Papers

High-fidelity two-qubit gates in neutral-atom arrays rely on the Rydberg blockade, which is intrinsically short ranged and requires long range connectivity to be achieved through atom shuttling. We propose a four level architecture, where the typical ground state qubit can be leveraged for its long lifetime and the Rydberg states couple to a microwave cavity, allowing for long range cavity mediated gates. We first find the thermal dependence of two established protocols, the dispersive iSWAP native to the Tavis-Cummings model and the Controlled phase gate generated from driving the cavity. We simulate them under the presence of Rydberg decay, thermal photons, finite cavity linewidth and find fidelities which accompany closed form bounds. We then introduce the bichromatic Raman gate, which only virtually populates the Rydberg states and cancels dispersive shifts to mitigate both atomic and cavity decay, achieving a fidelity of $F = 0.997$. Finally, we consider a full optical tweezer array in a microwave cavity, and show that using a cavity mediated gate to close the periodic boundaries of the toric code shortens an error correction round by a factor of 2.3 for realistic array sizes. This was then applied to the wider family of Bivariate bicycle codes, and we find that it shortens a round of the gross code by a factor of 4.8.

Despite the success of neural models in natural language processing, their black-box nature limits interpretability and conceals the linguistic phenomena underlying their predictions. We present SLITE, an explainable hybrid model for Recognizing Textual Entailment that integrates two complementary layers of semantic analysis: a structural-relational layer, based on semantic compatibility and incompatibility between compositional entities, and a distributional-informational layer, based on structured patterns of information change between embedding-based representations of the premise and the hypothesis. We propose 17 features that combine entity-level semantic relations, polarity-sensitive lexical matching, and alignment measures over semantic sub-representations of the similarity matrix, including measures based on entropy and transfer entropy. A logistic regression trained on these features achieves an accuracy of 83% on three-class SICK and 96% on SICK-CE, outperforming IsoLex by 4 percentage points and falling within 2 percentage points of RoBERTa with a fraction of its computational complexity. Ablation studies and SHAP analysis confirm that structural-relational features are the primary drivers of classification, while distributional-informational features provide essential complementary contributions, particularly for detecting neutrality and contradiction. Our results demonstrate that further exploration of hybrid approaches is a viable and scientifically productive alternative to massive neural architectures, and we hope they will strengthen the dialogue between linguistic theory and computational modeling of inference

Let $X$ be uniform on $\{-1,1\}^n$, let $Y$ be obtained by passing its coordinates independently through a binary symmetric channel with crossover probability $p$, and let $g:\{-1,1\}^n\to\{0,1\}$ be a Boolean function. We give a computer-assisted proof of the Courtade–Kumar conjecture $I(g(X);Y)\le1-H_2(p)$, where $H_2$ is binary entropy, with equality attained by dictator functions. The present work builds on the differential-equation method, itself a limiting form of the auxiliary-receiver approach in network information theory using a continuum of degraded receivers. The proof proceeds from a local inequality to a dimension-independent bound on entropy production. Differentiation along the Boolean noise semigroup expresses entropy production as an average of edge costs. The key estimate is therefore an unrestricted Bellman inequality with two mean constraints and two entropy constraints, allowing arbitrary couplings of the edge variables. This paper and its supplement provide the proofs and computational verification records. The document is lengthy because it is designed to be entirely self-contained, deriving all proofs from first principles and reproducing the proofs of cited results. We also give a self-contained expository note explaining the reduction to a low-dimensional inequality and the ideas behind the key lower bounds. The entire proof, including all numerical certificates, has been formally verified in Lean end-to-end, and is available online.

We construct global solutions of the defocusing cubic half-wave equation on the torus whose $H^s$ norms grow exponentially for every $1/2<s<3/2$. Such solutions exist at every positive mass. To the best of our knowledge, this provides the first example of a genuine infinite cascade for a defocusing fractional nonlinear Schrödinger equation on the torus. In particular, our result resolves an open question posed by Gérard and Grellier concerning the existence of unbounded Sobolev trajectories for the defocusing cubic half-wave equation on the torus.

