitors of their BCGs. We select 127 clusters and groups in the hydrodynamic Illustris-TNG100 simulation above a mass of 10^{13}~$M_{\odot}$. We divide the ICL from the BCG by applying a surface brightness cut at the Holmberg radius of 26.5 mag/arcsec^{-2}, where star particles within this radius are defined as attached to the BCG, and outside, the ICL. We then determine the masses and contributions of progenitor galaxies of the ICL and BCG. We find that the number of ICL progenitors increases with structure mass, and that the ICL has more progenitors than the BCG. The ICL has a larger percentage of material from low-mass galaxies. Quenched galaxies contributed a large fraction of the ICL, and this fraction increases with galaxy mass. The mean mass radial gradient of ex-situ material in structures for the ICL and the BCG+ICL is generally negative and increases with structure mass, indicating that material from more massive progenitors is found towards the centres of clusters. The mean mass radial gradient is significantly impacted by structure formation history. ICL progenitor properties are impacted by structure history and are therefore highly individual to each system. At a given structure mass, there is diversity in the properties of the progenitors that formed the ICL. Although the BCG and the ICL co-evolve, the BCG has fewer, more massive progenitors.

We develop a modular wall crossing theory for quasimaps to a projective variety, allowing independent variation of the boundary coefficients and the quasimap weight. Building on the K-stability of quasimaps introduced by Hashizume and the first author, we construct projective moduli spaces in the stable, Calabi–Yau, and log Fano regimes, together with wall crossing morphisms. A central construction is the moduli theory of boundary polarized Calabi–Yau quasimaps, which retains an ample polarization at the numerically trivial locus and allows comparison with suitable perturbations toward the stable and log Fano regions. The stable theory applies in arbitrary genus, while the comparisons through the Calabi–Yau locus concern genus zero. For degree-one boundary divisors, the resulting framework relates weighted stable maps and quasimaps to Hassett spaces and GIT quotients of weighted points on $\mathbb P^1$. In a companion paper, we apply this framework to give a modular interpolation between Miranda's GIT compactification of rational elliptic surfaces and the Baily–Borel compactification of an eight-dimensional ball quotient.

Spatial modelling and inference arise across many areas of science and engineering, with Kriging and Gaussian process (GP) regression serving as two widely used predictive models. Although grounded in the same random field theory, these approaches are often treated in isolation. As a result, their connection has been obscured by differences in terminology, notation, and practical implementation. This separation largely reflects their independent development within geostatistics and machine learning, respectively. To bridge this methodological divide, this work establishes a unified mathematical framework that connects the two paradigms. The underlying assumptions and formulations of each approach are detailed and compared within this framework. This comparison highlights their differences while clarifying the connections between them. The resulting perspective provides practitioners with a common foundation for translating concepts and methods between geostatistics and machine learning. In particular, it makes methodological developments in either field more accessible to the other, including advances in uncertainty quantification from the GP literature.

Reinforcement learning with verifiable rewards (RLVR) has become a standard recipe for post-training vision-language models (VLMs), but it typically assumes a static training environment. As the actor improves, fixed tasks drift out of its learning frontier: many become trivial, others remain unsolvable; and the learning signal collapses. We argue that VLM post-training should evolve the visual environment alongside the actor, not just the actor itself. We propose VICO, a co-evolutionary framework in which an actor and an Environment-as-Rewriter (EnvRewriter) are trained jointly: the EnvRewriter edits verifiable image-side structures, such as scene graphs, chart tables, or protected region masks, and re-renders them to produce label-valid training samples whose difficulty is calibrated to the actor's current ability through a pass-rate-based reward. This loop continuously realigns task difficulty with actor capability without any additional human annotation. Across nine multimodal benchmarks spanning mathematical reasoning and visually grounded understanding, VICO-8B improves over its base model by up to +5.0% on out-of-domain tasks, surpasses the strongest self-evolution and text-editing co-evolution baselines by +4.3% and +8.4% respectively, and stays comparable to chart-specialized RLVR methods using 16-160 times fewer labeled samples. By shifting from human-labeled supervision to image-editing co-evolution, VICO offers a scalable path beyond static-corpus RLVR for visual reasoning.

