Papers

This is an English translation of a book originally published in Japanese by Saiensu-sha in 2015. The book is an introduction to the 3d-3d correspondence, the relation between 3d $\mathcal{N}=2$ supersymmetric gauge theories and the geometry of 3-manifolds, which arises from the compactification of the 6d $\mathcal{N}=(2,0)$ theory. The presentation is bottom-up rather than top-down: instead of starting from the 6d theory, we begin by asking what a quantum field theory is, and let the geometry emerge on its own. Along the way we discuss renormalization and low-energy effective theories, gauging as an operation which glues field theories together, the resulting $Sp(2n, \mathbb{Z})$-action on 3d theories, 3d $\mathcal{N}=2$ supersymmetric theories and their dualities, the squashed three-sphere partition function and supersymmetric localization, duality domain walls of 4d $\mathcal{N}=2$ theories, quantum Teichmuller theory, complex Chern-Simons theory and the quantization of the moduli space of flat $SL(2, \mathbb{C})$-connections on 3-manifolds, with quantum dilogarithm functions as a recurring thread. The emphasis throughout is on geometric and algebraic structures which are invisible in a single field theory, and appear only in the theory space of quantum field theories. Appendices summarize supersymmetry in various dimensions, classical and quantum dilogarithm functions, and cluster algebras. Exercises with difficulty ratings are included in each chapter.

This paper investigates the threat to ballot secrecy in the Brazilian electronic voting machine (UEB) posed by electromagnetic side-channel attacks, also known as TEMPEST attacks. In these attacks, screen content can be reconstructed remotely by intercepting electromagnetic emanations associated with the target device's video signal. This work is motivated by a recent ruling by a Brazilian electoral court concerning an attempt to violate ballot secrecy using electronic equipment. Based on publicly available information about the electoral system, attack scenarios against polling stations are proposed. Experiments using software-defined radio show that the effectiveness of TEMPEST attacks strongly depends on the lack of oversight resulting from public unawareness of the threat. Finally, awareness guidelines are proposed for voters, poll workers, and party representatives to mitigate attack risks within a polling station.

Wide tables offer tabular foundation models more evidence, but accessing it can exhaust their memory: full-width pairwise mixing grows quadratically with the number of columns, while feature selection makes inputs affordable by discarding evidence. We ask whether using more features requires interacting over all of them at once. We introduce Support-Compiled Feature Folding (SCFF), a training-free inference framework that encodes wide tables through bounded calls to a frozen backbone. SCFF organizes support-ranked features into a strong Core and a candidate Tail, folds them into narrow feature groups, and support-checks the Tail's added evidence before a single contextual prediction. This converts quadratic feature-interaction work into linear-in-width work with a bounded local working set, without ensembling predictions or training new parameters. On the exhaustive 18-dataset wide-table slice of fixed AMLB-29, TabZilla, and TabArena snapshots, SCFF improves dataset-macro accuracy and NLL on all six evaluated backbones. All four matched-width comparisons retain favorable 95% dataset-bootstrap intervals on locked folds, with relative error reductions up to 26.1%. Median paired GPU-memory savings are 2.09-2.36x, and the ratio of separately observed maximum peaks reaches 34.3x. Under a measured peak-memory ceiling, SCFF uses the saved budget to preserve more support-selected evidence, improving accuracy by 4.06 and 3.72 points over the widest feasible single leaf on predeclared wide-Core strata of TabICLv2 and TabPFN-3.

In symbolic dynamics, the fixed-point construction from arXiv:0910.2415 defines shift spaces of finite type whose configurations embed infinite hierarchies of tilings. This article provides a "black box" abstraction of this method phrased in terms of substitutions and $S$-adic limit spaces operating over sequences of increasingly large alphabets. By quantifying the amount of information computed by the substitutions at each level, and using a suitable parallel model of computation, we provide a simple positive criterion of multidimensional soficity that generalizes classical examples from the literature.