In this paper, we study nonasymptotic $L^p$ error bounds for interval length and conditional coverage in split conformalized quantile regression (CQR). Our bounds rely on local regularity conditions and accuracy guarantees for the estimated quantiles. We further instantiate our bounds for quantile regression with sparse ReLU neural networks. We also consider covariate shift, where the calibration and test covariates have different distributions, and derive nonasymptotic bounds for this setting. We obtain matching minimax upper and lower bounds in expectation for two constructed fixed-score calibration benchmarks under known covariate shift. The bounds match for every $p\in[1,\infty]$ in the scalar problem and for finite $p$ in the $K$-threshold problem; for the latter, a high-probability minimax lower bound holds for every $p\in[1,\infty]$.

Autonomous software engineering agents (SWE-agents) automate coding tasks. Each agent update may require re-running the full benchmark to detect regressions and improvements, at a cost of hundreds of millions of LLM tokens per run, which makes evaluation a bottleneck. One solution is to evaluate only a subset of benchmark instances. Yet, simple approaches, such as random sampling or stratified random sampling based on past pass/fail outcomes, risk producing high variance and unrepresentative subsets. We turn to agent trajectories, the step-by-step record of the actions an agent took. We propose a trajectory-aware subset selection approach that replaces random sampling with deterministic selection based on trajectory embeddings. We first group test set instances by their test outcome in a recent full test run to preserve the historical pass/fail rate, then select the subset using the trajectory's embedding space. We evaluate 76 subset selection configurations, including random sampling, embedding-based selection, clustering-based selection, and hybrid shortlist-then-subsample strategies, across three regression scenarios: same-configuration reruns, model and configuration changes, and agent framework changes. Our best trajectory-aware method is the one selecting benchmark instances closest to the centroid of each outcome group in the embedding space. It achieves the lowest estimation error among all methods we evaluate. For instance, when evaluating a given agent version on a selected subset of 5% or 10% of the test instances, our approach reduces the average estimation error by 3–11% and the worst-case error by 4–11% relative to the typical draw and 38–46% relative to the 95th-percentile draw of the strongest baseline. Our results show that a 10% trajectory-aware subset keeps the median estimation error below 5% while cutting token cost by roughly 90%.

Personal AI agents make recommendations and take actions on people's behalf in high-stakes economic contexts, e.g., buying a flight, choosing health insurance, or selecting a graduate program. The agent is given access to the user's personal context, e.g., their email inbox and a structured profile of personal attributes, with the intention of making an optimal, personalized decision for the user. We show that by simply providing this personal context, the agent steers recommendations based on inferred wealth, without being explicitly instructed to do so. In a suite of 325K experiments on 13 agents across three types of economic decisions (flights, health insurance, and graduate programs), we find that 8 models systematically choose more expensive options for wealthier users when requests are identical. This steering continues even when it directly goes against the user's stated objective: when explicitly instructed to find the cheapest option, some agents still act on the wealth profile they have inferred. It also occurs when wealth is inferred from ambient data, such as emails unrelated to the task. And it persists under privacy controls that block specific attributes: blocking financial attributes largely removes the disparity, but blocking other attributes leaves it unchanged and can increase it by up to 40% for insurance, as agents rely on the remaining signals to infer wealth. Larger and more capable models are no better; Claude Opus 4.8 shows the largest effect. We term this misalignment "adversarial delegation", in which the very conditions that make a personal AI agent useful - access to personal information - enable it to act against the user's interests.

