Papers

We study the notion of a super caliber of a topological space, which is closely related to the classical notion of caliber and has appeared in the literature under several different names. We collect and unify several known results and establish new results concerning the collections of super calibers of topological spaces and their hyperspaces. In particular, we investigate the relationship between the super calibers of a space $X$ and those of hyperspaces $\mathcal{H}(X)$ lying between $\mathrm{CL}(X)$ and $\mathcal{F}(X)$. For infinite metrizable spaces, we characterize several cases in which $\mathsf{SC}(X)$ and $\mathsf{SC}(\mathrm{CL}(X))$ differ and establish an independence result over ZFC; see Theorem~5.12.

Stochastic reconfiguration (SR) is the standard optimizer for neural quantum states (NQS), but modern NQS often have far more parameters than Monte Carlo samples. We show that in this regime the diagonal shift is more than a numerical stabilizer. It acts as a statistical filter for finite-sample generalization. At a fixed wave function, SR is ridge regression from tangent features to the centered local energy. Its residual is the expressivity gap, the part of imaginary-time evolution outside the current tangent space. This gap is orthogonal to the tangent space in population, but finite batches make it act as noise that SR can overfit. The shift therefore balances shrinkage of useful update directions against variance from fitting sampled residuals. Exact diagnostics on a $4\times4$ Heisenberg graph separate two effects of overparameterization. Larger tangent spaces help when they reduce the expressivity gap, but they can hurt when they overfit a fixed gap. In a $100$-site transverse-field Ising family trained with a foundation NQS, validation risk is U-shaped in the shift while variance decreases, matching the noisy-ridge model. This view leads to multi-shift SR (MS-SR), which averages independent ridge solves at data-adaptive shifts to form a richer, lower-variance spectral filter. Checkpoint-local experiments show that MS-SR lowers validation risk and update variance relative to the fixed-shift SR baseline. We further compare MS-SR and SR in paired online training continuations, with independent endpoint energy evaluations and a separate update-cost benchmark.

Digital direct-to-consumer (DTC) health campaigns are usually measured after the fact. In-flight forecasting commonly relies on a separate classifier for every cutoff and horizon. We treat this task as a dynamic-system problem and build a compact patient world model. The architecture maintains a latent state per patient, learns exposure-conditioned state dynamics jointly with a weekly conversion hazard, and rolls forward into future conversion curves. We evaluate it on a US campaign dataset with 147{,}173 patients and 5.2 million at-risk person-weeks. In a retrospective evaluation conditioned on recorded future exposures, the model forecasts the remaining new-to-brand prescription volume through week 52 with a relative error of 2.9% from a week-4 cutoff and 0.8–2.6% from cutoffs at weeks 8–26. The strongest non-recurrent baseline, a pooled-hazard gradient boosting model given the same survival rollout and information, has relative errors of 13.6–33.1%. Per-horizon classifiers perform substantially worse. A Fisher-information analysis motivates dense next-exposure supervision when conversions are rare. Removing this auxiliary objective increases prescription-volume error by approximately $2$–$14\times$, while providing no consistent disadvantage on the more common specialist-visit outcome. We also evaluate scenario simulation. Switching all future exposure off raises predicted conversion from 0.31 to 0.89, a pattern consistent with selection effects in observational exposure data. This result highlights the limits of interpreting exposure-conditioned rollouts causally.

We study principal component analysis (PCA) under memory constraints, a setting that is increasingly important in large-scale data analysis. Our focus is on Oja's algorithm, which is a one-pass, memory-efficient algorithm requiring only $O(p)$ storage in the rank-one case and $O(pk)$ storage for $k$- PCA. The main goal is to develop a procedure based on Oja's algorithm that is optimal without prior knowledge of the eigengap, which is otherwise needed to tune the learning rates effectively. We do this by first introducing a geometric perspective on the convergence of $k$-PCA: by embedding the Oja iterates into the exterior space, we establish an exact equivalence between $k$-PCA in the ambient space and $1$-PCA in the exterior space. This geometric viewpoint enables us to establish several convergence guarantees, including one based only on a single learning-rate schedule. Building on this geometric perspective, we develop an averaging theory for $k$-PCA and show that the resulting averaged estimator is adaptive: it achieves the nearly optimal convergence rate without prior knowledge of the eigengap. As an application, we construct memory-efficient estimators for elliptical component analysis (ECA) \cite{han2014scale,han2018eca}. Simulation studies and real data analysis are conducted to demonstrate the benefits of our proposed algorithms.