Text-to-audio (TTA) generation aims to synthesize realistic audio that faithfully reflects natural-language descriptions. Most TTA systems adopt a two-stage latent paradigm: an audio tokenizer is optimized for reconstruction and then frozen, after which a generative model is trained in the resulting latent space. However, reconstruction-oriented representations may be suboptimal for generation, motivating joint representation and generative learning. To this end, we introduce Unite-Audio, to our knowledge, is the first to jointly learn continuous audio representations and latent flow matching for TTA. By coupling reconstruction with self-supervised generative prediction, Unite-Audio allows the generative objective to directly shape the latent space rather than treating it as a fixed intermediate representation. We further employ Flow-GRPO post-training to improve text-conditioned generation. Experiments show competitive TTA performance with a compact latent flow model, while ablation studies confirm the benefit of jointly learning the audio representation and generative model. Audio samples are available at https://runwushi.github.io/Unite-Audio.

The proliferation of smart devices exposes children to online risks like grooming and financial scams that are deeply embedded within legitimate applications. Current approaches rely on automated prevention and detection, a paradigm that is fundamentally limited by its inherent fallibility. Whether rule-based or AI-driven, they inevitably produce false positives and negatives, failing to provide reliable protection. In this paper, we argue for a complementary, human-in-the-loop, post-hoc forensic paradigm. We present GUIAuditor, the first system designed to realize this vision by creating GUI Provenance: a queryable, semantic record of a child's interaction sequence. To generate this, GUIAuditor leverages a Multimodal Large Language Model (MLLM) to translate the temporal sequence of GUI events into a human-understandable narrative. To make this practical on mobile devices, a novel evidence distillation pipeline reduces the data requiring analysis by over 89.2% compared to periodic sampling approaches adopted by industry standards, with negligible impact on accuracy. On a new dataset of 295 interaction clips, GUIAuditor achieves a 95.23% Macro-F1 Score in logging significant events and, crucially, its two-stage forensic query engine successfully retrieves the correct evidence as the top result for over 90.20% of natural language questions. An end-to-end evaluation on three modern smartphones shows that the full pipeline, including on-device MLLM inference, adds 2.1W of power draw and 7.4s of per-event latency, with a peak memory footprint of ${\sim}$3.1GB. These results show that post-hoc GUI forensics can run on modern mobile devices and provide useful context for guardian-led safety review.

The SuShi project aims at determining how sustainable materials can be used to shield against ionizing radiations. This contribution presents a comparison of the effect of concrete and rammed raw earth on photons. For energies around the MeV, where interactions by Compton scattering dominate, changes in the material composition have virtually no effect. The density difference results in 20% more thickness needed for earth to achieve the same flux attenuation as concrete. The same value is found for higher energies, where photons produce electromagnetic showers. Below 0.1 MeV, material composition and earth moisture content matter but the attenuation is much larger.

Let $\mathfrak{C}$ be a projective stacky curve over an infinite field $k$ with the coarse space $C$, a geometrically connected smooth projective curve, together with a generating sheaf $\mathcal{E}$ on $\mathfrak{C}$. We consider the moduli stack of $\mathcal{E}$-semistable vector bundles of fixed determinant and multiplicities on $\mathfrak{C}$, and show that it is $\mathbb{A}^1$-connected if and only if it admits a $k$-rational point. We show that this holds whenever genus of $C$ is at least $2$ and $C(k)\neq \emptyset$. As a consequence, we conclude that, for any system of weights $\boldsymbol{\alpha}$, the moduli stack of parabolic $\boldsymbol{\alpha}$-semistable vector bundles of fixed determinant and quasi-parabolic data on a geometrically connected smooth projective curve is $\mathbb{A}^1$-connected.

