Papers

This paper presents a lightweight semantic com- munication framework for diabetic retinopathy (DR) grading from fundus images pertaining specifically to the APTOS2019 dataset. The framework includes semantic encoder designed using ResNet34, U-Net, MobileNetV2, and EfficientNet-B0 architectures. Further, the trained models are used to train the same framework for IDRiD dataset using transfer learning approach. Such a framework will enable the telemedicine sector in the early detection of DR and prevent total blindness. The results reveal that for APTOS, task-oriented semantic systems can achieve satisfactory robust performance (more than 0.8 weighted F1 score for ResNet34 and EfficientNet-B0) across different channels. In particular, considering the trade-off between complexity, latency, throughput, and F1 score, MobileNetV2 is the best model with weighted F1 score of 0.76-0.78 for both task and reconstruction- oriented modules and end-to-end latency of only 8.162 ms.

Tolls for safe passage and attacks on shipping are usually treated as mutually exclusive: either ships pay or attacks happen. We argue they are complementary. In a Stackelberg escalation game for the Strait of Hormuz, the enforcer chooses an attack intensity and a toll schedule; the response is to pay, cross exposed, wait, reroute, or exit. Attacks create the willingness to pay; tolls harvest it. The model predicts asymmetry across trade forms: a toll where the cargo owner can pay and the vessel owner will consent, and none where either fails. Any such payment is clandestine, but the model's implications are testable against freight rates, insurance premia, and incident reports.

Egocentric human videos offer a scalable alternative to robot teleoperation for collecting dexterous manipulation data. However, two challenges limit their use as reliable training data: accurate hand-object interaction (HOI) reconstruction from monocular RGB and high-quality robot demonstrations, especially visual observations. We present EgoMatrix, an end-to-end data engine that converts monocular egocentric human videos into bimanual dexterous trajectories and paired robot observation videos, with the trajectories directly replayable on real robots. It reconstructs HOI with emphasis on relative geometry and contact rather than exact metric scene recovery, then uses retargeting and reinforcement learning (RL) to reproduce the demonstrated tasks in simulation. We jointly render robot hands and objects from these simulated trajectories to produce physically faithful observations synchronized with state and control records. Rendering the same trajectories in diverse, task-compatible backgrounds expands paired training data while preserving robot-object motion and contact. Across TACO, OakInk2, and self-collected data, EgoMatrix achieves 54.84% end-to-end success in simulation versus 14.52% for the strongest baseline. Reconstruction reaches state-of-the-art performance on most metrics of the two public benchmarks. Qualitative results show more faithful hand-object interactions than prior methods, while feature-space analysis shows closer alignment with real-robot observations than GPT-6 Astra. Our project page is available at https://spikew726.github.io/EgoMatrix/.

Planets form in the midplanes of protoplanetary disks, thus investigating the properties of the midplane region can shed light on the physical and chemical processes governing the evolution of planetary systems. In this work, we study the conditions near the midplane of the disk around DM Tau using 0."3 (~43 au) ALMA observations of N2H+ (J = 3 - 2) and DCO+ (J = 4 - 3). The radial profiles reveal that DCO+ is centrally peaked, with a depression near 120 au, while N2H+ exhibits a central depression and a peak near 100 au. In addition, both molecules display extended emission out to 400 au. Using parametric models to interpret our observations, we note that a fiducial model based on CO-derived parameters captures the features within 200 au, but fails to reproduce the outer disk emission. We explore various mechanisms that could account for this extended emission and conclude that it is best reproduced by an increased external UV penetration and cosmic ray/X-ray ionization rate, possibly enhanced by radial drift. These processes affect the precursors of N2H+ and DCO+ : increased UV leads to the photodesorption of CO and N2, while ionization enhances H3+ abundance. Besides, the observed N2H+ and DCO+ features are broadly consistent with previous CO snowline constraints, but can also be shaped by processes such as ionization, CO depletion, and multiple chemical pathways. Thus, using these molecular ions as robust CO snowline tracers requires additional constraints from complementary molecular tracers and detailed chemical modeling.