Point defects with optically addressable spin states are a key building block for quantum networks, but few solid-state emitters combine a spin-photon interface with emission in the low-loss telecommunications band. Vanadium (V4+) defects in silicon carbide (SiC) meet this requirement, emitting zero-phonon lines (ZPLs) throughout the telecom O-band in both the 4H- and 6H-SiC polytypes while retaining an addressable electron and nuclear spin system [1,2]. Although the orbital and spin structure of these defects has been characterized in detail, the polarization selection rules have not been fully mapped experimentally. Here we present polarization-dependent photoluminescence (PL) measurements of vanadium ZPLs in 4H- and 6H-SiC at cryogenic temperature, of two scattering geometries: edge and face-on (emission wavevector perpendicular and parallel to the crystal c-axis, respectively). Emission from two of the four {\alpha} sites, ({\alpha}2 and {\alpha}3) and the 6H-SiC {\gamma} sites, are polarized parallel to the c-axis ({\sigma}-polarized), whereas emission from {\alpha}1 and {\alpha}4 are polarized perpendicular to the c-axis ({\pi}-polarized). Additionally, we report preliminary, lower signal measurements of the e̱ta} sites.

Let $P$ be a set of $n$ points in the plane. Given an integer $K$ with $1\le K\le {n\choose 2}$, the distance selection problem asks for the $K$-th smallest distance among all pairwise distances of the points of $P$. The problem has been studied extensively over the past four decades. Recently, Chan and Zheng (2023) gave a randomized algorithm with $O(n^{4/3})$ expected running time, while the best known deterministic algorithm runs in $O(n^{4/3}\log n)$ time. In this paper, we present a deterministic $O(n^{4/3})$-time algorithm for the problem, matching the best known randomized complexity. We also consider the more general bichromatic version of the problem, where two point sets $A$ and $B$ are given, with $m=|A|$ and $n=|B|$, and the goal is to find the $K$-th smallest distance among the $mn$ distances between points of $A$ and points of $B$. For this problem, the best previously known algorithm runs in $O((m\log n+n\log m+m^{2/3}n^{2/3})\log(m+n))$ time. We present a new deterministic algorithm with running time $O(m\log^2 n+n\log^2 m+m^{2/3}n^{2/3})$.

Galaxy recession velocities are commonly used to measure the Hubble constant, $H_0$, with peculiar velocities treated as random noise. Around massive clusters, however, these motions can be predicted by the gravitational potential of the central halo, allowing them to be modeled rather than averaged over. Past analyses relied on analytic approximations for the distance-infall-velocity relation, whose accuracy has not been tested using realistic cosmological simulations. We use halos from the IllustrisTNG simulation to quantify the bias and precision of several commonly used Hubble-flow models. We find that widely used fitting functions systematically underestimate $H_0$, whereas the full analytical solution reduces but does not eliminate these biases. We develop a simulation-based method to infer $H_0$ and apply it to TRGB distance samples around the Virgo Cluster. We find $H_0=74.4\pm 2.9$ and $73.4\pm 3.9$ km s$^{-1}$ Mpc$^{-1}$ (stat) for the minor and the major infall models, respectively. Correcting for the bias calibrated on TNG halos, these measurements raise the value of $H_0$ to $81.6 \pm 7.8$ and $87.3 \pm 8.8$ km s$^{-1}$ Mpc$^{-1}$ (stat+sys), where the minor infall model has the smallest bias from the Virgo mocks. We show that statistical errors are dominated by the residual velocity scatter around the infall model, while systematic errors are dominated by the transformation to the structure's comoving frame and halo population variance. These results establish a framework for interpreting cluster infall measurements and explain trends in previous $H_0$ inferences.

Long-term agents face growing storage demands as they accumulate experience. World models capture reusable regularities that can reduce the information stored for each experience. We formulate the problem of memory allocation conditioned on a world model and introduce MemoWM, a framework that uses shared predictions to compress retained information and reconstruct omitted content. Its task-aware allocation rule balances the expected impact of reconstruction errors against storage cost, retaining information with downstream value beyond the predictive prior. Across five long-term agent-memory benchmarks, MemoWM achieves 42.42% average answer accuracy, exceeding the strongest baseline by 2.62 percentage points, while reducing average experience-specific storage by 53.9% relative to MIRIX, the most storage-efficient baseline. Further analysis shows that stronger world models reduce per-experience storage at comparable task quality. Accounting for model parameters reveals a trade-off between shared model capacity and recurring storage costs, with the capacity that minimizes total storage increasing as more interactions are retained. Our code is available at https://github.com/Feld-maxiu/MemoWM.