The 6–18~GHz upper mid-band is a promising spectrum range for future sixth-generation (6G) networks due to its favorable balance between available bandwidth and propagation capability, while its same-site coverage performance remains a key deployment concern. This paper presents a wideband channel measurement campaign at 13 spatially aligned frequency points from 6 to 18~GHz in an urban macrocell (UMa) environment, and investigates the frequency evolution of channel characteristics and same-site coverage capability. The results show that path loss generally increases with frequency, while the higher-frequency channels tend to exhibit smaller root-mean-square (RMS) delay spread (DS) and larger PDP-based $K$-factors. Based on the measured path-loss characteristics, the additional link-budget requirement and service-aware same-site coverage are further evaluated. Under the baseline service configuration, the 80% coverage distance $d_{80}$ decreases from approximately 129~m at 6~GHz to 58~m at 18~GHz. Further analysis quantifies the impacts of service rate, resource allocation, interference, and link-budget degradation on coverage, providing measurement-based insights for same-site deployment across the 6–18~GHz band.

MARVEL's first direct observation of Migdal ionization in neutron scattering marks an experimental milestone and opens a new avenue for probing electronic response to nuclear recoil. Hydrogen, both the simplest atom and a constituent of its molecular target, provides a controlled benchmark. Within the nonrelativistic sudden approximation, we compute its energy-differential and integrated ionization probabilities with the full recoil phase. At the recoil parameter $\beta\equiv v_N/(\alpha c)=1.04$, the full-to-dipole spectral ratio rises from $0.43$ when the emitted-electron energy is $1\%$ of the hydrogen binding energy to $5.0$ when it is $2.3$ times that energy. Near $\beta=10$, partial waves with orbital angular momentum $\ell\ge3$ carry more than $90\%$ of the calculated continuum probability. An independent bound-state-closure evaluation verifies the absolute normalization: at eight recoil values, its ionization probabilities agree with the continuum-integrated results to relative discrepancies below $4.4\times10^{-7}$. These results extend the hydrogen dipole response to the fast-neutron regime and establish energy and angular-momentum redistribution as linked consequences of resolving the recoil phase across an atom.

Every particle-physics experiment builds detector-health monitoring, and many end up rebuilding it, because a first system written under commissioning pressure often proves too rigid to maintain. ARGUS (Automated Anomaly-detection, Run-quality and General Unified Surveillance) is a configuration-driven framework that separates what is generic in this problem (the health monitors, their validation, and the reporting) from what is not (the data schema and the thresholds). Standing it up for a new detector requires a data adapter and a configuration file, not a rewrite. Detector health is judged by four independent monitors: expert cuts, which are authoritative; a machine-learning second opinion that is additive and off by default; a trend forecast that gives early warning before a threshold is crossed; and a reference-histogram comparison with pluggable statistical tests. The monitors are compared and never merged, and an alerting layer turns their flags and warnings into deduplicated notifications. We demonstrate the full chain on a synthetic reference detector with planted pathologies and a fault-injection campaign that manufactures ground truth: the cuts recover every planted pathology with no false positives, the machine-learning monitor reaches a ROC AUC of 0.896 on injected faults and extends coverage to fault classes no cut was written for, the forecast flags a drifting channel before its cut fires, and the histogram comparison catches every planted shape distortion while holding its configured false-positive rate on clean pairs. A second demonstration shows the framework adapting to a reorganized file layout with no change to code or configuration. Every result and figure in this paper regenerates from the code alone. The framework has been implemented for two particle-physics experiments, where it is under evaluation; adoption decisions rest with the collaborations.

