Papers

Auto-bidding is now widely adopted in online advertising platforms, allowing advertisers to specify high-level campaign objectives–such as maximizing total value subject to a return-on-spend (ROS) constraint–rather than manual per-query bids. A central question in algorithmic mechanism design is characterizing the worst-case efficiency loss, or Price of Anarchy (PoA), across auction formats in this prior-free setting. While randomized auctions are known to strictly improve efficiency over deterministic mechanisms for two bidders, two fundamental questions have remained open: (1) what is the optimal PoA for two bidders, and (2) can any mechanism beat the barrier of 2 for general $n \ge 3$ bidders? We resolve both questions using the family of $r$-proportional first-price auctions ($\text{pFPA}_r$), in which each bidder wins with probability proportional to their bid raised to an exponent $r > 0$ and pays their bid upon winning. First, for two bidders, we prove that the standard proportional first-price auction ($r = 1$) achieves a tight $\text{PoA} \le 1.5$, complemented by a matching lower bound showing that no anonymous, monotone mechanism can do better. Second, for general $n \ge 2$ bidders, setting $r = 2n$ achieves $\text{PoA} \le 2 - \frac{1}{4n+1} = 2 - \Omega(1/n)$ across all undominated bid profiles, breaking the deterministic barrier of 2 for every finite $n$ and asymptotically matching the known $2 - \Theta(1/n)$ lower bound.

We present Cascadia, a system for serving large language models on fleets of commodity Intel AIPCs using their CPU, integrated-GPU, and NPU resources. Every node embeds ingress, scheduling, and execution; inference requests require no dedicated routing control plane. Nodes join a libp2p QUIC mesh using CA-issued ed25519 admission certificates, gossip signed capabilities, exchange live load over direct peer streams, and route OpenAI-compatible requests to eligible peers. An operator-run certificate authority handles admission and fleet management outside the inference path. Three serving modes share one interface: whole-model execution on one node, load-balanced replicas, and pipeline-sharded chains using the compilation and speculative decoding mechanism of our companion paper. Optional KV-cache mobility reuses compatible conversation prefixes after a routing move, with cold recomputation on a miss. Signed response receipts and hash-chained logs support provenance and audit. A three-node Phi-3.5-mini NPU testbed delivered 3.10x the response throughput of its one-node configuration under ten concurrent requests; a separate four-node deployment recorded 4.06x the throughput of direct single-node serving. Paired latency observations, runtime measurements, and internal functional checks characterize the tested configurations. We compare Cascadia with IBM, Nutanix, VMware, and HPE platforms on deployment footprint, hardware requirements, scheduling, scaling, licensing, and trust, using vendor documentation. The paper repository provides benchmark scripts, curated measurements, and a claim-to-evidence map.

Let $\Sigma_{1} = \mathbb{N}^*$ and $\Sigma_{k+1} = \overline{\mathbb{N}^* + \Sigma_{k}}$ be the cumulative depth filtration of $\beta\mathbb{N}$, the analogue for $(\mathbb{N},+)$ of a chain of closed ideals that Protasov and Protasova studied for discrete groups, where strict descent follows from a theorem of Lutsenko and Protasov. For every $k$ we give an explicit set whose closure meets $\Sigma_{k}$ but not $\Sigma_{k+1}$. Fix the doubly exponential sequence $e_{n} = 2^{2^{n}}$, partition it into $k$ subsequences $E_{0}, \dots, E_{k-1}$ by the residue of the index modulo $k$, and set $A_{k} = E_{0} + \cdots + E_{k-1}$. We prove that any sum $q_{0} + \cdots + q_{k-1}$ of free ultrafilters with $E_{t} \in q_{t}$ lies in $\Sigma_{k} \setminus \Sigma_{k+1}$. The engine is a master lemma, proved by induction on $j$: if a sum $F_{1} + \cdots + F_{j}$ of subsequences of $\{e_{n}\}$ with pairwise disjoint index sets belongs to a free ultrafilter $s$, then $s \notin \Sigma_{j+1}$. The proof rests on a single rigidity of the doubly exponential sequence: a fixed difference forces the largest index in any shift-intersection, once it is large, to cancel within its own subsequence, which makes every shift-intersection descend by at least one level. The same witnesses lie in the gaps of the pure filtration.