We establish tight randomized higher-order oracle complexity for finding first-order stationary points of nonconvex finite sums. Let $n$ be the number of components, $\Delta>0$ the initial objective-gap bound, $L_p>0$ an individual $p$-th derivative Lipschitz bound, and $\epsilon>0$ the target gradient norm. For every fixed integer $p\ge 2$, the minimax number of exact component queries returning the value and all derivatives through order $p$, with success probability at least $2/3$, is \[ \Theta_p\!\left( n+\Delta L_p^{1/p}n^{1-1/(2p)} \epsilon^{-(p+1)/p} \right), \] where the constants depend only on $p$ and the worst case ranges over all finite dimensions. The lower bound holds for unrestricted randomized adaptive algorithms and closes the $\sqrt{n}$ gap between the previously known general-order upper and lower bounds in their dependence on $n$. We extend dense weak hiding to complete higher-order replies while keeping each component's regularity independent of the chain length. The matching upper bound retains the known finite-sum exponent, requires only mean-squared $p$-th derivative increments, and removes the fixed-confidence logarithmic loss by verifying entire recursive-estimation epochs with exact function values. The characterization includes the additive $n$ term for every positive parameter regime; it counts oracle calls with unrestricted internal computation.

We employ Computational Taxonomy (CT) to reanalyze the penguin data set penguins_lter by validating and addressing two biological issues: Sexual Size Dimorphism (SSD) and mate-selection criteria. Via Scientific Data Analysis (SDA) computing, CT constructs a Taxonomic Hierarchy by splitting Species first and then Sex, without involving Island, to achieve less complexity. This Taxonomic Hierarchy validates SSD as a branch comparison: (Species, Sex = Male)-vs-(Species, Sex = Female), upon which SDA explores all potential pieces of associative information from all covariate feature-sets, including interacting effects from order-2 to order-4, and then confirms them via their idiosyncratic reliability checks. The collective of confirmed information pieces are displayed on a heatmap platform to manifest underlying dynamics of SSD with explicit block-structured heterogeneity found within males and females. SSD dynamics is explained through mechanistic dependence pertaining to one chief factor consisting of up to 8 feature-sets: Body-Mass coupled by combinations of {Culmen-length,Culmen-depth, Flipper-length}, and two minor factors consisting of low-order combinations of {Culmen-length,Culmen-depth, Flipper-length}. Such Intra-Sex heterogeneity invalidates all Logistic regression modeling on SSD in the original paper. Further, we explore potential mate-selection criteria through the data-frame of Nest-ID within-species homogeneity.

Friedlander and Iwaniec proved that the number of points of the orbit $\{\gamma i \colon \gamma\in\SL_2(\Z)\}$ lying at a distance $p-2$ from the origin $i$ of the upper half-plane, with $p\le x$ prime, is of order $x/\log x$; the upper bound is unconditional, while the lower one rests on a strong hypothesis concerning the distribution of primes in arithmetic progressions. We consider instead square-free distances and prove unconditionally an asymptotic formula, whose main term is of order $x$. Employing the weighted linear sieve, we also show unconditionally that the square-free distances $n$ with at most $7$ prime factors contribute $\gg x/\log x$. Finally, assuming that the sequence $r(n-2)r(n+2)$ has level of distribution $x^{\theta}$ in arithmetic progressions, where $r(n)$ is the number of ways to write $n$ as a sum of two squares, we obtain the same lower bound for the distances with at most $N$ prime factors (the value $7$ corresponds to $\theta=1/6$).

Long physiological recordings contain many routine measurements, while predictive information often lies in rare events, sustained burden, and recurring patterns. These properties can be computed as label-free evidence, but directly using them as features leaves limited labeled data to separate reproducible associations from sample-specific ones. Learning to reconstruct evidence can exploit unlabeled recordings, yet joint reconstruction does not explicitly require the decoding rule to transfer across individuals. We introduce transferable evidence reconstruction (TER): a Ridge regressor fits evidence from representations in one group and predicts it in an identity-disjoint group without refitting. The transfer error trains the encoder through the differentiable fit. For continuous glucose monitoring (CGM), clock-aware encoding preserves the multi-day content and timing needed for evidence recovery. Matched interventions connect the gains to reduced fitting-group sensitivity, with structured targets improving on raw recovery. Across ten leading CGM and time-series baselines, TER sets a new best metric on 12/14 phenotype tasks and exceeds the strongest prior overall PR-AUC/ROC-AUC/Macro-F1 by 4.95/4.43/0.66 percentage points; the PR-AUC and ROC-AUC gains are $2.6\times$ and $2.2\times$ the respective gaps between the two strongest baselines. Meal-response and future-CGM studies further demonstrate predictive utility. TER thus uses meaningful signal properties to supervise not only what a representation preserves, but how reliably it can be read across individuals.