Heterogeneous integration combines complementary material properties in a single photonic platform. Here, we demonstrate on-chip $f$-2$f$ self-referencing in a heterogeneously integrated Si$_3$N$_4$/LiNbO$_3$ platform, in which supercontinuum generation in a Si$_3$N$_4$ waveguide and second-harmonic generation in a LiNbO$_3$ layer are spatially separated and linked by adiabatic escalator couplers. Pumped by a 1560 nm mode-locked laser with 75 pJ on-chip pulse energy, we detect the carrier-envelope offset frequency with 30 dB signal-to-noise ratio in 300 kHz resolution bandwidth. A comparative measurement confirms that the second harmonic originates in the LiNbO$_3$ layer and indicates opportunity for further improvements through periodic poling. These results establish heterogeneous Si$_3$N$_4$/LiNbO$_3$ integration as a viable building block for self-referenced ultrafast pulse sources in low-loss Si$_3$N$_4$ photonics.

We present a construction with seven points on a circle that is not Ramsey, disproving a conjecture of Erdős, Graham, Montgomery, Rothschild, Spencer and Straus.

We develop a bihomotopy argument to estimate the discrete material time derivatives of consistency functionals. Combined with summation-by-parts, this argument yields a directional super-convergence estimate for the consistency contribution when tested with the normal error velocity. Together with the super-approximation of the reversely weighted discrete normal, these techniques establish $L_t^\infty H_x^1$ super-convergence of the projection error and optimal $L_t^\infty L_x^2$ convergence of the trajectory error of a stabilized BGN method for curve-shortening flow with piecewise linear parametric finite elements.

Single-cell foundation models (scGPT, scBERT, Geneformer) achieve cell-type classification accuracy up to 97.5% in our experiments, yet this aggregate accuracy can mask systematic failure on rare, often disease-relevant cell populations that long-tail loss functions are widely assumed to address. We present a systematic benchmark of six long-tail loss functions (cross-entropy, weighted CE, class-balanced loss, focal loss, LDAM, logit-adjusted softmax) across three architectures and three datasets (Multiple Sclerosis, Zheng68K, human Pancreas), totaling 162 controlled training runs (3 backbones x 3 datasets x 6 losses x 3 seeds). The gap between overall accuracy, Macro-F1, and rare-class recall under plain cross-entropy is consistent across all nine (architecture, dataset) settings, driven by dataset structure rather than pretraining. Rare-class failure itself splits into two regimes with distinct embedding-geometry signatures, visible before any loss is chosen: some classes are recoverable by the right loss, while others retain linear separability yet are absorbed into unrelated classes' neighborhoods under every evaluated loss and architecture. Among the recoverable classes, the efficacy of reweighting is predicted by a class's absolute training-set size, rather than its share of the dataset or the dataset's overall imbalance ratio. Class-balanced loss and LDAM are the most consistent choices across all nine settings, while logit adjustment trades rare-class precision for recall rather than improving both. Our results give both a reusable benchmark and mechanism-grounded practical guidelines for combining foundation models with imbalanced biological data.

For each positive integer $N$, we construct global spectral group actions for the defocusing and focusing nonlinear Schrödinger hierarchies on initial-data classes containing $W^{2N+1,\infty}(\mathbb R)$. For $N\ge2$, the quadratic flow gives global classical cubic NLS solutions. The construction extends the Sato–Segal–Wilson and Kotani frameworks to matrix Dirac systems; a homogeneous tau-function identity supplies the focusing positivity. No decay, smallness, periodicity, arithmetic condition, or prescribed spectral background is required for the initial-data inclusion. As a principal application, we prove global well-posedness on $M_{\infty,1}^{5}(\mathbb R)$ for both signs, with finite-time bounds and locally Lipschitz dependence on initial-data norm balls. The passage to this Banach-space flow uses near-real-axis Weyl asymptotics and continuity of normalized Toeplitz operators on compact initial-data sets to obtain uniform spatial bounds from five bounded derivatives. In the defocusing case, the flow extends to $M_{\infty,1}^{5}(\mathbb R)+H^1(\mathbb R)$. Further consequences include quantitative approximation, preservation of spatial Bohr almost periodicity and its frequency module, conjugacy of spatial translation hulls, and preservation of the full complex Dirac spectrum and spatial transfer growth rates.