Generative AI has dramatically accelerated the rate at which new treatments—from novel pharmaceuticals to online marketing campaigns—can be conceived and deployed. As a result, modern experimentation platforms often run continuously, with treatments added as they are ready and removed when they underperform. We formalize this "Always-On" experimental setting, in which treatments can be dynamically generated, added to, and removed from a running experiment, and study the statistical problem of deciding whether to accept or reject each treatment while controlling for the false discovery rate. We develop sequential tests that achieve time-uniform Type-I error control under arbitrary stopping times and "predictable" treatment schedules. Our approach builds on the testing-by-betting framework: we construct test supermartingales for testing the average treatment effect of each treatment, and show that the construction of these test supermartingales is growth-rate optimal in an almost-sure sense.

ESO 243$-$49 HLX–1 is one of the first known compelling intermediate-mass black hole (IMBH) candidates, but the origin of its recurrent X-ray outbursts remains unsettled. In this work we fit the HLX–1 outbursts simultaneously with a relativistic thin-disk time-dependent model. The black-hole and disk-geometry parameters are tied across epochs, while the injected mass and timing parameters are fitted separately for each outburst. We also include a contemporaneous HST UV/optical/IR spectral energy distribution obtained near the peak of one outburst, which constrains the global temperature and radius scales of the disk. The soft-state data are consistent with a common global solution, with black hole mass $\log_{10}(M_{\bullet}/M_\odot)=4.5\pm0.2$ and disk formation radius $\log_{10}(r_0/r_g)=3.8\pm0.3$. The differences between outbursts are mainly described by modest changes in disk mass and viscous timescales. The inferred injected masses are typically $\sim 10^{-3}\,M_\odot$ per outburst, requiring a total fuel supply of at least a few $\times 10^{-3}\,M_\odot$ across the observed sequence. This mass scale, and the disk size, are consistent with repeated partial stripping of a low-mass donor. A simple Keplerian mapping of the flare gaps and fitted disk radius implies a highly eccentric orbit with a pericenter just outside the donor's tidal radius. These results support a repeating partial tidal disruption interpretation for the origin of HLX–1.

Batting average factors exactly as BA = c times f, where c = (AB - SO)/AB is the rate of avoiding a strikeout and f = H/(AB - SO) is the rate at which non-strikeout at-bats become hits. Using the 256 major-league hitters with at least 300 at-bats in 2025, we show that the two factors behave very differently. Strikeout avoidance is highly repeatable, with a median year-to-year correlation of 0.86 over 19 consecutive-season pairs from 2004 to 2025. The finishing rate is not: its median correlation is 0.44, and batting average itself (0.44) is no more repeatable than its noisier factor. A bivariate logistic-normal random-effects model fit to the 2025 season estimates the correlation between the two talents at -0.68 (95% profile interval -0.85 to -0.50), far stronger than the raw correlation of -0.44, and implies single-season reliabilities of 0.91 for c and 0.37 for f. The model also yields a closed-form bivariate shrinkage estimator in which a hitter's strikeout rate informs the estimate of his finishing rate. Applied to decades of American and National League data, the decomposition revisits Gould's explanation for the disappearance of the .400 hitter. Since the dead-ball era, the talent variance of strikeout avoidance has grown roughly 4.6-fold while that of finishing has halved, and the correlation between them has moved from near zero to about -0.53. That emerging trade-off, rather than a general narrowing of talent, accounts for the reduced spread of modern batting averages.

Imputation-based causal estimation is typically viewed as relying exclusively on an outcome model, in contrast to augmented inverse-probability weighting, whose consistency is protected by fitting two nuisance models. This paper argues that this view can be misleading by highlighting a hidden dual weighting structure in least-squares sieve regression imputation. Although only outcome regressions are explicitly fitted, the resulting imputation estimator admits an exact weighting representation whose induced weights balance every function in the sieve space and the corresponding population weighting functions are the $L^2$ projections of the inverse propensity scores onto the same sieve space. This projection structure yields an implicit form of double robustness and, under standard sieve approximation and growth conditions, asymptotic linearity with the efficient influence function. Thus, weighting, covariate balance, double robustness, and semiparametric efficiency can all emerge from imputation alone through the geometry of least-squares projection.