We establish the natural scale of instability in real Gaussian phase retrieval at the critical injectivity threshold. Let $A$ be a $(2M-1)\times M$ matrix with independent standard Gaussian entries and let $K_M=\binom{2M-1}{M}$. For every $w_M\to\infty$ with $\log w_M=o(M)$, we prove that $\mathbb{P}\{(w_M\sqrt{M}K_M)^{-1}\le\omega(A)\le w_M/(\sqrt{M}K_M)\}\to1$, where $\omega(A)$ is the Balan–Wang stability parameter. Consequently, $-M^{-1}\log\omega(A)\to\log4$ in probability. For full-spark matrices at this threshold, $\omega(A)$ equals both the optimal lower Lipschitz constant of $x\mapsto|Ax|$ and the minimum least singular value over all square row submatrices. The upper bound follows from a second-moment analysis of overlapping minors. A weighted Gaussian inverse-tail asymptotic and inverse-Wishart concentration yield asymptotic independence for central overlaps; rectangular hard-edge bounds control the remaining overlaps. The matching lower bound follows from a union bound and a square Gaussian hard-edge estimate.

As Large Language Models (LLMs) evolve into autonomous agents that alter real-world states, ensuring operational safety across multi-step workflows has become a critical challenge. While recent work has moved beyond single-turn evaluation toward multi-turn paradigms, key limitations persist: step-level methods treat actions in isolation, missing how risks accumulate, while trajectory-level evaluations operate post-hoc, offering no opportunity for timely intervention. To address these limitations, we formalize Decoupled Proactive Safety Monitoring along three dimensions: whether to intervene, when to intervene, and what the risk is. We introduce PASTABench, a benchmark of 1,139 multi-turn trajectories spanning 5 risk categories and 13 subcategories. We further propose the Optimal Intervention Window (OIW), anchored by annotated Earliest-Signal and Trigger turns, to quantify intervention timeliness. Evaluation of 16 LLMs reveals that proactive intervention remains largely unsolved, with the best model achieving only 40.74% optimal-timing interventions. Fine-grained diagnosis further uncovers pervasive lexical overfitting: competitive safety scores of smaller models mask keyword hypersensitivity rather than genuine risk comprehension, as their proactive capability largely collapses once hazard vocabulary is neutralized.

Positioning-assisted beamforming is a novel enabling technology for massive multiple-input multiple-output in modern wireless communications, as it provides reliable beam steering without requiring explicit channel state information. However, the channel capacity analysis under positioning error remains mathematically intractable, which limits both performance characterization and beamforming design. In this work, we derive instantaneous and ergodic channel capacity approximations in closed forms for both two-dimensional and three-dimensional positioning-assisted beamforming systems. Based on the new expressions, we provide closed-form optimal joint Gaussian beam pattern that maximizes the asymptotic ergodic capacity. Numerical results verify the theoretical capacity expressions and the optimal beam pattern. The derived expressions enable efficient beam design to maximize channel capacity and provide a theoretical basis for positioning-assisted beamforming design.

Let $q=p^k$ be prime power, let $F= \mathbb{F}_q$ and let $V$ be the vector space of 2 by 2 matrices over $F$ with trace zero. Let $G = \mathrm{SL}_2(F)$. Then $G$ acts on $V$ via conjugation. Let $\Omega = S(V^*) \otimes \Lambda(V^*)$ be the algebra of differential forms on $V$. A minimal generating set for $\Omega^G$ when $q=3$ was computed by the author and Meyer. In this article we compute a minimal generating set for $\Omega^G$ for all $q$.