Using K-moduli spaces for log quasimaps $q_t\colon\left(\mathbb P^1,\frac{1-t}{12}D\right)\to[\mathbb A^2/\mathbb G_m]$ of degree twelve with twelve points and weight $t/12$, we construct a modular interpolation $\{\mathcal M_t\}_{0\le t\le1}$ between the Baily–Borel compactification of the Heckman–Looijenga ball quotient $X_o$ and Miranda's GIT compactification of the moduli space of rational elliptic surfaces. We completely determine the wall-crossing and, for every rational $t\in[0,1]$, identify \[ \mathcal M_t\cong\operatorname{Proj}R\!\left(X_o,\mathcal L+\frac t2\Delta(6)+\frac t3\Delta(9)\right), \] where $\mathcal L$ is the automorphic $\mathbb Q$-line bundle and $\Delta(6),\Delta(9)$ are distinguished Heegner divisors. On the automorphic side, we construct a new automorphic form on $X_o$ via a Borcherds product, whose divisor gives an independent relation among the Heegner divisors. This relation provides a key input for determining the birational transformations in the K-moduli wall-crossing. As part of this analysis, we show that the first positive chamber $\mathcal M_t$ for $t\in (0,1/7)$ is Looijenga's semi-toroidal compactification.

Equivariant graph neural networks have emerged as foundational architectures for machine-learned interatomic potentials, approaching quantum-chemical accuracy at a fraction of the computational cost. These models describe local atomic environments accurately, but finite spatial cutoffs truncate long-range information flow, and stacking message-passing layers can lead to over-smoothing and over-squashing. Existing long-range extensions either prescribe a fixed analytical propagation kernel, restrict long-range communication to scalars or degree-preserving channels, are only approximately equivariant, or incur super-linear computational cost. Combining learnable long-range equivariant transport with multiscale many-body expressivity and efficient scaling for larger systems remains a central challenge. We introduce Neural Equivariant Multipole Operators (NEMORA), a neural equivariant extension of the Fast Multipole Method (FMM) for learning long-range tensorial representations. NEMORA generalizes the FMM's analytical multipole expansion and translation operators to learned equivariant counterparts on an adaptive spatial hierarchy. Its operators couple angular degrees and form many-body interactions across length scales, retaining the FMM's hierarchical organization and analytical radial factors as physical inductive biases while learning data-dependent long-range couplings. NEMORA evaluates in linear time and memory complexity, allowing it to treat larger systems than other long-range methods reaching hundreds of thousands of atoms, and it augments both symmetry-constrained and unconstrained short-range backbones. On non-local benchmarks, it reduces force and energy errors relative to the short-range backbones by over an order of magnitude and up to three orders of magnitude, respectively, which is better than or competitive with existing long-range extensions in accuracy.

Let $\mathop{Mod}_{g,n}$ be the mapping class group of a genus-$g$ surface with $n$ punctures and let $\mathcal{C}_{g,n}$ be its curve complex. For a finite-index subgroup $G < \mathop{Mod}_{g,n}$, Boggi proved that $\widetilde{H}_k(\mathcal{C}_{g,n}/G;\mathbb{Q}) = 0$ for $g+n \gg k$. This plays an important role in the work of Putman-Wieland on the virtual first Betti number of $\mathop{Mod}_{g,n}$. The proof of Boggi's theorem uses mixed Hodge theory and is embedded in his flawed paper purporting to show that the mapping class group has the congruence subgroup property. We give a detailed exposition of Boggi's proof aimed at geometric topologists.