This paper investigates robust beamforming and antenna position design for movable antenna (MA)-enabled integrated sensing and communication (ISAC) systems under antenna position errors. In particular, deviations between the actual and nominal antenna positions in practical MA arrays are inevitable due to limited mechanical accuracy. Therefore, the conventional ISAC design based on nominal positions may suffer from substantial performance degradation. To address this issue, we consider a monostatic downlink MA-ISAC system in which each transmission frame consists of a low-power pilot and an ISAC payload. The target angle, reflection coefficient, and antenna position-error vector are jointly estimated based on these two observations, thereby enabling sensing with imperfectly known antenna positions. We derive the resulting angle Cramer-Rao bound (CRB) and formulate a problem that minimizes its worst-case value subject to each user's signal-to-interference-plus-noise ratio (SINR) requirement under all possible position errors. By exploiting a common phase-response decomposition, we obtain tractable reformulations and develop an alternating optimization (AO) algorithm for the beamforming vectors and nominal antenna positions. Numerical results demonstrate that, compared with conventional nominal-position designs, the proposed robust scheme achieves improved communication reliability while maintaining competitive sensing accuracy under practical antenna position uncertainty.

The general broadcast channel (BC) has attracted considerable attention because it is a central problem in network or multi-user information theory. The deterministic BC (det-BC), in which both output symbols are functions of the input symbol, plays a vital role in understanding general BCs. In the 1970s, Marton and Pinsker investigated the det-BC independently using a random coding approach and hence quantified its capacity region as functions of the entropy of output symbols. In this paper, we present a purely deterministic and combinatorial treatment of the deterministic BC, which is in contrast to Marton and Pinsker's probabilistic treatment. In particular, we show that each det-BC can be uniquely and completely characterized by a bipartite graph. Based on the bipartite graph model, we present the explicit capacity region of the general det-BC and a deterministic capacity-achieving coding scheme. Specifically, each point on the capacity region boundary is expressed as an explicit function of the degree sequences of the two parts, with boundary coordinates parametrized by the tangent slope. As a result, a closed-form capacity region, which was previously unknown except for special cases such as the Blackwell channel, can be analytically determined, without optimizing the probability distribution of input symbols numerically. For a bipartite graph consisting of multiple isolated subgraphs, there can exist a commonly decodable message while preserving the maximum achievable sum rate, and its achievable rate is explicitly characterized. Finally, the bipartite-graph formulation allows us to construct optimal finite-blocklength coding for the det-BC through binary linear programming.

Low-rank adaptation (LoRA) has become a key technology for serving large-scale personalized large language models and diffusion models in the cloud. However, the co-occurrence patterns, resource contention relationships, and evolutionary regularities of adapters under production inference workloads have not been systematically or quantitatively studied. Based on GenTD26, Alibaba's production diffusion model inference dataset, this paper adopts a graph-theoretic framework to construct an adapter co-occurrence network and conducts a characterization from both static structure and dynamic evolution. Our main findings are as follows. (1) The co-occurrence network is extremely sparse, and adapter usage frequency follows a significant heavy-tailed distribution. (2) Introducing the first adapter incurs a 66.1% execution-latency overhead, with diminishing marginal costs afterwards. (3) Co-occurrence relationships are driven by base models: in 90.6% of multi-adapter requests, all adapters share the same dominant base model; 66.2% of significant co-occurrence edges connect same-model adapter pairs; and in 85.8% of multi-adapter requests, all adapter pairs form significant co-occurrence edges. (4) The adapter ecosystem exhibits a core-periphery bipolar structure, with a weekly Jaccard similarity of 0.696 at the model level and a churn rate of 54.5% for the top-10 hottest models within a 12-hour window. Based on these findings, we propose a preloading strategy built on top-k co-occurrence statistics; offline experiments show that it covers 81.0% of test-set co-occurrence pairs at k=3, and sensitivity analyses across frequency thresholds and time windows verify the robustness of the conclusions. These results provide a data-driven basis for cache preloading, adaptive scheduling, and GPU memory management in LoRA inference services.