Large language models (LLMs) generally rely on sampling temperature to regulate the amount of randomness in their outputs. Mainstream methods for selecting temperature typically involve fixed, heuristic global settings and context or token-level calibration, rather than a geometrically interpretable representation of the communicative scenario. In this work, we introduce a simple and interpretable temperature selection framework, the Scenario-Actor, which adapts decoding to the inferred situational characteristics. Scenario-Actor extracts scenario-relevant structures from Transformer hidden states and determines the temperature from scenario embedding, a structured geometric representation of the communicative setting. Empirical results show that on Llama-3.1-8B-Instruct, Scenario-Actor achieves strong goal-completion performance in interactive social scenarios, significant gains on open-ended instruction following, and competitive performance on multi-turn conversation compared to multiple baselines.

Complex image editing requires faithful task interpretation and accurate execution, but a failed edit does not reveal which responsibility failed. We present DuplexBridge, which uses a unified model's own understanding capability to enhance prompts for its own generation capability, without an external understanding module. A source-grounded bridge specifies targets, final-state changes, and preservation constraints. Understanding is supervised on fidelity to the original request without observing the generated image; generation is supervised on execution of the condition it actually receives. Reciprocal trust checks selectively admit global task feedback to each role while retaining independently valid local supervision. We introduce CE-Bench, a 1,200-task benchmark measuring joint satisfaction of task-derived change and preservation requirements. Across three model configurations, the full system improves complete compliance over direct editors by 21.75-25.75 percentage points, with gains also observed on KRIS-Bench, RISEBench, ImgEdit, and GEdit-Bench. From a common supervised Wan-Image initialization, gated joint training reaches 77.08% complete compliance, compared with 70.92% without gates and 75.00% when generation-local supervision instead checks the original task with both gates retained. These results support distinct local responsibilities and selective shared feedback for joint understanding-generation adaptation.

Pre-trained Large Language Model (LLMs) are effective on many tasks in zero-shot and few-shot settings. For machine translation of low-resource languages, the obvious options are few-shot prompting and fine-tuning on a small parallel set. We ask: what if moderate amounts of low-resource monolingual data are also available? We argue that, rather than continued pretraining, a more effective use of this data is the pre-LLM era technique of back-translation (BT). The current fine-tuned LLM translates monolingual sentences in each language, and the resulting pairs train it in the reverse direction. Updates on the parallel set are interleaved for stable learning. With 1K parallel pairs on Odia and Swahili, BT beats continued pretraining into the low-resource language by 7.7 to 16.4 XCOMET-XXL points in domain. With beam-decoded intermediate translations, it also beats a model with 10 time more parallel data. In-context examples retrieved from the parallel data further improve BT. We also analyze the source, quality and amount of monolingual text. Across five low-resource languages, with Hindi as a high-resource control, and two 3B backbones, BT improves translation into the low-resource language by 16 to 173% XCOMET-XXL over parallel-only fine-tuning. Blind human evaluation on Odia and Sanskrit agrees with the automatic metrics.

Anyons are particles with quantized fractional statistics. In theory, a single anyon can be stabilized as a localized fractional charge within the bulk of a topologically ordered two-dimensional insulator. However, experiments to date have focused on probing anyons in structures in which many anyonic excitations coexist and interact. Here, we demonstrate the trapping of a single anyon in a device consisting of a graphene-based quantum point contact with an embedded tunable quantum Hall dot. Benchmarking our device at v = 1, we demonstrate backscattering between Fermi liquid edge states mediated by the whole-electron Coulomb blockade of the dot. The cleanliness and control available in our device allow depletion of the dot to the last quasihole, and we observe spin blockade for transitions to the opposite-spin Landau level. At v = 1/3 and 2/3, we observe backscattering resonances with three times the frequency, consistent with resonant transmission of e/3 charges via a single anyon transistor. We demonstrate controlled depletion to the last quasiparticle to form a single anyon quantum dot. Tracing the charge addition spectrum for quasiparticle number Nqp = 1-5, we observe highly irregular addition energies, consistent with DMRG modeling showing a complex orbital shell-filling behavior. At higher Nqp = 10-20, the addition energies show a striking pattern: quasiholes at 1/3 (and quasiparticles at 2/3) show a regular addition spectrum while quasiparticles at 1/3 (and quasiholes at 2/3) do not. We trace the origin of this irregularity to an attractive component of the inter-anyon interaction: by experimentally tuning the confining energy, we observe complete suppression of alternating charge sectors, after which the dot charges in increments of twice the fundamental charge. This observation indicates the emergence of an anyon binding energy as large as the charging energy.