Streaming video generators allow users to dynamically modulate video synthesis via mid-stream prompt switching. Existing streaming methods can respond to the updated instruction while still cutting corners, prematurely realizing goals or taking heuristic shortcuts that bypass necessary intermediate state changes needed for a plausible transition. In this study, we present SEGUE, a novel framework that makes this process explicit and trains the generator to execute these transitions faithfully. At each switch, a training-free planner parses the latest frame and prompts, writes a few segue prompts with roles and durations, and then hands control back to the user's prompt. Furthermore, to address the inherent difficulty of training causal models on short-lived temporal schedules without corrupting preparatory supervision, we introduce SPANDMD, which evaluates each active prompt using the full rollout as temporal context while retaining its DMD residual only within the prompt's assigned span. On OpenTrans-360, a benchmark of 1,800 switches that scores how the old state exits and the new one begins, SEGUE ranks first on all eight transition metrics and raises the overall score over the strongest baseline from 0.866 to 0.887. It also ranks first on four of six instruction-response metrics of StreamAV-Bench, while the planner transfers to frozen autoregressive generators without retraining. Project Page: https://anonymous.4open.science/w/No-Corners-Cut-6C5D/

Spatial transcriptomics enables spatially resolved gene expression analysis from slide-level images while preserving morphological features, providing valuable information for studying disease mechanisms and developing treatments. However, spatial gene expression profiling typically requires expensive and time-consuming tests. While existing image-based prediction optimizations mostly revolve around including positional embeddings and further image-based changes, text-based optimizations remain relatively unexplored. We present GATE-ST, which incorporates text-based inputs into image-based spatial gene expression predictions. With this approach, generated text descriptions of genes are utilized to better spatial transcriptomics prediction results. Gene summaries are put through a text encoder, generating embeddings that integrate with image embeddings through cross-attention layers to align with morphological features. We demonstrate the effectiveness of such text inputs by benchmarking performance against random gene embeddings and multiple other image-text fusion architectures, and show that GATE-ST outperforms these alternatives. Our results demonstrate the effectiveness of GATE-ST in pathology imaging, which may greatly reduce the time and cost of accurate spatial transcriptomic predictions, proving the potential of text-guided spatial gene expression prediction.

Immersive displays can enable rich and diverse virtual experiences. Manually authoring every possible experience to realize this potential, however, is prohibitively expensive, difficult to scale, and impractical. Generative AI models could remove this bottleneck, but today's models are built for conventional displays and cannot generate the high-resolution, stereoscopic $360^\circ$ content required for immersive viewing. Further, temporal and stereo inconsistencies that may be tolerable on conventional displays can become highly disruptive when viewed through an immersive headset. Here, we address this gap with a zero-shot generative pipeline that extends existing video diffusion models into 4K stereoscopic $360^\circ$ videos. Inspired from binocular vision and depth perception, we develop an epipolar-aware $360^\circ$ image matching metric that captures the temporal and stereo geometric inconsistencies across views. We then use this metric as a preference signal for direct preference optimization with limited training data. Our work enables $360^\circ$ stereo video generation and provides a scalable path for bringing generative content to immersive displays, allowing diverse mixed reality experiences on demand.

In liquid ammonia, an imbalance between available hydrogen-bond donor and acceptor sites limits water-like tetrahedral connectivity, leaving sparse and short-lived associations within a densely packed liquid. We ask whether quantum-sensitive local rearrangements can nevertheless contribute appreciably to diffusion in this weakly connected liquid. We compare classical and thermostatted ring polymer molecular dynamics from 170 to 250 K using an r$^2$SCAN-trained machine learning force field. Ammonia can change its molecular geometry as the nitrogen atom passes through the plane of the three hydrogen atoms, a motion known as pyramidal inversion. Nuclear quantum effects increase the inversion rate and reduce its apparent activation energy. Inversion events are accompanied by transient reductions in hydrogen-bond coordination and local density within the first solvation shell. Although nuclear quantum effects lower density and viscosity throughout the studied range, diffusion remains only weakly affected in the warmer liquid. The quantum enhancement of diffusion emerges below approximately 210 K and reaches 18% at 170 K, tracking the enhancement of cage escape. These observations support an inversion-assisted contribution to diffusion, in which a spatially localized, quantum-sensitive internal motion couples to cage relaxation without a persistent tetrahedral network.