Social bot detection is essential for protecting online platforms from misinformation amplification, coordinated manipulation, and distorted public discourse. However, large language models have made social bots much harder to detect from text alone because semantic camouflage is now cheap, fluent, and scalable. The resulting challenge is modality conflict: an account may look human-like in semantics while remaining suspicious in graph structure, profile attributes, or cross-modal consistency. Recent graph-based detectors tackle this limitation by adding graph-side complexity, such as sparse prototype selection, adaptive gating, or architecture-specific control logic, yet our experiments suggest that complexity alone is not the most reliable way to resolve such conflict. We therefore propose CSC, a calibrated-simplicity framework for conflict-aware LLM-era social bot detection. The framework combines three design choices: a simplified prototype-guided graph expert that retains useful structural biases while removing unstable graph-side heuristics, calibrated simplex-constrained fusion that aligns heterogeneous confidence spaces before late fusion, and a lightweight inconsistency expert that models cross-modal disagreement. Experiments on TwiBot-22, TwiBot-20, and MGStBot-large show that CSC improves calibrated operating-point decision quality while remaining competitive across external benchmarks. Further analyses show that calibration improves confidence reliability, the inconsistency expert mainly provides localized corrections in high-conflict or near-threshold regions, and simplified graph-side control yields a better stability-cost trade-off. A targeted semantic-camouflage stress test further shows that replacing selected bot text with matched human text sharply degrades the standalone text expert while leaving graph and fused evidence stable on a balanced challenge set.

Physical layer (PHY) information hiding supports critical applications, such as digital fingerprinting for transmitter identification and undetectable side channels for covert communication, and has attracted considerable attention from the research community. One category of prior studies focuses on theoretical analysis, proposing techniques such as artificial noise or reconfigurable intelligent surfaces to enable undetectable covert transmission. However, hardware prototypes are rarely presented due to their algorithmic complexity or hard-to-satisfy assumptions. Another category of studies focuses on system-level solutions, achieving PHY information hiding by customizing existing modulation schemes. However, these methods are typically designed for specific wireless protocols, limiting their generalizability. In this work, we introduce a new PHY information hiding paradigm that differs fundamentally from the previous two categories of approaches. Inspired by recent advancements in other domains such as image information hiding, we migrate encoder-decoder neural networks to the PHY information hiding field, embedding secrets by introducing imperceptible distortions within the preamble waveform. Sim-to-real fine-tuning is additionally proposed to tackle unique challenges, e.g., fading and hardware imperfections. The designed methodology is practical and protocol-agnostic. We provide case hardware prototypes of two commercially popular wireless technologies, i.e., LoRa and Bluetooth Low Energy (BLE), using commodity software-defined radio (SDR) transceivers, demonstrating excellent feasibility and generalizability.

For n>=2, we prove a rigidity theorem for the Hermitian boundary kernels L_{t,s}(x,y)=|1-<x,y>|^t exp(is arg(1-<x,y>)), x != y, on S^{2n-1}, with L_{t,s}(x,x)=0, t>0, and s in [-1,1]. Every finite Gram matrix of L_{t,s} has positive index at most one if and only if 0<t<=1 and s=+-t. The proof combines Fourier analysis on boundary circles with restrictions to two orthogonal complex directions. The dimension threshold is sharp. By normalizing the Gram kernels of equivariant boundary maps, we show that the translation-length factor t and the signed Cartan factor s of every continuous irreducible representation from PU(n,1) to the holomorphic isometry group of infinite-dimensional complex hyperbolic space satisfy s=+-t. Combining this with the known endpoint rigidity, Monod's constructions, and Ruiz Stolowicz's complete-invariant theorem yields the classification: the holomorphic conjugacy classes are parametrized by (t,epsilon) in (0,1) x {+-1}. Allowing anti-holomorphic conjugacy identifies the two signs. Using Monod's automatic-continuity argument and the same boundary rigidity, we also classify all irreducible self-representations of the full isometry group of infinite-dimensional complex hyperbolic space. Up to conjugacy, these are precisely Monod's representations with parameter 0<t<=1. In particular, the canonical-orbit hypothesis in Monod's classification theorem is automatic.