Recent DESI baryon acoustic oscillation measurements, combined with cosmic microwave background and type-Ia supernova data, suggest that dark energy may evolve with cosmic time. Along a cosmological background, an evolving dark-energy density can be expressed locally as a function of a monotonic curvature invariant, motivating an effective curvature-dependent cosmological term. Moreover, quantum field theory in curved spacetime and approaches to quantum gravity with running gravitational couplings provide complementary motivations for exploring such a term. Here we study how the phenomenology of nonsingular rotating black holes embedded in a Universe dominated by dark energy can differ substantially from that of the Kerr and Kerr–de Sitter geometries. The problem is directly formulated in phase space using a null geodesic super-Hamiltonian and a Mino-type parameter. The shadows of the black holes are calculated by backward ray tracing from a zero-angular-momentum observer. We define and analyze a comprehensive set of standard shadow observables, characterizing the size, shape, and displacement of the shadow. We show that the area of the shadow and its vertical diameter provide particularly clear signatures of a running cosmological term. In this way, joint analyses of multiple strong-field observables and of several black holes with different masses and spins could provide a realistic route to tightly constraining, or potentially measuring, the effective regularization scale behind the running of the cosmological term and statistically distinguishing the non-singular black hole geometry from Kerr/Kerr-dS solutions.

(Abridged) In this work, we investigate the role of atomic hydrogen (HI) gas in the galaxy merger lifecycle. In order to both identify galaxies in mergers, as well as to predict their time since coalescence, we present an extension of the MUlti Model Merger Identifier (MUMMI) machine vision pipeline applied to Dark Energy Camera Legacy Survey (DECaLS) imaging. The new MUMMI-DECaLS catalog contains 19,951 post-mergers, of which 14,638 have robust time post-merger (T_PM) predictions. The MUMMI-DECaLS post-merger galaxy catalog is cross-matched with the Arecibo Legacy Fast ALFA (ALFALFA) survey. For the 752 post-mergers thus identified, as well as a matched control sample, we produce median spectral stacks of 21~cm emission, finding that the post-mergers are HI deficient by 0.11 dex compared with non-interacting galaxies. When divided into T_PM bins we find that the HI deficit (or excess) is strongly dependent on both the time since coalescence and whether the galaxies are star-forming or quenched. Star-forming post-mergers in particular show a strong HI evolution with T_PM, exhibiting a 0.1 dex MHI excess immediately after coalescence, a 0.3 dex MHI deficit at 0.16 < T_PM < 0.96 Gyr and normal gas masses by ~ 1.5 Gyr after coalescence. On the other hand, despite being matched in star formation rate, stellar mass and redshift, quenched post-mergers are HI deficient at both short and long post-coalescence times. Nonetheless, a significant mass of HI (>10^9 M_sun) remains even in these late-time quenched post-mergers, representing a resource which could potentially re-fuel star formation in the future. Our results demonstrate the complexity of quantifying the HI behaviour in mergers, which depends not only on timing, but also star-forming status, which can complicate comparisons between different studies and samples.

Radical truncation forgets information about a module. We study the ambiguity created by this loss: which nonisomorphic modules remain indistinguishable after all proper radical truncations have been fixed, how the resulting families are organized, and what information can be recovered from them. We introduce terminal ambiguity geometry to make this residual indeterminacy into a geometric object. The remaining ambiguity is governed by the terminal radical layer, and we classify terminal completions by Grassmannian orbit spaces, with projective ambiguity appearing as the rank-one case. This classification gives criteria for rigidity and nonuniqueness and, in the split case, determines the dimensions of the completion spaces and gives exact finite-field counts of nonisomorphic terminal completions. We also establish reconstruction and symmetry results for the rank-one projective geometry. Under suitable rank hypotheses, the ambiguity geometry recovers the corresponding residue division-algebra data, terminal species, and terminal radical layer, while its automorphisms are described by classical projective semilinear groups. Thus the paper studies both sides of radical truncation: the ambiguity produced by the information it forgets and the extent to which that information can be recovered from the resulting geometry.

In this short paper, we prove the bi-exactness of all wreath-like product groups $G\in\mathcal{WR}(A,B\curvearrowright I)$, whenever $A$ is amenable, $B$ is bi-exact, and the action $B\curvearrowright I$ has amenable stabilizers. As applications, we obtain solidity for the associated group von Neumann algebras and, by combining our result with existing rigidity theorems, new examples exhibiting the McDuff superrigidity.