It is proved that every Borel ensemble of pure states on a separable bipartite Hilbert space with finite average entanglement admits a countable ensemble with the same barycenter and arbitrarily small additional average entanglement. Consequently, the discrete and continuous versions of the Entanglement of Formation coincide on the whole space of states of infinite-dimensional bipartite quantum system (with infinite values allowed). The main idea of the proof (realized with the AI-assistance) is the lifting a Borel ensemble of pure bipartite states to a Borel probability measure on the unit sphere in the space of Hilbert–Schmidt operators followed by dividing the support of this measure into appropriate cells and replacing each cell by its conditional barycenter. The resulting countable ensemble is obtained by a recursive construction.

We prove a case of a conjecture of Gundlach on the number of Galois extensions over $\QQ$ with bounded multi-invariants for the group $G=Q_8$. We also obtain results when imposing local conditions at the wildly ramified place. As an application, we prove asymptotics for the number of $Q_8$-extensions with bounded product of ramified primes.

Stochastic resetting with stochastic return (SR) has recently emerged as an effective and practically relevant strategy for controlling first-passage phenomena and optimizing search processes by significantly reducing completion times in a wide class of stochastic systems. While most theoretical studies assume instantaneous return (IR), in realistic systems the return to the resetting position typically occurs over a finite time. We consider a 1-d diffusing particle in a harmonic trap with stiffnesses $k_1$ and $k_2$ during search and return, respectively. The particle searches for the target and, upon resetting at rate $r$, enters the return phase, continuing until it reaches either the origin or the absorbing target at $L>0$. Notably, the model permits target detection throughout the return phase, distinguishing it from IR scenarios. We analytically derive the MFPT for our model and determine parameter regions where SR enhances or suppresses search efficiency over the underlying dynamics, constructing the corresponding phase diagram using the coefficient of variation criterion. We further identify regimes in which SR is more efficient than IR using the SR criterion. This behavior is tested across different parameter sets taken from experimental studies by Goerlich et al., Biroli et al., and Besga et al. We map the parameter values reported in existing experimental studies onto our theoretical phase diagram, thereby identifying the regimes in which SR outperforms IR. In particular, we find that the most relevant region of the phase space, where SR is most beneficial corresponds to larger values of the potential strength in the search phase and lower values of potential in the return phase. Our results provide experimentally testable predictions and bridge the gap between theoretical resetting models and optical trap mediated finite-time return dynamics.

Harness self-evolution revises an agent's software scaffolding, including prompts, memory, workflows, and executable components, while keeping model weights fixed. We formalize a feedback-driven process in which accepted revisions persist across runs. The framework separates update targets from proposal and admission mechanisms. It distinguishes changes to interpreted state from revisions to tools and code, repository-level control logic, and plugin composition. We characterize search through evolutionary optimization and examine its reliability through continual PAC-learning. Under explicit assumptions, the analysis yields an expected generalization bound, a retention bound conditional on historical regression budgets, and a high-probability admission rule using fresh, independent validation data. We examine how persistent harness revisions affect knowledge sharing and organizational workflows, with implications for scientific reliability, physical safety, and institutional accountability. Cases from prior work illustrate model–harness co-design, distributed execution, and plugin reuse. Reliable deployment requires continual validation as task distributions and evaluators change, with independent safeguards for learning, runtime privileges, and consequential actions. We provide a comprehensive 66-page discussion of related work, theory, algorithms, evaluation, applications, and the broader impact of Harness RSI, together with continuously updated code and supplementary materials, at https://github.com/zgcagi/Harness-RSI.