Old-growth forests develop over centuries under minimal anthropogenic disturbance, producing structurally complex and biodiverse stands. In Europe, protecting them requires mapping that is accurate for individual forest parcels yet deployable continent-wide. Geospatial foundation model (GFM) embeddings enable label-scarce land classification, but their value for old-growth detection remains unknown. Here, we map old-growth forests across 211,893 ha of Romania's Southern Carpathians, a beech-spruce landscape typical of the Alpine Biogeographic Region. We construct high-confidence, expert-informed reference labels for old-growth and non-old-growth parcels. We add AlphaEarth, TESSERA v2 and Sentinel-1/2 features to a common baseline of topographic and human-access predictors, then compare them under spatially blocked validation with and without 10 km train-test buffers to limit residual autocorrelation. With buffering, GFM and Sentinel-1/2 predictors increase precision-recall AUC by 0.21-0.25 [95% CIs: 0.15-0.34] relative to baseline, indicating spectral data contain a spatially robust old-growth signal. With a PR-AUC of 0.84 [0.79-0.88], TESSERA outperforms Sentinel-1/2 (+0.08 [+0.05 to +0.11]) and AlphaEarth (+0.08 [+0.04 to +0.12]) under unbuffered spatial validation. At a 10 km buffer, however, this advantage narrows to +0.04 [-0.01 to +0.11] and +0.03 [-0.04 to +0.10], intervals consistent with no difference. At 10 m resolution, convolutional neural networks add no benefit over pixel-based XGBoost. Comparisons with four national- and continental-scale products show the importance of non-old-growth labels, and reveal 81% agreement between our predictions and a field-calibrated map. We conclude that buffered spatial validation is vital when transferring old-growth detection models to unseen landscapes, and provide our labels and predictions for future work.

Long-lived ($\sim 10$ s) high-frequency oscillations (HFOs, $50-450$ kHz) near the plasma edge have been reported and experimentally described in L-H transition studies at JET and AUG. In this work, we show that these HFOs are a general phenomenon observed in various plasma scenarios and compositions (H$^1$, D, D-He$^3$, D-T) under different heating schemes, including pure Ohmic, ICRH and NBI. We demonstrate that dominant axisymmetric ($n=0$) HFOs are Global Alfvén eigenmodes (GAEs) tied to the shear-Alfvén continuum (SAC) minima arising at the plasma edge due to the sharp decrease of the density and increase of the safety factor. This hypothesis is corroborated by the remarkable agreement found between the measured frequencies of HFOs and the SAC minima computed by the ideal MHD code CSMISH for a comprehensive set of JET pulses. This result, along with the fact that HFOs are observed over long time windows and across a variety of plasma scenarios, makes them convenient MHD constraints for accurate equilibrium reconstruction near the edge. In view of this pragmatic application, we derive a first-order analytic expression for the two lowest coupled branches of the $n=0$ SAC, disclosing their dependence (and, consequently, that of the HFOs) on the plasma density, safety factor, and elongation profiles. In addition, we discuss the nature of $n\neq 0$ HFOs observed along with the dominant $n=0$ HFOs.

Remote sensing change detection (RSCD) is essential for monitoring land-cover changes and urban development. However, most methods demand pixel-level change masks, which are costly and time-consuming to annotate. Weakly supervised methods reduce this cost by using image-level change labels. Yet these labels indicate only whether a change occurs, leaving models to recover the location of the change and semantic meaning through additional and complex mechanisms. This missing information can be supplied directly by change captions, which describe what changes, what it becomes, and where it occurs. Therefore, we introduce change-caption-guided RSCD, using change captions as the sole task-specific supervision to learn change masks without manually annotated change masks. Our framework has two components: a caption-driven generation pipeline that produces bi-temporal remote sensing image pairs at scale with controlled changes matching each caption, and a change detector guided by the caption's transition semantics. The detector uses our Semantic-Appearance Agreement Framework (SAAF) to combine caption-grounded semantic responses with RGB differences for change localization, while text conditioning guides dense prediction. Experiments on our newly constructed Flair-RSGen dataset and WHU-CDC show that SAAF outperforms the closest reproduced limited-supervision baselines in macro-averaged IoU and F1 under the evaluated protocols. Code is publicly available at https://github.com/qianyuancs/SAAF.