In this paper, we show that the two intuitionistic modal logics IS4 and IK4 are decidable. We provide a constructive decision procedure, that, given a formula, produces either a proof showing the formula to be valid or a finite countermodel falsifying the formula, thus also proving the finite model property for both logics. The main ingredient of our strategy is the introduction of (possibly unsound) loop rules, which encode repeating behaviour in proof search. This paper fixes a previous mistake in our LICS'23 contribution.

Scientific weak signals are early, low-visibility research directions that later become central to mature scientific topics, yet existing resources such as trend tracking, citation forecasting, and foresight reports rarely provide validated reference sets that link concrete early precursors to later paradigms. We introduce BackTrend, a retrospective benchmark in which, given a mature target topic and a temporal evidence constraint, systems must recover two types of precursors: problem-space signals, underrecognized research problems, and solution-space signals, emerging methods for known problems. BackTrend contains 25 mature target topics in artificial intelligence and machine learning and 66 human-validated weak signals, reconstructed from large-scale literature by grounding each candidate in its 2019-2024 publication-frequency trajectory. We evaluate frontier LLMs, RAG systems, and agentic research systems using semantic matching and coverage-based metrics. Current systems often generate plausible but misaligned precursors, exhibiting topic drift, granularity mismatch, near-miss matching, and incomplete coverage; the strongest system achieves only 10.1% F1, while Coverage10 reaches at most 18.5% of the reference signals. Our budget analyses show that additional retrieval and web-search evidence can improve performance up to a moderate budget, but does not by itself close the substantial performance gap.

We establish a function field analogue of a recent conjecture of Andrews–Petsche. Our main result characterizes abelian dynamical Galois groups to be precisely the isotrivial ones, whenever the degree of the polynomial is smaller than $p$, the characteristic of the field. The proof of this characterization is achieved in four independent steps as follows: $$\text{Abelian} \implies \text{Finite ramification} \implies \text{PCF map} \implies \text{Isotrivial map} \implies \text{Isotrivial pair}, $$ and works more generally for maps with a superattracting fixed point. We observe that this chain of implications is sharp in the degree: as soon as one reaches $p$ there are new non-isotrivial examples coming from Drinfeld modules. We propose a full conjectural classification in all degrees, taking into account all of the new exotic examples coming from Drinfeld modules and their associated Lattès maps.

Recent advances in pixel-space diffusion models have narrowed the image quality gap with latent-space diffusion, but still converge more slowly and lag behind in final image quality. We argue that a key reason is the lack of an explicit representation prior: unlike latent diffusion, which usually denoises in a compact and structured latent space, pixel diffusion needs to learn denoising-friendly representations and pixel generation simultaneously from raw RGB space. To address this problem, we propose PixelDiT2, an end-to-end pixel-space diffusion model designed to decouple representation learning from pixel generation without introducing an autoencoder or latent reconstruction bottleneck. We propose representation grounding that uses a frozen pretrained vision foundation model to provide explicit per-patch representation guidance throughout denoising, allowing the pixel diffusion transformer to focus more on pixel generation. On ImageNet-256x256, PixelDiT2 achieves an FID of 1.46 after 600 epochs; at 512x512 resolution, PixelDiT2 achieves an FID of 1.48 after 680 epochs. Project page: https://pixeldit.github.io/pixeldit2/