The resilience and censorship resistance of a blockchain depend on where the validators and proposers of that blockchain physically operate. We study the economic incentives behind this location choice, both with a single proposer and with multiple concurrent proposers. Formally, we study a game where proposers first choose locations and then compete in a first-price auction for an opportunity whose common value is driven by information from geographically dispersed sources. A single proposer minimizes variance-weighted delay, locating at a weighted median of the sources and co-locating with any dominant one. By contrast, with two proposers, information both observe equally early earns no rent, and each proposer's expected profit is proportional to the standard deviation of the information it receives before its rival. We show that the location game admits the jointly unobserved variance as an ordinal potential, so global solutions of a weighted two-median problem are equilibria. With two sources, one proposer locates at each, however weak one is. With more proposers and at least as many sources, equilibrium locations are distinct under regular bidding. Multiple concurrent proposers thus do more than limit any single proposer's control over inclusion: by rewarding exclusive rather than shared information, they create an economic force toward geographic decentralization.

In this work, we study grokking in a simple, analytically tractable setting whose rich phenomenology allows us to disentangle the effects of initialization, signal strength, weight decay, sample size, and input dimension. These factors can produce superficially similar learning curves through distinct mechanisms, complicating their interpretation. Our analysis distinguishes early fitting through nuisance features, core feature learning, and delayed generalization. We identify sharp conditions under which grokking provably occurs and derive analytic asymptotic expressions for the lengths of the generalization plateaus. Our results also characterize regimes of early generalization and failure to reach a prescribed test accuracy target. We show that the interpolation edge constitutes a distinct dynamical regime, where vanishing spectral gaps separate core learning from generalization, helping clarify the role of proximity to interpolation in existing accounts of grokking. The resulting picture is analogous to fast and slow phases in chemical kinetics and suggests that the lazy-to-rich transition discussed in the literature may reflect a similar separation of dynamical time scales. Our theoretical results are faithfully supported by extensive experiments.

We investigate the differential luminosity response of the optical Balmer series from H8 to H-alpha in Galactic B5-A5 luminous stars using homogeneous measurements of central depth, FWHM, and equivalent width at a resolving power of approximately 12,000. Direct line-to-line comparisons show a systematic change in the central-depth response toward the lower-order transitions. For the primary 72-star luminosity sample, the fitted luminosity coefficients show an overall positive trend with upper-level quantum number, with a point-estimate gradient of dq/dn = 0.0419. A joint Monte Carlo analysis with 10,000 realisations gives a median dq/dn = 0.0387 and a 95 percent interval from 0.0253 to 0.0532, with no non-positive gradients obtained. The higher-order H8-H-delta coefficients form a statistically unresolved plateau, followed by a well-supported increase in response magnitude from H-delta toward H-alpha. The result is robust to the adopted effective-temperature scale. The FWHM coefficients show no comparable Balmer-order progression, and the directly fitted profile-shape response is consistent with zero from H8 through H-beta. For H-alpha, the full logarithmic sample is not formally significant, whereas removal of the three remaining strongly filled-core profiles yields a significantly negative shape response. The observed behaviour is qualitatively compatible with the systematic variation of pressure broadening across the Balmer series, while the enhanced H-alpha response may additionally reflect non-LTE and wind-related effects.

Residual connections propagate information through a network by additively accumulating layer outputs. Recently proposed alternatives, such as Manifold-Constrained Hyper-Connections (mHC) and Attention Residuals (AttnRes), instead use more expressive depth aggregation mechanisms that improve language modeling performance at scale. In this work, we consider the mixing of representations over depth as a problem of storing and retrieving information across layers. Formalizing this perspective, we introduce Depth Memory (DM), a unified framework that describes the standard pre-layer-norm (PreLN) transformer, mHC, and AttnRes in terms of streams that carry representations through the network. One such stream, for example, could be an explicit memory stream that is queried to enrich the input to every layer, and whose output is subsequently written back into the memory for use by later layers. For AttnRes, this memory stream is a growing cache of explicit layer representations. For mHC, it is an expanded residual stream. Building on this view, we propose Linear Depth Memory (LDM), which formulates information retrieval across depth as a regression problem solved using recursive least squares. The resulting architecture propagates three streams across depth: the standard residual stream, a linear associative memory stream, and an inverse covariance stream. For high-throughput training and inference, we propose a hardware-aware implementation of LDM that reduces peak activation memory and memory traffic. LDM consistently achieves the lowest perplexities among PreLN, mHC and AttnRes baselines at the 400M and 1.5B parameter scales, alongside competitive zero-shot accuracy.