T Coronae Borealis is the nearest symbiotic recurrent nova and is expected to undergo a new eruption soon, offering a rare opportunity to study shock evolution and particle acceleration. We predict radio emission from the outburst and assess how radio observations can constrain the circumbinary medium (CBM) and cosmic-ray acceleration. We post-process three-dimensional (3D) hydrodynamic nova simulations with a multi-zone model for particle acceleration and radio emission, computing thermal free-free and non-thermal synchrotron radiation, including the Razin effect and free-free and synchrotron self-absorption for different CBM configurations. Early radio morphology should not be interpreted directly as the intrinsic shock geometry, because free-free absorption selectively obscures regions of the 3D emitting volume. The intrinsic radio emission is dominated by synchrotron radiation from electrons accelerated at the forward shock, with unabsorbed fluxes reaching 100-1000 Jy at GHz frequencies during the first day. Dense ejecta and shocked CBM material strongly absorb the emission, reducing the observable flux by several orders of magnitude. The source becomes largely transparent at GHz frequencies within about one month. Radio emission remains predominantly non-thermal during the first year, while thermal emission becomes important only for dense equatorial enhancements. The radio spectral index evolves from positive values caused by absorption to the optically thin synchrotron value of about 0.5 after several weeks. A short-lived polarized signal may arise during the first few days if the red giant's magnetic field contributes to the cosmic-ray-generated field. Early multi-frequency radio monitoring and polarimetry of the forthcoming T CrB eruption will probe density structure and magnetic field, testing particle acceleration in symbiotic recurrent novae.

We study connectivity-preserving finite-jump dispersion of anonymous, identical, and oblivious agents under an idealized range-only sensing model. Each agent measures only the distances to its visible neighbors, without bearings, identifiers, communication, memory, or a shared coordinate system. We derive the largest isotropic displacement certifiable as safe from these measurements alone. The resulting rule requires only the distance to the farthest visible neighbor: each agent selects a random direction and moves by half of its remaining visibility margin. The rule preserves every existing visibility edge under synchronous finite motion and therefore preserves connectivity. For two agents, we prove positive conditional drift in squared distance, almost-sure convergence to the visibility boundary, and finite expected time to reach any fixed neighborhood of that boundary. A one-million-run Monte Carlo experiment agrees with the exact first-round moments and estimates approximately 9.5 rounds to reach distance 0.97V from coincident initial positions; an independent Bellman-equation computation gives the same estimate. For general swarms, 1,000 runs across five initial-topology classes reproduce the deterministic safety guarantee at implementation level and reveal a consistent topology-dependent ordering of attainable diameter under the tested protocol. These results provide a theoretical foundation for connectivity-preserving multi-robot dispersion under minimal sensing, while isolating the guarantees achievable from anonymous range measurements alone.

Let $G$ be a $p$-adic classical group (orthogonal, symplectic, or unitary) and $\pi$ be an epipelagic representation of $G$ in the sense of Reeder-Yu. Using Mœglin's theory of extended cuspidal supports and Bushnell-Kutzko's theory of covering types, we determine explicitly the endoscopic lift of $\pi$ to the general linear group, whose Langlands dual expresses the dual group of $G$ as a complex matrix group, in terms of the inducing type of $\pi$ that extends the character of the first Moy-Prasad filtration subgroup defined by a stable functional. We interpret the inducing type of $\pi$ via Stevens' construction of supercuspidal representations by skew semisimple strata and introduce what we will call epipelagic strata, requiring only that the residual characteristic $p$ be odd. As an application, we reprove M. Oi's results on the endoscopic lifts of simple supercuspidal representations, in the sense of Gross-Reeder, of quasi-split classical groups. Finally, on the Galois side, we show that the epipelagic Langlands parameters of $G$ constructed by Reeder-Yu can be recovered via the self-duality of Bushnell-Henniart's admissible triples and endoscopic embeddings of L-groups. We also establish some related results concerning epipelagic parameters that were previously proved under restrictions on $p$, including a parity result on rectifying characters and an adjoint Swan conductor result related to the Hiraga-Ichino-Ikeda conjecture.