Integrated quantum photonics benefits from photon-pair sources that generate photons directly in waveguides, where they can be efficiently collected, routed, and manipulated. Here, we investigate spontaneous four-wave mixing (SFWM) in a fused tapered-fibre microcoupler formed from two single-mode fibres, and report four contributions. First, we observe SFWM photon pairs in this multimode device: its elliptical central region supports three spatial mode profiles, each with two polarisations, giving six guided modes, and pumping it near 800 nm yields two photon pairs at 648/1048 nm and 660/1021 nm. Second, because several allowed SFWM processes produce similar wavelengths and wavelength alone does not identify their origin, we distinguish the processes by combining phase-matching calculations and selection rules with two independent polarisation measurements: the dependence of the coincidence rate on pump polarisation and polarisation tomography of the generated photons. Third, within the present geometrical model, we find that the 660/1021 nm pair is generated by co-polarised pump photons in a process occurring entirely within a single higher-order mode, whereas the 648/1048 nm pair is generated by orthogonally polarised pump photons in an intermodal process coupling a fundamental and a higher-order mode; the signal photons from the two processes have similar output polarisations, while the idler photons are nearly orthogonal. Fourth, extending the analysis beyond the measured operating point, we theoretically identify pairs of simultaneous SFWM processes driven by a common pump that could generate either polarisation entanglement or composite spatial-polarisation entanglement, depending on the pump wavelength. More generally, this work provides a practical strategy for identifying intermodal SFWM processes in multimode waveguides when spectral information alone is insufficient.

We develop a new algorithm for counting the number of subgraphs of a network isomorphic to a given query graph (#SubgraphIsomorphism), motivated by network motif search. High-degree vertices (hubs), common in real-world networks, contribute to a combinatorial explosion in the number of subgraphs, making existing motif search algorithms intractable for motif sizes greater than $\approx 8$ on a wide variety of networks of interest. Our procedure leverages the $k$-core decomposition and a novel subtree-counting technique to quickly scan the periphery of a network. These two innovations allow our algorithm to significantly speed up its predecessors in practice, especially as most real-world networks have a relatively large periphery. We prove that #RootedSubtreeIsomorphism, a key subroutine in our algorithm, is #P-complete via a reduction from counting bipartite matchings. We provide analytic upper bounds on our algorithm's execution time, and evaluate its performance on 11 real-world networks of varying topologies.

In this paper, we develop a new auction-based framework for matroid intersection and use it to obtain improved approximation algorithms in several computational settings. Our framework is inspired by Fleiner's generalized stable matching algorithm and extends the semi-streaming auction algorithm for bipartite matching due to Assadi, Liu, and Tarjan. Using this framework, for any $\varepsilon > 0$, we present a simple $(1-\varepsilon)$-approximation algorithm in the rank-oracle model whose query complexity matches that of the current fastest algorithm. Furthermore, by extending this result, we obtain the first $(1-\varepsilon)$-approximation algorithm for the weighted problem that requires only a near-linear number of rank-oracle queries, achieving the best known rank-oracle query complexity for the problem. We also obtain a $(1-\varepsilon)$-approximation semi-streaming algorithm for matroid intersection in the multi-pass streaming model, where the elements of the ground set arrive sequentially. It is the first algorithm achieving this approximation ratio using a constant number of passes and nearly linear space in the ranks of the matroids. When viewed in the standard offline setting, the same algorithm yields the first deterministic $(1-\varepsilon)$-approximation algorithm for matroid intersection that requires only a near-linear number of independence-oracle queries.

Knowledge-intensive language-model systems typically represent external knowledge as text chunks or static graphs, with limited support for concept evolution, point-in-time reasoning, and distinctions between validated and inferred knowledge. We introduce the Concept Lifecycle Model (CLM), which represents concepts as persistent, graph-grounded, temporally versioned entities with explicit provenance and epistemic status, and Concept-Grounded Attention (CGA), which injects concept-graph structure into transformer computation through graph-biased self-attention (Form A) and gated cross-attention over concept nodes (Form B). We evaluate the framework in controlled settings using disabled-mechanism baselines. On 200 MuSiQue and HotpotQA questions with retrieval fixed, concept-graph retrieval recovers explicit multi-hop paths but does not improve evidence recall. Form A appears to steer attention, with 2.76 times more attention on gold than distractor concepts, but the same ratio occurs when Form A is disabled; the learned bias is negligible and no answers change. An identity-preserving Form B improves F1 from 0.188 to 0.221, but control concepts yield 0.213, indicating that most of the gain reflects added capacity. On LongMemEval, explicit temporal representation improves answer accuracy by 13 to 25 points across all tested generators, up to 122B parameters, while simplified CLM version resolution performs similarly to dated serialization because concept identity is not established reliably. On a synthetic source-independence task, protocol-derived epistemic status reduces unsupported assertions from 28% to 0.1% in a fine-tuned small model and from 19-68% to 0-5% in 72-122B models. Overall, the results support making temporal validity and epistemic status explicit, while showing that graph-attention diagnostics are not informative without disabled-mechanism controls.