Magnetars are systematically more luminous than other neutron stars. Previous studies suggest that supporting such high luminosities requires a heat source beyond standard Ohmic dissipation– the “magnetar heating problem”. We previously demonstrated using periodic box simulations that de Haas–van Alphen (dHvA) oscillations of the Landau quantization-induced magnetization in a neutron star could repeatedly generate large-gradient field components that undergo rapid Ohmic dissipation. Using the QMFM finite volume code developed for this purpose, we perform axisymmetric 2.5D electron magnetohydrodynamics plus thermal evolution simulations of a realistic neutron star crust, including all Landau quantization effects, to quantify this enhancement to field dissipation and heating of the star. We show that Landau quantization effects generate strong, small-scale magnetic field structures whose dissipation can heat the field-confined equatorial hot spot beyond its temperature in the absence of Landau quantization. Enhanced heating is greatest for weaker initial fields $B\sim10^{14}$ G, for which magnetic energy is dissipated 30% faster: in this case, the crust cools sufficiently for the dHvA oscillations to reach large amplitudes. For the stronger fields $\gtrsim B\sim5\times10^{14}$ G required to power the most luminous magnetars, the enhancement is modest, as dissipation of these fields heats the crust sufficiently to thermally suppress dHvA oscillations. In cases where heating is significantly enhanced, most of the heat goes into increasing the neutrino luminosity, and surface photon luminosity is only slightly increased. For the simple crust-confined fields that we simulated, Landau quantization-enhanced Joule heating is thus insufficient to explain the magnetar heating problem.

In 1959, Snapper showed that the Euler characteristic of the tensor powers of a line bundle on a normal projective scheme is a polynomial, later named the Snapper polynomial. Positivity of coefficients of Snapper polynomials implies various notions of positivity of line bundles, which we study through the lens of magic positivity and real-rootedness. We introduce zonotopal classes in the Grothendieck $K$-ring of vector bundles of the toric variety for any loopless matroid, and prove that their Snapper polynomials are magic positive. Our proof realizes such a Snapper polynomial as a weighted independence polynomial of the Dilworth truncation along certain lines of the matroid. As a consequence, their coefficients are positive, and their $h^{\ast}$-polynomials are real-rooted. In the realizable case, this polynomial is the multigraded Hilbert polynomial of the wonderful variety embedded in a product of projective lines. We introduce analogous line bundles on the Deligne–Mumford–Knudsen moduli space $\overline{\mathcal M}_{0,n}$ and prove that their Snapper polynomials are magic positive. For cotangent line bundles whose first Chern classes are distinct $\psi$-classes, which are not zonotopal, we nonetheless prove that their $h^{\ast}$-polynomials are real-rooted, whereas their Snapper polynomials are magic positive if and only if $n\leqslant7$. More generally, we introduce saturated and weakly saturated $K$-classes of matroids, which furnish a sufficient and a necessary condition for magic positivity of Snapper polynomials in terms of their dragon Hall–Rado polymatroids.

Combining scanning tunneling microscopy (STM) with terahertz pulses (THz-STM) enables ultrafast dynamics of phonons, spins, and charge carriers to be probed with atomic-scale spatial and sub-picosecond temporal resolution. However, coupling THz radiation into a low-temperature STM junction presents some technical challenges as it requires optical access for laser illumination while maintaining junction stability. Instead of designing a completely new STM head with customized optical access and optics within the ultra-high vacuum chamber, we modified a Besocke "Beetle" style STM with minimal changes of the cryogenic radiation shields. Despite the given geometrical conditions, we achieved efficient coupling of THz and optical pulses to the STM junction while maintaining temperatures below 6 K. We designed the optical setup on a separate laser table, starting with femtosecond laser pulses that are used to generate THz pulses in a LiNbO$_3$ crystal. We show the obtained THz pulse shapes and determine the effective time resolution using cross-correlation measurements. We further demonstrate the stable performance of the modified STM by measuring THz-induced tunneling currents from monolayer molybdenum disulfide (MoS$_2$) grown on Au(111). The resulting current maps resolve atomic-scale contrast revealing a point defect. The measurements confirm efficient THz coupling and stable low-temperature STM operation with atomic resolution.

Fisher-information-based optimization of programmable optical front ends in situ generally requires a response model or parameter-labeled measurements. We show that natural parameter fluctuations can instead provide the training signal. We construct proxies for the Fisher information (FI) of one parameter and the prior-weighted FI spectrum of multiple parameters from measured covariances after subtracting conditional detection noise, assuming locally affine responses. We use simulated photon counts from two incoherent point sources to train a mode sorter that approaches the quantum limit for separation and the Nagaoka–Hayashi single-copy bound for joint centroid–separation estimation. We demonstrate count-only updates that require no instrument response model and achieve performance comparable to model-based gradients. Our results provide a route to adaptive optical measurements without controlled parameter scans.