For each $g\ge 2$, we show that there are finitely many cyclic commensurability classes of closed, fibered arithmetic hyperbolic $3$-manifolds with genus $g$ fiber. More generally, we show that there are only finitely many conjugacy classes of admissible surface subgroups of PSL$_2(\mathbb{C})$ whose image is contained in the fundamental group of some arithmetic hyperbolic $3$-manifold. We also give an effectively computable upper bound with effective asymptotic rate on both finiteness statements. This affirms a conjecture of Bowditch, Maclachlan, and Reid.

Self-supervised vision transformers trained with DINO-style objectives exhibit striking emergent semantic representation quality across visual tasks, yet the mechanisms underlying this behavior remain unclear. We present a systematic empirical dissection of the DINO family and show that semantic representations arise primarily from enforcing consistency between geometrically distinct global views of the same image instance. This instance-specific global alignment acts as the semantic anchor of DINO-style learning. Across controlled retraining experiments evaluated on semantic correspondence and a diverse suite of 2D and 3D downstream tasks, we find that patch-level masking objectives enhance semantics only when trained jointly with this global alignment, indicating that the iBOT objective refines and densifies existing semantic structure rather than creating it independently. In contrast, local-to-global view alignment does not substantially improve semantic qualities at fixed compute beyond a purely global alignment. Beyond training design, we revisit how semantic representation quality should be evaluated: while classification accuracy is the standard validation score, semantic correspondence provides a complementary axis that more reliably predicts downstream task performance. Together, these findings provide a functional decomposition of DINO-style learning and represent an important step toward understanding how semantic representations emerge in self-supervised vision models.

Understanding the interfacial structure of multi-site polymer adsorption is critical for the rational design of functional nanomaterials. However, the distribution of chains attached via one, two, or more anchor points has remained inaccessible to experiments and conventional simulations. Experiments typically measure ensemble averages such as total adsorbed mass, while molecular dynamics simulations are limited to timescales far shorter than the relevant adsorption processes. To address this challenge, we introduce the State-Resolved Integral of First-Passage Times (SR-IFS) method. This approach decouples fast intra-layer conformational adjustments from the slow kinetics of external chain exchange, enabling quantitative prediction of the time-dependent distribution of attachment states ($p_1$, $p_2$, $p_3$) within a multi-site adsorbed layer. Using 3-arm star-like polymers as a model system, we show that the interfacial state distribution evolves from an initial prevalence of three-point attachments to a more heterogeneous mixture over long time scales, and that the equilibrium distribution can be systematically tuned by adjusting the monomer binding energy. The SR-IFS method provides access to this state-resolved information, offering a connection between microscopic kinetics and macroscopic interfacial properties.

We address the interpretation of transient spectroscopy signals proportional to average excitation number in terms of discrete number of excitations. Building on our recent intensity cycling approach, we derive a general scheme to isolate multi-particle dynamics from any transient signal under minimal assumptions. The key result is a general formula expressing the extracted nonlinear signal terms by multi-excitation propagators. We demonstrate the approach on exciton transport and annihilation in organic nanoparticles, and carrier recombination in silicon nanocrystals.

Robotic operation in previously unseen environments requires both semantic understanding and reliable metric information. While vision–language models (VLMs) provide strong semantic capabilities, their geometric estimates remain less reliable. In this paper, we propose a VLM-driven, modular perception framework for scene understanding using off-the-shelf approaches. Starting from a single RGB-D observation, the scene is segmented into object-level regions, annotated by a VLM, and grounded with depth information to construct a task-independent object-centric representation. Experiments on 151 tabletop scenes show that the proposed decomposition preserves strong semantic performance while substantially improving localization and depth estimation over direct VLM inference. The resulting representation is also integrated with a task-planning framework for robotic execution.