Cinematic camera motion is a fundamental storytelling tool, defined not only by where the camera is positioned in the scene, but also by how it moves in terms of direction and speed. Recent work on camera trajectory generation and alignment to text relies on pose-centric representations. While in principle a network could derive direction of movement and speed, we find that in practice this might not happen. In fact, in this paper we discover that decomposing the camera trajectory representation from the traditional per-frame poses to direction and speed has surprising benefits across multiple tasks, including trajectory-to-text alignment as well as text-to-trajectory generation. To accurately evaluate the former, we introduce a simple and reliable protocol that overcomes the limitations of prior evaluation baselines. For the latter, building on this representational insight, we propose a novel generative model for camera trajectories, CineGEN, that achieves superior performance across a variety of metrics. We also propose a novel dataset, CineScript, containing movie clips that are enriched with scene descriptions as well as higher-level metadata. This novel data allows us to test models' ability to capture high-level cinematographic information. We show that, despite its simplicity, representing camera trajectories through direction and speed not only helps numerically to achieve better alignment and generation, but also inherently encodes complex directorial intent.

The neutron star merger event GW170817 provided the first direct evidence of $r$-process nucleosynthesis. Observed spectra of its electromagnetic counterpart AT2017gfo exhibited several features that encode information on the nature and abundance of the synthesized $r$-process elements. In this study, we investigate the late nebular-phase spectral features of AT2017gfo, which provide important probes of the elemental abundance of the ejecta. We construct an analytic spectral model that computes emission features produced by the radiative decay of collisionally excited ions through allowed and forbidden transitions. By comparing our model to AT2017gfo, we identify La III and Ce III as the main contributors to the emission features at $1.4\,\mu{\rm m}$ and $1.6\,\mu{\rm m}$, respectively. We also confirm Te III as the dominant contributor to the $2.1\,\mu{\rm m}$ feature proposed in previous works. We infer mass fractions of $X({\rm La})\approx 0.025-0.05$, $X({\rm Ce})\approx 0.05-0.1$, and $X({\rm Te})\approx 0.04-0.08$, although the La and Ce abundance estimates remain tentative due to uncertainties in the radiation field. From the non-detections of Kr and Sb lines, we derive upper limits of $X({\rm Kr})\lesssim 0.03$ and $X({\rm Sb})\lesssim 0.003$. These results suggest that nucleosynthesis in the inner ejecta of GW170817 produced a suppressed first $r$-process peak and an enhanced heavy-element abundance compared to the solar $r$-process pattern, with an estimated lanthanide fraction of $X_{\rm LN}\approx (3-6) \times 10^{-2}$. Our conclusions are consistent with the apparent universality of heavy $r$-process elements and the lanthanide fraction inferred from observations of $r$-enhanced metal-poor stars.

We develop a three-stage adaptive procedure for principal component analysis (PCA) when high-dimensional observations are collected sequentially and additional sampling incurs a cost. The procedure balances PCA compression loss against sampling cost while selecting the retained dimension through a prescribed explained-variance criterion. Starting from a pilot sample, an intermediate stage updates the PCA quantities before determining the final sample size, thereby avoiding reliance on unknown population eigenvalues. Under suitable regularity conditions, we establish both first- and second-order efficiency relative to the population oracle. Comparison with the corresponding two-stage rule shows that the additional recalibration yields sharper second-order control and reduces the influence of the pilot stage on the final sampling decision. The theory allows the ambient dimension to exceed the sample size under appropriate covariance and spectral conditions. Simulation studies demonstrate the strong finite-sample performance of the procedure across increasing dimensions and several dense covariance structures. As a real-data application, we conduct a retrospective study of gene-expression data from 32 cancer-type cohorts in The Cancer Genome Atlas, illustrating both cost-effective early stopping and settings in which additional observations are recommended.