Audio generation models can translate natural-language descriptions into sound, but their outputs are typically waveforms. Their audio quality is constrained by audio compression, and their outputs do not readily support direct edits to notes, timbral parameters, or modulation relationships. We present AutoSynth, which represents MIDI performance events, fixed synthesizer parameters, and variable-length modulation routes as a unified sequence for a synthesizer, and learns their dependencies with an audio-conditioned autoregressive model. A single model supports both tasks. Given reference audio, the model directly predicts a synthesizer program; given text, it uses a pretrained audio generation model and converts the generated audio into a program. Training consists of two stages: supervised learning on large-scale audio-program pairs automatically constructed from a small set of native presets, followed by group-relative policy optimization with a mixed reward combining semantic similarity, pitch-related features, acoustic similarity, and sound usefulness. The pipeline requires neither paired text-target-program annotations nor a differentiable synthesizer. Experiments show that AutoSynth produces complete, editable synthesizer programs and achieves competitive results in both synthesizer inversion and text-driven generation. Audio demos and source code are available at https://auto-synth.github.io/.

Let $U$ be the ring of upper triangular $2\times2$ integer matrices. For $N\in U$, a Jordan $D(N)$-set is a set of distinct nonzero matrices in $U$ such that $(AB+BA)/2+N$ is a square in $U$ for any two distinct elements $A$ and $B$. We determine all $N$ for which an infinite Jordan $D(N)$-set exists. If no infinite set exists, every such set has at most six elements. If $N$ is not a difference of two squares in $U$, the bound is five. Both bounds are best possible. We also give necessary and sufficient conditions for the existence of infinite sets with nonzero pairwise Jordan products and of infinite sets consisting of nonsingular matrices.

The Minimum Birkhoff Decomposition (MBD) seeks a sparse weighted sum of matchings and is a challenging optimization problem with applications in network scheduling and energy trading. We scale a quantum-assisted decomposition method by combining single-layer QAOA sampling with Extended Fully-Corrective Frank-Wolfe (E-FCFW) optimization, spectral graph partitioning, and greedy feasibility repair. We demonstrate the pipeline on the 1,354-node PEGASE bus test case (representing a 1,354-bus transmission grid with 1,710 transmission lines), whose 1,710 edges define a native 1,710-variable matching optimization problem requiring 1,710 qubits in the unpartitioned encoding. Partitioning enables distributed execution on IBM superconducting quantum processors. The best reported hardware result uses a 50-qubit partition bound, while reducing partitions to 20 qubits degrades convergence in the partition-size comparison. Larger partitions are more demanding for matrix product state (MPS) simulation, and bond-dimension tests show that truncating quantum correlations reduces candidate quality. The results therefore motivate retaining a substantive quantum sampling task within each partition as the overall problem scales. On the PEGASE-1354 benchmark, repaired QAOA samples achieve lower residual decomposition error than both simulated annealing and uniform random sampling baselines, while spatial circuit packing reduces hardware execution time by approximately a factor of three. These results demonstrate that combining spectral partitioning, spatial circuit packing, and classical feasibility repair provides an executable path for deploying gate-based quantum sampling on thousand-variable constrained optimization problems on current hardware.

We determine the infrared-sensitive contribution to the pressure of hot and dense massless quantum electrodynamics (QED) at $O({e}^6)$ in the electric charge $e$, obtaining a representation valid across the crossover between the thermally dominated and degenerate regimes. This contribution arises from a hard-thermal-loop (HTL) resummed soft photon dressed by either the one-loop power correction or the two-loop next-to-leading-order photon self-energy. After separating the static and nonstatic sectors, we obtain the static contribution in closed form and perform the nonstatic Matsubara sum analytically in terms of the digamma function, reducing the remaining finite coefficient to a one-dimensional numerical integral. The finite-temperature HTL counterterm cancels the factorization divergence before expansion; at strictly zero temperature $T$, this divergence instead cancels against the hard four-loop contribution. At vanishing chemical potential, the static sector reproduces the complete known $O\left(e^5\right)$ pressure. Taking the cold limit of the dimensionally regulated, unsubtracted nonstatic contribution reproduces the correct cold mixed result. Crucially, at any fixed $T>0$, the nonstatic result remains analytic in $e^2$. The zero-temperature $O(e^6\ln e)$ term in QED arises only in the nonuniform limit ${T}/{m_{\rm{E}}}\to0$ where $m_{\rm{E}}$ is the electric screening mass, demonstrating that the weak-coupling and zero-temperature limits do not commute.