In cooperative Multi-Agent Reinforcement Learning (MARL), agents must learn to coordinate their actions to achieve shared objectives. A key indicator of effective coordination is behavioral diversity, i.e., the agents' potential to enact distinct yet complementary control policies given the same set of observations. Although behavioral diversity can enable role specialization and richer joint behaviors, its appropriate level is highly context- and task-dependent and often costly to tune. We propose Adaptive Diversity Control (ADiCo), a two-timescale framework that adapts behavioral diversity online during training. On a fast timescale, Diversity Control (DiCo) regulates system diversity toward a target value. On a slower timescale, an Extremum Seeking Controller (ESC) adjusts this target using only mean episodic returns, without requiring an explicit model or analytical gradient of the diversity-performance landscape. We evaluate ADiCo on six configurations across two cooperative MARL tasks, where it maintains task-appropriate diversity levels: low diversity when homogeneous policies are beneficial and higher diversity when heterogeneous policies are required. Through this adaptation, ADiCo matches or exceeds the mean performance of DiCo (best grid-searched diversity target) and Unconstrained DiCo (diversity allowed to emerge without target regulation). These results demonstrate that incorporating classical feedback control into MARL training enables effective coordination by providing a systematic alternative to task-specific manual selection of the diversity target.

Agentic reinforcement learning (RL) enables large language models (LLMs) to learn from multi-turn interactions with verifiable outcomes. Textual skills can improve exploration by distilling prior interactions into reusable guidance. However, existing skill-based RL approaches often either assume skill injection is beneficial or rely on indirect feedback or rollout-intensive evaluation to assess its utility. Our pilot studies show that rollout-based utility estimation for skill credit assignment is costly and unstable under limited sampling, while skill benefits vary across candidates and depend on the current policy's competence on each query. To address these challenges, we introduce SkillScaffold, a policy-adaptive training scaffold that combines low-cost skill-utility estimation with selective skill injection. By reusing outcome-verified training trajectories, SkillScaffold generates candidate skills and estimates their utility through outcome-aware likelihood comparisons, without candidate-specific environment rollouts. The resulting utility guides whether and which skill to inject, retaining skill-free execution when no candidate is estimated to help. Joint training enables the Generator to produce skills tailored to the evolving Executor. Scaffolded RL encourages skill internalization for skill-free inference. Experiments on ALFWorld, WebShop, ScienceWorld, and $\tau^2$-Bench demonstrate gains over strong agentic-RL and skill-based RL baselines across both short- and long-horizon tasks. Ablations and further analyses support the importance of utility-based selection and abstention. Our code is available at https://github.com/Vaidurya00/SkillScaffold.

Planets are inherently three-dimensional objects shaped by their thermal structure and dynamics. Observations of transiting exoplanets have begun to uncover this three-dimensional nature, with JWST measuring their dayside atmosphere structure with eclipse mapping, and exploring spectroscopic asymmetries in the limbs of planets during transit. We apply the novel mapping method of transmission strings to the hot Jupiter WASP-17b. With this method, we are not only able to extract hemispheric limb asymmetries from east-to-west, but can map equator-to-pole variations around the transmitting atmosphere as a function of angle, spanning 0.6-12$\mu$m. We find a clear transition in the thermal scale height around the limb of the atmosphere, with a $\sim$650K temperature difference between the morning (T=858$^{+434}_{-233}$K) and evening (T=1522$^{+116}_{-114}$K). These results are consistent with both nightside emission and dayside eclipse mapping measurements, and represent a fully comprehensive set of observations for a transiting exoplanet. We are also able to constrain the abundances of H$_2$O and CO$_2$ to constant values around the limb, providing observational constraints to results from global circulation models. The transmission string technique combined with the outstanding observability of WASP-17b pushes the study of exoplanet atmospheres further into a three-dimensional understanding of hot Jupiter dynamics and chemistry

We give a general formula for minimal projective presentations and for minimal discrete-injective presentations of finite-dimensional modules over basic pseudocompact algebras. We also show that the representation-theoretic g-vector of a module coincides with its DWZ-g-vector. These results generalize the description that Derksen, Weyman and Zelevinsky gave of minimal projective presentations for modules over certain finite-dimensional Jacobian algebras. In particular, we can drop their finiteness assumption, and we may work over fields of arbitrary characteristic.