Text-to-image diffusion models are personalized to a subject by DreamBooth fine-tuning on a handful of its images. Increasingly, these images come from a diffusion model rather than a camera. We show that fine-tuning on such synthetic images degrades subject fidelity, producing oversaturated color and excess high-frequency detail. To isolate the cause, we fine-tune two models from the same base model with the same DreamBooth recipe, one on real photos of a subject and one on synthetic images of that subject generated by the first. We trace the degradation to classifier-free guidance (CFG). For the model personalized on synthetic images, the angle between the conditional and unconditional noise predictions, and with it the norm of their difference, is much larger than for the model personalized on real photos. This inflation grows toward high frequencies and also appears at other prompts semantically close to the subject, such as its class noun, but not at unrelated ones. We propose ReGain, a training-free correction applied at sampling time that measures how much each frequency band of the guidance is inflated relative to the base model and scales that band down accordingly. ReGain needs no real photos. On Stable Diffusion v1.5, ReGain closes 51-64% of the subject-fidelity gap to the model personalized on real photos, as measured by DINO, DINOv2 and CLIP-I. It also improves subject fidelity on SDXL and SD 3.5 and preserves text alignment on all three backbones.

The solid electrolyte interphase (SEI) is essential for the long-term stability of batteries because it influences the reactions between the electrode and electrolyte. Despite previous studies, the SEI evolution from dense to porous phases remains incompletely understood. Here, we investigate the SoC-dependent evolution of the SEI using a phase-field framework under open-circuit conditions. Spatially correlated noise is introduced to describe stochastic transport perturbations, and the dense-to-porous transition time is evaluated from the evolution of interface roughness arising from the competition between noise-induced transport and surface relaxation. The simulations reveal three distinct roughness evolution regimes. The predicted transition time generally increases from approximately one month at 20% SoC to more than seven months at 80% SoC, with a pronounced change between 55% and 60%. This change corresponds to the graphite SoC-OCV relation, which controls the interfacial Li0 radical concentration through the Nernst condition. Under dynamic SoC conditions caused by irreversible capacity loss, the transition behavior changes as the SoC evolves during storage. These results show that the SoC-OCV relation is central to determining SEI phase stability and the dense-to-porous transition time under open-circuit storage.

Quantum sensing traditionally focuses on using quantum resources such as squeezing and entanglement to improve precision for sensing fixed signals. However, in many applications such as gravitational-wave detection and electromagnetic-field sensing, the signal evolves continuously and varies through time. Additionally, the learner is free to prepare, control, and measure the sensor at arbitrary times, possibly chosen adaptively. In this work, we establish exponential separation in sensing time for continuously evolving signals due to the available squeezing. The signals we study are characterized by a pattern size $T$, and we find that a sensor with squeezing at least $\omega(\sqrt{\log T})$ offers a $\mathrm{poly}(T)$ sensing time, whereas those with squeezing at most $o(\sqrt{\log T})$ must use an exponential sensing time in $T$.

We prove that Parity requires $2^{n^{\Omega(1)}}$ size De Morgan circuits of constant depth using a new method which is completely "top-down" in the sense of [HJP95]. The proof relies crucially on the core ideas developed in a line of work [HJP95, PPZ99, MW19, GRSS24] which previously established top-down lower bounds for circuits of depth 3 and 4. We first present a proof of a lower bound $\exp(n^{3^{-d}})$. In this case, nearly all of the relevant combinatorial ideas necessary for the proof are already present in some form in [GRSS24]. We then present two extensions of this argument, the first achieving a lower bound $\exp(\epsilon_d n^{1/(2d-2)})$ for some $\epsilon_d>0$ depending only on $d$, and the second achieving the essentially tight lower bound $\exp(\epsilon_d n^{1/(d-1)})$. These improved results each hinge on establishing a key lemma which quantifies the extent to which a high entropy random variable in $\{0,1\}^n$ will look close to uniform after projecting it onto a random small set of coordinates $R \subseteq [n]$.

In a bulk ferromagnet, magnetic energy is six orders of magnitude weaker than elastic energy. Slenderness removes this disparity. In a thin ferromagnetic rod, the two energies scale differently with aspect ratio, and an ordinary nickel wire deforms nonlinearly even under modest remote fields. We develop a three-dimensional variational theory of a ferromagnetic Kirchhoff rod under gravity and magnetic loading and study it through bifurcation analysis, computation, and experiment. A uniform field can stabilize a vertical rod against buckling under its own weight, the classical Greenhill instability. We give sharp criteria for clamped and pinned supports in terms of an Airy-type principal eigenvalue, and give a fine description of the character of the bifurcation landscape, which has qualitatively different features than its non-magnetic counterpart. When subject to the field generated by a permanent magnet, we identify a rich bifurcation landscape as the magnet is rotated quasistatically along a circle of radius slightly larger than the rest length of the rod. We prove that instability occurs only through a planar mode and that each snap is a nondegenerate saddle-node. We also locate the two folds that produce hysteresis. Experiments on $50\,\mu$m nickel wires confirm the Greenhill threshold, restabilization at ~$30$ mT for both clamped and pinned supports, as well as the salient features of the hysteresis loop such as switching angles, width, and geometry of folds accurately. Our analysis and experiments offer principled design rules for field-stabilized filaments and remotely switched bistable actuators. Our analysis also offers a well-conditioned numerical method is valid near the switching events, where the direct numerical minimization is strongly ill-conditioned.