Epileptic seizures arise from complex, nonlinear interactions within brain networks, yet reliable electroencephalographic (EEG) prediction remains challenging due to the nonstationary and heterogeneous nature of neural dynamics. Existing methods typically analyze EEG data as static or weakly time-dependent snapshots, overlooking the intrinsic dynamics and lacking the geometric sensitivity to capture the hierarchical, localized evolution of the epileptogenic zone. To address these limitations, we propose an offline, patient-specific evaluation of chaotic dynamics-regulated topological learning (CDRTL) for distinguishing preictal from interictal EEG states. This framework unifies chaotic dynamics, multiscale algebraic topology, and local network differentiation. Specifically, we partition EEG signals into discrete functional subnets based on correlation strengths, capturing the multi-scale connectivity of the brain. By modeling each node as a Lorenz oscillator, we embed the underlying chaotic dynamics into the network architecture. We then apply the persistent Laplacian to simultaneously extract topological invariants and geometric shape evolution through harmonic and non-harmonic spectral analysis. Additionally, a node-removal topological differentiation strategy isolates localized neural contributions. Our framework was evaluated on the CHB-MIT database using balanced preictal and interictal labels and stratified channel-level cross-validation within each patient. The results support offline discrimination of preictal and interictal channel-level nodes within fixed patient-specific networks. Because representations are constructed from the complete network, including held-out unlabeled nodes, before cross-validation, the reported performance is specific to this transductive setting and does not establish generalization to unseen EEG windows, seizures, or patients.

For a general entanglement-assisted or unassisted quantum error-correcting code, a set of erasures, and an associated repair group, we propose a linear algebraic procedure to compute a reduced set of observables and a reduced repair group of codeword qudits for correcting the given erasures. The procedure has cubic complexity in the repair group size and the computed set of observables has the smallest possible size for correcting the given erasures. We specialize the general procedure to quantum codes constructed from Euclidean and Hermitian orthogonality, and provide closed-form upper bounds on the size of reduced repair groups for those special cases. Based on these closed-form bounds, we propose quantum counterparts of the information locality of classical local recovery.

Graph databases are frequently positioned as categorically necessary for connected-data workloads, yet the systems dimension along which they actually differ - query planning, indexing, and data-readiness cost - is rarely isolated from vendor framing. We construct a synthetic, biomedical-shaped property graph (1.02 million nodes, 5.34 million total node and edge rows) and a twenty-query workload spanning neighborhood lookups, bounded paths, set intersections, anti-joins, grouped aggregation, top-k ranking, temporal filters, full scans, and relational joins. We benchmark Corvic AI - a purpose-built columnar query engine underlying Corvic's ontology management layer ("memories")- against seven purpose-built or graph-extension database systems (LoraDB, Ladybug, DuckPGQ, Memgraph, Neo4j, HugeGraph, and FalkorDB) at three graph scales spanning three orders of magnitude. We report query latency geomeans, bulk-ingest throughput, point-update latency, and answer correctness for each system, and we derive a simple total-cost-of-ownership model that expresses the ingest/query trade-off as a function of query volume. Our central finding is that no system in this sample is categorically fastest: a native graph engine (Ladybug) outperforms Corvic AI on narrow, bounded-neighborhood shapes, while Corvic AI is faster on shapes that scan or join a large fraction of the graph, and a system implementing graph query syntax via SQL/PGQ (DuckPGQ) is measurably slower purely due to query-plan choice. The dominant cost differential in our data is not query latency but the cost of making data queryable at all: bulk-ingest throughput varies by three orders of magnitude across engines (5.0k-4.3M rows/s), a gap that a simple crossover-point calculation shows dominates total cost for any workload with fewer than roughly 105 queries per data refresh.

Modern LLMs with QK-normalization, gated attention, learned attention sinks, or logit softcapping exhibit weaker persistent attention sinks, on which existing KV cache eviction methods primarily rely. We observe that across these models, weaker sinks co-occur with greater value-vector dispersion relative to key-vector dispersion. Motivated by this value-side dispersion, we present ValueDiff, a value-geometric eviction that ranks tokens by the L2 deviation of their value vectors from the cache mean. The same score arises as the minimal-disturbance eviction under a max-entropy assumption about future attention. We evaluate under fixed cache budgets, with eviction at every block boundary during prefill and at every decoding step during generation. On RULER at a tight 2k token budget, ValueDiff retains 88-99% of dense across seven sink-suppressed models (best on 6 out of 7). On LongBench at the 4k budget, ValueDiff averages 92% retention across sink-suppressed models versus 83% for the strongest prior baseline. On MATH-500, ValueDiff is the strongest non-dense method on every sink-suppressed model tested at the 25% cache budget, outperforming prior methods by up to ~20 points on gated-attention models. Across all three benchmarks, value geometry emerges as the more reliable query-invariant eviction signal for sink-suppressed models.