How might AI alter how we understand and experience the self? This scoping review analyzes 102 papers to examine how the self is defined in the field of human-computer interaction (HCI), how AI-self relationships are conceptualized, and what risks emerge when AI becomes entangled with selfhood. Our synthesis makes three contributions. First, we define AI-mediated self as a conceptual umbrella that connects dispersed work across education, workplace, health, and creative practices. Second, we consolidate six framings of the self with four domains of ethical risk-agency/autonomy, identity/authorship, relational capacity, and meaning-making-into a conceptual map that provides a reusable vocabulary across contexts. Third, we introduce the Inclusion of AI-Self framework, which situates AI-self relationships along a spectrum of proximity. Together, these contributions position selfhood as a central design space in HCI.

The island proposal guarantees a unitary Page curve for evaporating black holes, implying that operators deep behind the horizon must be fully reconstructable from asymptotic Hawking radiation. However, because the interior is causally disconnected and highly dynamical, standard entanglement wedge reconstruction methods, relying on global isometries or continuous modular flow, fail to provide this mapping. We resolve this by constructing a protocol for island reconstruction using the algebraic Petz map. By using modular theory, we reflect island operators into the accessible complement, transport them to the boundary, and map them into the radiation algebra. Furthermore, we demonstrate that this purely algebraic derivation naturally yields the structure of Papadodimas-Raju mirror operators. This framework provides a rigorous operational dictionary for the island formula, proving that information trapped inside a black hole can be decoded.

The global challenge of climate change has driven significant steps to reduce CO2 emissions, guided by international agreements like the Paris Agreement of 2015. Acting too slowly could result in future losses and reputational damage, while moving too quickly could jeopardize shareholder value due to the marginal profitability or potential losses due to technology immaturity of many renewable projects. To navigate this complex transition, energy companies must adopt Sequential Decision Making (SDM) strategies to maximize value creation from decision flexibility under uncertainties. To support this, we developed a custom simulation environment to model the dynamic energy landscape up to 2050. Building on this, we designed a multi-criteria SDM framework that explores various decision strategies related to different portfolios for allocating funds across three sectors: oil & gas, renewables, and CO2 reduction. It aims to maximize value during the transition while accounting for uncertainties in productions, energy prices, and costs. This framework has three objectives: maximizing profit, minimizing CO2 social costs, and enhancing competitive advantage in the renewable energy sector. This research evaluates the use of Reinforcement Learning (RL) to identify optimal investment policies within the defined SDM framework. The agent's sequential decisions shape a virtual dynamic environment by influencing key variables such as oil and gas production, renewable energy output, CO2 emissions, and revenues. Through repeated interaction, the RL algorithm explores the state space and learns an optimal policy under uncertainty. We benchmark the RL strategy against a set of manually defined baseline policies and find it consistently outperforms them in adaptability and long-term value creation.

Low-loss dielectric films are an important component of superconducting circuits with applications ranging from quantum information to superconducting detectors for astrophysics. In millimeter-wave detector circuits, dielectric loss can be the limiting factor on efficiency and resonator performance. Some advantageous detector fabrication architectures require dielectric deposition at temperatures substantially lower than those conventionally used to achieve low dielectric loss. In this work, we characterize silicon nitride (SiN$_x$) films deposited by inductively coupled plasma chemical vapor deposition (ICPCVD) at $150\,^{\circ}\mathrm{C}$ for use in temperature-constrained superconducting detector fabrication. We measure the dielectric loss tangent of these films at $\sim 4-7$ GHz using superconducting niobium microstrip resonators and extract the loss by fitting the temperature-dependent resonant frequency to a two-level-system model. We vary the N$_2$/SiH$_4$ precursor-flow ratio between dielectric depositions and find a clear trend of decreasing loss with decreasing N$_2$/SiH$_4$. We additionally find that applying an RF substrate bias during deposition reduces the loss compared to films deposited without bias. These results identify precursor ratio and substrate bias as practical process parameters for improving low-temperature SiN$_x$ for superconducting detector circuits.