Electrocardiography (ECG) contains subject-specific morphology that supports biometric recognition, yet image-based performance depends on how the waveform is rendered. We introduce representative-morphology heatmaps, a deterministic ECG-to-image representation adapted from ECGXtractor. Within each block of ten aligned beats, the five beats closest to the block mean are averaged into a 400 by L matrix and rendered either as a conventional trace or as a dense cardiac-time-by-lead heatmap. Since both representations contain identical physiological samples, their comparison isolates the effect of rendering. We evaluate verification and closed-set identification on PTB, ECG-ID, and MIMIC-IV-ECG-DEMO. Five compact models, including ZACH-ViT, are trained from scratch, while six ImageNet-pretrained CNN and transformer backbones assess model scale and visual transfer. Heatmaps improve both FNMR operating points and both identification ranks in all 15 compact model-dataset comparisons, while EER improves in 14. Across the matched experiments, EER decreases by 9.59 percentage points and Rank-1 increases by 24.69 points on average. ConvNeXt-Tiny reaches 2.43% EER on PTB and 5.79% on ECG-ID, whereas DeiT-Base reaches 14.92% on MIMIC-DEMO. ImageNet initialization clearly benefits the two multilead datasets but has a mixed effect on ECG-ID, and performance does not increase monotonically with model size. The best heatmap systems approach the strongest signal-domain EER on PTB and ECG-ID, while DeiT-Base provides the strongest evaluated performance on MIMIC-DEMO. Lead-channel ablation further shows that useful channel combinations depend on the cohort and biometric task. Overall, representative-morphology heatmaps provide an effective image representation for ECG verification and identification.

Coordinating a large population of flexible grid-edge devices can alleviate the need for time-consuming and capital-intensive network upgrades. Artificial intelligence (AI)-based control methods such as multi-agent reinforcement learning or imitation learning are promising to this coordination due to their real-time decision scalability. However, system operators still need an independent and rigorous way to decide whether a given AI system is safe enough for deployment. This paper develops a finite-sample probabilistic safety certification framework for AI-based grid-edge coordination. The central idea is to reduce the complete input–AI–decision–evaluation workflow to a binary unsafe outcome under an operator-defined safety specification, and then use exact binomial inference to certify the corresponding unsafe operation probability. Given a set of held-out calibration scenarios, the framework returns the tightest one-sided upper certificate and an accept/reject deployment criterion that controls the probability of false safety certification. Because the certification is for the calibration distribution that may deviate from the future operation, we further combine the nominal certificate with physically interpretable sample-space adversarial attacks, a concept widely used in AI models to investigate their fragility. Case studies on grid-edge flexibility coordination with 1{,}000-agent AI models (independent parameters) verify the safety guarantee and the value of integrating adversarial attacks into a rolling-window training-certification-deployment flow.

Personalised pricing maximises expected revenue from a market but requires detailed information about individual customers. How much of this revenue can be recovered using a simple posted price based on a finite number of samples from the underlying value distribution? We answer this question by maximising the worst-case ratio between the expected revenues of posted and personalised pricing over the fundamental class of $\lambda$-regular value distributions. Our results reveal a structural transition as a function of $\lambda$. For the class of monotone hazard rate (MHR) distributions, corresponding to $\lambda = 0$, the sample mean is an optimal statistic: the entire sample can be compressed into its average without any loss of revenue. Beyond the MHR class, corresponding to $\lambda > 0$, this property disappears. We show that the sample mean is no longer optimal, revealing that optimal sample-based pricing rules become substantially more intricate. Nevertheless, we show that a remarkably simple order-statistic based pricing rule is asymptotically optimal as the number of samples $n$ grows, achieving the optimal approximation ratio up to a tight error of order $1/n$. Our analysis combines techniques from probability, approximation theory and optimization, including doubly infinite linear programming, hypergeometric functions, and combinatorial identities involving incomplete Beta functions.