Digital traces may complement population surveys in the measurement of well-being, but the two sources do not necessarily capture identical constructs. We compare the Human Flourishing Geographic Index (HFGI) with World Values Survey and European Social Survey measures across three domains using structural equation models. The results show strong within-source coherence and construct-specific cross-source correspondence. Cross-source convergence varies across domains; the observed pattern is consistent with stronger correspondence where the underlying indicators are more closely aligned conceptually. Near-perfect agreement would be unexpected, since surveys elicit standardized self-reports, whereas HFGI captures naturally occurring public expressions. HFGI should therefore be viewed as a distinct but empirically connected measurement system that complements survey-based evidence on well-being.

The standard approach to predicting behavioral phenotypes from functional MRI is represented by Kernel Ridge Regression (KRR) applied on functional connectivity (FC) matrices. However, this approach is limited: separate models must be fit and tuned for every score and cohort, they do not transfer across datasets, and accuracy degrades sharply when only a handful of subjects are available, as is typical of clinical or cognitive studies. Despite an increasing interest in developing brain foundation models, none has consistently outperformed KRR on behaviour prediction; most reported gains come from easier targets such as age, sex, or diagnosis rather than continuous behavioural scores. We introduce BrainPFN, a Prior Data Fitted Network for brain behaviour regression. BrainPFN is meta-trained on a domain-specific prior built from ~7k real FC matrices, from which we sample one billion synthetic training samples. At inference, a labelled context is simply passed through the network in a single forward pass, with no per-score or per-cohort refitting required. Across four independent cohorts, BrainPFN beats KRR on small sample prediction, and leads recent foundation models pre-trained at four to nine times larger scale. Our meta-training pool, aggregated from open repositories, is a fraction of the size of the corpora behind competing models, most of which sit behind restrictive data use agreements such as UK Biobank. We release this pool publicly alongside code and checkpoints, showing that a modest, openly available pool can match or beat models trained at Biobank scale.

We develop ML models that predict when cross-factor predictability will erode, enabling prospective risk management. A decay prediction model achieves C-index $= 0.93$ on held-out factor pairs, providing early warning of signal erosion—the key predictor is initial signal strength: stronger signals decay faster (“regression to the mean”). An online regime detector enables real-time classification with 6.6-day average detection delay. Prior work explains why factors decay (arbitrage, publication effects); we predict when decay will occur. Limitation: The primary HML$\to$SMB signal does not replicate in post-break OOS (2013–2024); this null result is consistent with genuine decay but limits confirmatory claims. Motivation: Among 30 directed Fama-French factor pairs (1990–2024), predictability targeting the Size factor (SMB) decays fastest. Of 7 pairs showing exponential decay ($R^2 > 0.3$), 4 target SMB (Mkt-RF$\to$SMB, CMA$\to$SMB, HML$\to$SMB, RMW$\to$SMB; half-lives 2.4–4.1 years). This SMB-concentration pattern motivates the predictive models. Methodology: Using a regime-conditional Granger framework with Student-$t$ HMMs, we document structural breaks clustering around June 1998 ($p < 10^{-10}$). A pre-break OOS test (HMM trained 1990–1995, tested 1996–2007) confirms signals existed: HML$\to$SMB shows $p = 0.013$ (Elevated) and $p < 0.001$ (Crisis). The primary HML$\to$SMB signal does not replicate in post-break OOS (2013–2024), consistent with genuine decay rather than overfitting—after ${\sim}6$ half-lives, the expected signal is $<$1% of its 1990s peak. International analysis finds 2/4 non-US markets with Bonferroni-surviving OOS effects; correction for full specification search was not applied, so results remain exploratory.