Microscopic black holes may form at the centers of neutron stars through the accumulation and collapse of dark matter. While Standard Model particles produced by Hawking evaporation are efficiently absorbed by the dense stellar medium, sufficiently weakly interacting and long-lived particles can escape and subsequently decay into high-energy neutrinos, photons, or charged particles, providing an indirect probe of Hawking radiation. We examine the joint energy–angular distribution of these secondary particles, incorporating mediator propagation, energy-dependent decay, and relativistic decay kinematics. For relativistic mediators, the normalized energy-integrated angular profile becomes approximately independent of the black hole temperature, with its characteristic extent controlled primarily by the combination $c\tau_S/D$ of the mediator lifetime and source distance, as the boost enhancement of the decay length is compensated by relativistic beaming. We demonstrate the viability of this mechanism and illustrate its phenomenology with gravitationally coupled scalars, axion-like particles (ALPs), dark photons, and heavy neutral leptons. Comparing with monochromatic mediator production from dark matter annihilation, we find that the energy-integrated angular profiles can be nearly degenerate, while the energy spectra and energy-resolved angular distributions remain distinct. Although the predicted signals may lie beyond the reach of current observatories, these complementary spectral and angular signatures provide potential targets for future high-energy neutrino and gamma-ray searches.

Boson stars are self-gravitating solitons of the Einstein-Klein-Gordon equations for a massive complex scalar field, and arguably the simplest horizonless compact objects arising in General Relativity. Beyond spherical symmetry, their construction requires solving a system of nonlinear elliptic partial differential equations, a difficult task per se and that each group has traditionally addressed with its own numerical implementation. A systematic comparison of different methods applied to the same physical model has so far been lacking. In this work, we carry out such a comparison for the two simplest non-spherical configurations: rotating boson stars and static dipolar boson stars. We employ three independent codes, based respectively on finite differences (FIDISOL/CADSOL), finite elements (FreeFem), and spectral methods (Kadath), and assess their accuracy through different diagnostics. The three solvers agree on the global observables to typically eight significant digits. We further compare the runtime of each code on identical hardware and provide precise benchmark values of the relevant physical quantities, intended to serve as reference data for future numerical studies of boson stars. As a further proof of concept, we also present the use of physics-informed neural networks to construct a rotating Q-ball solution.

Inflation driven purely by the quantum running of the curvature-squared couplings of quadratic gravity was shown to accommodate the high scalar tilt favored by recent cosmic microwave background observations, starting from a Euclidean four-sphere at a maximum of the running $R^2$ coupling. That maximum exists only in one renormalization scheme, and is not stationary once the Euler trace anomaly is included. We show that the standard one-loop running, with the usually neglected Gauss–Bonnet coefficient retained, recovers the missing de Sitter state: the Euler running balances the scale dependence of the $R^2$ term at a unique coupling ratio, giving a de Sitter solution that is stationary for the gravitational constraint and for the compact Euclidean action alike, and whose scalaron potential is an extremely flat hilltop ($m^2/H^2\simeq-5\times10^{-10}$) joined to an inverse-linear inflationary plateau. The last $N_*\simeq50$–$60$ $e$-folds are scheme independent, with scalar tilt $n_s\simeq1-4/(3N_*)$, while the tensor-to-scalar ratio, $r$, is set by the number of matter fields that enhance the running. The current tensor bound excludes pure gravity and sets a minimum matter content, some $4\times10^6$ conformally coupled scalars or $3\times10^5$ vectors—$2.6$ times fewer than the momentum-induced scheme requires—while one-loop control to the end of inflation sets a maximum about ten times higher. Across that window the model predicts $r\gtrsim0.008$ with $0.973\lesssim n_s\lesssim0.978$, within reach of upcoming CMB polarization surveys.