Raw image intensities are a poor surrogate for similarity across images in correspondence problems. Further, while auxiliary segmentation labels can provide semantic identification and improve matching, they can assign only coarse identities to fine-grained anatomy and often cover only a subset of structures, particularly in whole-body settings. We present an approach that instead establishes correspondence using complementary representations of anatomy and demonstrate its utility for longitudinal whole-body PET/CT registration in the Learn2Reg 2026 PSMAReg Challenge. Our 3D foundation model, anatomix, is used to derive fine-grained, per-voxel semantic representations that are consistent across volumes, and we further employ off-the-shelf segmentation models to obtain coarse anatomical identities. Together, these representations drive a GPU-accelerated iterative registration solver (FireANTs) in a hybrid multistage framework: the first stage estimates alignment from dense multi-channel features, after which a second refines the deformation using both anatomix- and segmentation-based losses. Lastly, because registration should not introduce non-biological tumor volume changes across time, we develop lesion-specific component-wise volume preservation schemes. Without any task-specific training, our system won first place in the PSMAReg Challenge leaderboard. Code and interactive visualizations are available at http://www.neeldey.com/reps-for-reg.

Building on work of Kauffman–Saleur and earlier work of the second author, we derive a determinant formula for the Links–Gould polynomial of links. As an application, we prove a 20-year-old conjecture of Ishii: for any alternating link, the Links–Gould invariant is an alternating polynomial.

We resolve the long-standing non-extinction problem for Brownian Fleming-Viot systems in bounded domains. For every fixed N >= 3, we construct a bounded connected domain in R3 in which branching explosion occurs with positive probability before every prescribed positive time, from every interior initial configuration. On this event all particles converge to one boundary point. Together with two-particle non-extinction, this gives the sharp population threshold for bounded-domain Brownian explosion. The mechanism is directed transport generated by uniform copying in a periodic absorbing environment. We compute a positive cubic current for the same two-harmonic killing profile at every N >= 3, with an explicit population coefficient and a controlled fourth-order remainder. To realize this transport by spherical absorption, we develop a marked genealogical transfer theorem that retains the Euclidean displacement inherited at each copy. Common ancestry makes the integer winding reconstructible from phase records and yields convergence of the stationary signed current. A boundary restart law with P'olya weights supplies the continuity needed to turn that current into stable escape. Diffusion coefficients adapted to a common Kelvin clock preserve the joint Brownian law and uniform donor marks while compressing escape into finite lifetime. Disjoint spherical holes in a ball accumulate only at the explosion point. The boundary is smooth elsewhere, with finite area and perimeter. Boundary area within distance r of the singularity is of order r. For three particles, the transfer theorem covers every smooth positive periodic killing rate.

We introduce a diagram algebra $\mathcal{K}_L$ based on Kuperberg's $A_2$-webs and prove a Schur–Weyl duality $\mathcal{K}_L \cong \operatorname{End}_{U_q(\mathfrak{sl}_3)}((V^+ \oplus V^-)^{\otimes L})$, where $V^\pm$ are the fundamental representations of $U_q(\mathfrak{sl}_3)$. Thus, $\mathcal{K}_L$ is a natural $A_2$ analogue of the Temperley–Lieb algebra. We construct an explicit cellular structure for $\mathcal{K}_L$, with the web basis as its cellular basis and cell modules indexed by dominant $U_q(\mathfrak{sl}_3)$-weights. The bases of these modules are parametrized by dominant lattice paths via a recursive growth algorithm. Using this structure, we determine local generators of $\mathcal{K}_L$ and establish web formulations of the first and second fundamental theorems of invariant theory. In particular, we show that the braid-group image, augmented by local idempotents, does not generate $\mathcal{K}_L$, and identify an additional local generator. Finally, we derive a bimodule decomposition of $(V^+ \oplus V^-)^{\otimes L}$, yielding a complete set of irreducible $\mathcal{K}_L$-modules for formal or generic $q$.