We present DiffStent, a differentiable finite element framework for simulating arterial deformation during in silico stent deployment, where nearly incompressible, anisotropic vessel walls undergo large deformation and frictional contact with the stent. DiffStent combines the fiber-reinforced Holzapfel-Gasser-Ogden constitutive model with an implicit discrete adjoint that differentiates the converged mechanical equilibrium without unrolling the nonlinear solver, thus reducing the memory cost by three orders of magnitude. We identify three mechanisms that can lead to inaccurate, unstable, or uninformative gradients: nonsmooth switching, state mismatch, and gradient cancellation. To address these, we apply a contact surrogate in the backward pass while retaining the original physical model in the forward pass. We show superior gradient accuracy of our method over AutoDiff and finite differencing across constitutive benchmarks, idealized stented vessels, and patient-specific calcified coronary anatomies, and use the resulting sensitivities to quantify how tissue properties and calcification patterns govern lumen expansion and arterial wall stress. Finally, we demonstrate that DiffStent enables gradient-based system identification from retrospective clinical images of atherosclerotic coronary anatomy. Together, these results establish a practical approach for differentiating through nonlinear biomechanical simulations with stiff constitutive laws and nonsmooth contact, enabling patient-specific parameter inference and optimization in computational cardiovascular mechanics.

Heart failure (HF) following myocardial infarction (MI) is a major clinical challenge with severe complications. Epicardial sleeves and patches are increasingly investigated to improve heart function post-MI, yet their passive mechanical effects remain underexplored. This has resulted in limited insight into how sleeves mechanically interact with the infarct and remote myocardium. This study used 3-D in-silico cardiac models to examine how sleeve shape, material properties, and architecture affect global and regional mechanics. A high-fidelity biventricular model is used to investigate how a continuum cardiac sleeve alters function. Designs that improve regional mechanics successfully limited pathological bulging, modulated fiber strains, and influenced torsional behavior without over-constraining remote tissue, whereas overly restrictive and stiff sleeves penalized healthy myocardium and reduced the intended relief of infarct bulging. These findings highlight the importance of considering regional biomechanical markers when developing sleeve designs. Building on these continuum sleeve insights, a spheroidal left ventricle model demonstrated the proof-of-concept advantage of an "auxetic" metamaterial sleeve, engineered with a negative Poisson ratio. This programmed architecture provided region-specific benefits beyond those of conventional continuum sleeves. Ultimately, this work contributes to an improved understanding of passive sleeve-heart interactions and improves the targeted biomechanical support therapies following MI.

This study investigates inhalation-exhalation asymmetry in population-derived median unilateral human nasal cavity under pressure-driven breathing using time-resolved computational fluid dynamics (CFD). A standardized geometry reconstructed from averaged CT data of 30 adults was subjected to a sinusoidal nasopharyngeal pressure waveform over a complete breathing cycle. Low, intermediate, and high pressure amplitudes were considered to quantify breathing-phase-dependent changes in flow rate, Reynolds number, wall shear stress, nasal resistance, and olfactory-region airflow. For identical imposed pressure magnitudes, inhalation produced a consistently larger flow rate and lower aerodynamic resistance than exhalation, demonstrating a direction-dependent pressure-flow response. Increasing breathing intensity increased Reynolds number and nasal resistance while largely preserving the spatial pattern of the flow. During inhalation, stronger airflow penetrated further into the superior nasal cavity and produced higher and more localized wall shear stress, whereas exhalation exhibited smoother airflow redistribution. The breathing-phase asymmetry also affected regional ventilation: the fraction of total airflow reaching the olfactory region increased with inspiratory intensity and reached approximately 6% under the high-pressure condition, while the expiratory fraction remained comparatively insensitive to breathing intensity. These results demonstrate that pressure-driven transient simulations naturally capture geometry-dependent inhalation-exhalation differences that are suppressed when identical flow rates are prescribed for the two breathing phases, with consequences for both global nasal resistance and regional airflow delivery.

In this paper, we give a new proof of the Hopkins-Morel-Hoyois theorem for fields $k$ of characteristic unequal to $p$ containing all primitive $p$-power roots of unity for a fixed prime $p$. This new proof follows Quillen's proof for the structure of the homotopy groups of $\mathrm{MU}$ which utilizes topological power operations. To this end we define a motivic analog of the Steenrod power operations, using the theory of normed motivic spectra as developed by Bachmann–Hoyois and their application for the definition of motivic colimits as developed by Bachmann-Elmanto-Heller.