Social simulation offers the social sciences an experimental instrument that the real world cannot supply, and generative agents have transformed it by acting as silicon samples that unite agent-based modeling with real behavioral data. Existing platforms verify collective behavior, align simulated populations with real societies in cross-sections, and employ autonomous agents for the research process. However, two social science requirements remain without systematic support: intervention in the content of a simulation and the researcher's control over the process that produces it. We present SocioVerse2, which extends SocioVerse 1.0 into a human-AI co-evolutionary paradigm built from two loops and one infrastructure. The longitudinal simulation loop simulates the target population with evolving environments and forks counterfactual branches via interventions. The controllable research loop takes the study itself as an editable state and updates state versions via controllable editing. The social science agentic infrastructure carries both loops through composable skills with researcher checkpoints, a population service over five persona pools, and an environment service over 21 real-world signal sources with point-in-time guarantees. We validate SocioVerse2 across three case families and seven case studies, from reproducing canonical agent-based models to modeling policy processes on real records and nowcasting macro-economic indices beyond the response model's knowledge cutoff. With the human-AI co-evolutionary paradigm, these cases go beyond system demonstrations to become substantive studies that investigate frontier questions in their respective disciplines. Code, data services, and a workbench are released as open-source resources.

In this contribution I present a calculation of the inclusive cross-section for the associated production of a top-anti-top pair and a W boson at next-to-next-to-leading order in QCD, based on the first exact computation of the two-loop QCD amplitude at leading colour. I discuss a strategy to express the amplitude in terms of a set of special functions with rational coefficients, overcoming the obstacle posed by the presence of elliptic functions. The special functions are evaluated through the method of differential equations, while the rational coefficients are computed using finite field techniques. For the computation of the inclusive cross-section, the double-virtual correction is evaluated by interpolating a five-dimensional grid.

We prove that the cone $C(\Sigma)$ in $\mathbb R^4$ over a suitable minimal Möbius band $\Sigma\subset \mathbb S^3$ is locally mass-minimising with coefficients in $\mathbb Z_2$. This proves a conjecture by Brian White in the context of models of boundary singularities of Plateau's problem in ambient dimension $4$ or higher. The key insight is that the cylindrical slices $C(\Sigma)\cap \{(z,w)\in \mathbb R^2 \times \mathbb R^2 : |w|=r\}$ are minimal surfaces in a flat rank-one translation quotient of $\mathbb R^3$. In fact, they correspond to non-orientable minimising helicoids previously studied by Antonio Ros. We also show that, up to rigid motions, the minimising cones $C(\Sigma)\times \mathbb R^{n-4}\subset \mathbb R^n$ are the only non-planar minimal hypercones with boundary $\mathbb R^{n-2}$ which are smooth away from the boundary that satisfy the minimal cylindrical slice property.

The best constructive lower bounds on the capacity of the binary deletion channel come from random codes with independent run lengths, yet the two strongest such bounds, due to Drinea and Mitzenmacher and to Venkataramanan, Tatikonda, and Ramchandran, have been evaluated mainly for geometric or low-parameter run-length laws. We let a learning algorithm choose the run-length law freely, which raises three challenges. First, the Drinea-Mitzenmacher functional is an infinite sum over the ways deletions merge runs; we show that it depends on the law only through its mean, its full-deletion probability, and bilinear forms in the law and its renewal weights, so that gradients of truncations are exact and every truncation can only lower the bound. Second, for non-Markov inputs the output is no longer Markov and the Venkataramanan-Tatikonda-Ramchandran analysis breaks down; we show that the residual length of the current input run turns the output into a hidden Markov chain, which extends the bound to every finite-support law. Third, its correction term counts only output runs formed from three input runs; we prove a larger correction that accounts for every output run formed by several input runs, which improves the published bound even for truncated geometric laws. Certified by interval arithmetic, the new bounds exceed all previously published deterministic lower bounds at every tabulated deletion probability, by up to $6.86\times10^{-3}$ bits per channel use and 6.8%. At large deletion probability the learned laws concentrate on run-length clusters with survivor counts about two standard deviations apart, like a pulse-amplitude constellation.