We establish theoretically that transverse spin textures are generically induced by the spin-orbit interaction at the Fermi surface of centrosymmetric ferromagnetic metals. We confirm this prediction with ab initio computations for Fe, Co and Ni. By symmetry, this cannot be associated with spin-orbit torques under a uniform current. However, a new current-gradient-induced torque emerges in nanoscale geometries. For a series of Ni-based bilayers, the computed Ni thickness dependence of the current-gradient-induced torque is in quantitative agreement with measurements previously attributed to orbital torques. We discuss how this opens a new avenue for the electrical control of magnetic orders, possibly also including the Néel vector of metallic altermagnets.

A series of recent works has established EFI pairs as the "minimal" assumption for quantum cryptography. Recently, Cavalar et al. [CCC+26] showed that EFI pairs are equivalent to non-uniform expanding single-copy pseudorandom state generators (1PRS), and obtained a non-uniform meta-complexity characterization of EFI pairs. We remove the non-uniformity in their construction and prove that EFI pairs are equivalent to expanding 1PRS. As a corollary, we obtain the first uniform meta-complexity characterization of EFI pairs. Together with the equivalence of statistically verifiable one-way state generators and commitments proved by Batra and Jain [BJ24], this gives a quantum analogue of the classical equivalence between one-way functions, commitments, and pseudorandom generators.

We introduce the formalism of non-wellfounded and cyclic linear nested sequent calculi, developing concrete systems for linear temporal logic (LTL). The paper addresses two central problems, which we call "cycle recognition" and "unraveling." Cycle recognition concerns identifying cycles in non-wellfounded proofs in order to extract corresponding cyclic proofs, while unraveling studies the converse transformation, from cyclic proofs to non-wellfounded ones. Although these processes are well understood for Gentzen sequents, they have received little attention for more expressive sequent formalisms and become more challenging in the linear nested sequent setting. To address cycle recognition, we show the completeness of non-wellfounded proofs relative to a particular normal form exhibiting a property we call "saturation recurrence," which enables the systematic extraction of cyclic proofs. To address unraveling, we introduce a specialized procedure that shifts rule applications forward along linear nested sequents, allowing non-wellfounded proofs to be reconstructed from cyclic ones. Overall, our work provides new proof-theoretic techniques for cycle recognition and unraveling in expressive multisequent formalisms.

We prove the global existence of solutions to the Navier-Stokes equations for any divergence-free distributional initial data. The solutions are smooth in both time and space at positive times. When the initial data belong to the Sobolev spaces $W^{-1,p}$ for $1<p<\infty$, our constructed solutions are weak in the classical sense. We also characterize the distributional initial data admitting weak solutions and obtain the sharp ranges in Besov and Triebel-Lizorkin spaces.

In this work, we investigated how variations in spatial confinement affect the electron correlation between two electrons in a symmetric double quantum dot. In strong confinement regime, the ground-state energy can be obtained using the Hartree-Fock method neglecting the electron-electron repulsion term. Under a weaker confinement, the FCI method provides a more accurate description. Using the mutual information as a measure of correlation, we determine the confinement regions where electronic motion is uncorrelated. We conjecture that the Shannon entropy can serve as a qualitative guide to to study the electron correlation. We identified an approximately linear relationship between mutual information and relative correlation energy.

Mortgage credit risk may exhibit dependence across economically connected areas, even when they are geographically distant. However, current models typically represent cross-area dependence through fixed geographical neighbourhoods, potentially overlooking economic connections that extend beyond physical proximity and evolve over time. These models may fail to capture shared risks among geographically distant but economically similar areas, and cannot describe a changing dependence of risk; it therefore risks retaining economically obsolete connections while omitting newly emerging ones. This paper uses similarities of industrial composition as a measure of economic proximity and develops a discrete-time survival model with dynamic industrial graphs to capture evolving cross-area dependence in mortgage default risk. The resulting graphs are reconstructed annually, allowing both their topology and edge weights to change as regional industrial compositions evolve. Jointly combining a proper conditional autoregressive process with a first-order autoregressive process governs the temporal cross-area dependence and the temporal persistence in latent risk simultaneously. The model is estimated using Integrated Nested Laplace Approximation and evaluated on U.S. mortgage loan-level data against the static industrial graph specifications. The results show that the proposed dynamic model achieves better in-sample fit and out-of-sample discrimination, while its estimated parameters indicate substantial graph-induced cross-area dependence and temporal persistence. These findings demonstrate the value of allowing economically defined neighbourhoods to evolve when modelling mortgage default risk.