Nucleosomes are structures made up of proteins called histones that bind and compact DNA, driving the mesoscale organization of the chromatin polymer. Although histone proteins have diversified over evolutionary time, their contributions to the corresponding diversification of chromatin structure are poorly understood. Here, we mine protein databases for histones and create in silico nucleosomes for 3241 organisms spanning $>$1.5B years of evolution. Using a combination of electrostatic calculations and coarse-grained molecular dynamics simulations, we reveal extensive biophysical diversification of the nucleosome unit. Finally, we perform coarse-grained oligonucleosomal simulations on a subset of evolutionarily and biophysically divergent nucleosomes, demonstrating dramatic differences in bulk phase behavior of chromatin. Taken together, our results suggest a paradigm in which histones may have evolved to facilitate particular types of mesoscale chromatin behavior.

Dormant tree pruning is labor-intensive yet essential for maintaining modern high-productivity fruit orchards. In this work, we focus on pruning of modern planar tree training systems - V-Trellis apples and UFO cherries - where trunks and primary branches are trained into approximately planar walls. We introduce an end-to-end pipeline to learn a closed-loop visuomotor controller for robotic pruning. This controller is trained entirely using simulation and synthetically generated data and deployed in real orchards in a zero-shot manner. The pipeline comprises synthetic generation of planar orchard tree meshes, construction of a physics-based orchard simulator, automated collection of successful pruning trajectories via motion planning, and policy learning with a novel hybrid reinforcement-learning algorithm that combines offline demonstrations with online simulated rollouts. The controller uses optical-flow inputs from a wrist-mounted camera - avoiding the need for full 3D-reconstruction - and continuously guides the cutter through cluttered branch environments to a specified cutpoint with correct tool orientation. In exhaustive simulated task-space evaluations over 3,000 pruning points, the policy attains 49.9% success on V-Trellis apples and 46.0% on UFO cherries. We validate the learned controller across 38 physical trials - comprising 28 outdoor field trials in commercial and experimental orchards and 10 indoor laboratory tests - demonstrating zero-shot sim-to-real transfer. The learned policy also outperforms a classical RRT-Connect baseline on physical hardware in laboratory trials.

The quantum metric quantifies the total ground-state response along a parameter direction, but does not resolve how excitations share that response. We define channel concentration (CC) as the sum of squared normalized response weights over specified excitation channels, such as momentum blocks. An exact finite-size theorem yields thermodynamic CCs of 2/3 for the field response of the critical transverse-field Ising model and 1/3 for the half-filled XX pairing response, despite the same leading metric scaling. In finite-size approaches to the XY Lifshitz point, field and anisotropy perturbations yield different concentrations despite a common limiting Hamiltonian with quadratic dispersion. In a unitary 1+1-dimensional conformal field theory (CFT) on a circle, we consider a nondegenerate vacuum in a fixed sector perturbed by one spatially integrated scalar primary. We derive complete zero-momentum energy-level response weights, including descendants. For scaling dimension $0<\Delta<3/2$, these weights determine the normalized response distribution and an exact universal concentration function. The expression reproduces the exact Ising lattice limit 2/3 and gives approximately 0.8515 for the three-state Potts thermal field, compared with approximately 0.800 from an exponent-only approximation. Finite-size interacting calculations compare concentrations and ranked response weights over many-body energy levels. These exact benchmarks show which response distinctions total metric scaling misses and guide comparisons with finite-size interacting spectra.

The demands of modern applications require the construction of ever more complex integrated systems, with AI applications in particular serving as a significant driver for increased system size, potentially going beyond the trilliontransistor mark. The path to building these systems requires the use of advanced packaging, with heterogeneous integrated 2D and 3D chiplets placed atop a substrate. Such computationally powerful systems require significant power for computation: reliable and robust power delivery is a major challenge in light of high power densities and pin count bottlenecks. This paper overviews approaches to building design methodologies that overcome this problem, through the design of multistage distributed power delivery systems, optimized for performance and reliability, and built to coexist within stringent performance, thermal, and reliability constraints.