We show that full negative regression dependence implies neither negative right-tail dependence nor negative left-tail dependence. A strictly positive distribution on a 2*2*3 rectangular state space provides an exact counterexample for the right-tail case, and its coordinatewise reflection yields a counterexample for the left-tail case. We further prove that this state-space size is minimal. The counterexample is established via a finite upper-set criterion using exact integer arithmetic. We also resolve the open question of whether full negative regression dependence implies negative association. A strictly positive distribution on {0,1,2}^4 satisfies full negative regression dependence yet violates negative association; this counterexample is verified by 17532 exact integer inequalities. The main results of this paper were first uncovered by the multi-agent mathematical system Eureka and later verified by the authors.

In environments with large movable obstacles, detour-only navigation can be inefficient or even infeasible, while obstacle interaction requires reasoning about navigation benefit, feasible placement, and executable manipulation. We present a hierarchical navigation among movable obstacles (NAMO) framework for mobile manipulators. At the high level, the planner identifies key blocking obstacles from reference paths and searches for relocation plans that jointly satisfy geometric, manipulation, and downstream navigation constraints. When direct relocation is hindered by other movable objects, a large language model (LLM) is selectively invoked to infer auxiliary manipulation dependencies, which are then verified by deterministic geometric planning. To execute the resulting relocation goals, we define discrete contact modes on the surfaces of box-shaped obstacles and select contact faces and regions online based on position and orientation errors, enabling straight, side, and corner pushing through contact switching. A recurrent reinforcement-learning policy coordinates the mobile base and manipulator to track tool center point (TCP) targets while preserving end-effector reachability during sustained pushing. Simulation and real-robot experiments demonstrate feasible navigation-manipulation in detour, single- and multi-obstacle relocation, and dependency-constrained scenarios, validating the framework for interactive navigation with large non-graspable obstacles. The open-source project is available at https://cloudytosunny.github.io/NAMO_DCPushing/.

Unstable thermal stratification modifies near-wall momentum and heat transport, causing the mean velocity profile to depart from the classical logarithmic law and complicating wall modelling for turbulent mixed convection. We develop a buoyancy-modified logarithmic-quadratic wall model for incompressible Poiseuille–Rayleigh–Bénard flow. The model combines an approximately linear relation between the near-wall mean temperature and mean streamwise velocity with a thermally modified mean-gradient representation inspired by mixing-length scaling. A priori assessments using wall quantities from the direct numerical simulation (DNS) database show that the calibrated wall law reconstructs near-wall velocity and wall-function-equivalent eddy-viscosity profiles. We implement the wall model in wall-modelled large-eddy simulations (WMLES) at friction Reynolds numbers up to $Re_\tau\approx6000$ and Rayleigh numbers up to $Ra=10^{10}$. For cases with DNS reference profiles at $Ra=10^8$ and $10^9$, the maximum pointwise absolute relative errors are $3.6\%$ for the mean velocity and $1.9\%$ for the mean temperature. For cases with available DNS global-transport data, the maximum relative deviations in the Nusselt number $Nu$ and skin-friction coefficient $C_f$ are $11.7\%$ and $15.9\%$, respectively. The WMLES reduces the mesh count by factors of approximately $195$–$542$ relative to the corresponding DNS meshes. For the $Ra=10^{10}$ and $Ri_b=0.1$ case, extrapolation of reference DNS resolution strategies gives a mesh count of order $10^{11}$, approximately three orders of magnitude larger than the present WMLES mesh count. We also examine how the balance between shear and buoyancy reorganises flow structure, and we identify signatures consistent with the coexistence of streamwise-elongated motions resembling very-large-scale motions and buoyancy-associated streamwise rolls.

Communication can bring agents into agreement while making their decisions worse. We identify two limits of aggregate descriptions of communication gain in distributed inference. First, stable linear systems with fixed evidence, network and readout can have interaction and finite-time state operators with identical eigenvalue and singular-value spectra, yet produce gains of opposite sign. Changing only message orientation raises accuracy from 72.6% to 91.2% or lowers it to 65.9%. A standard task-projected local-response approximation retains the directional information missing from spectral summaries. Using labeled calibration data separate from the test set, it predicts multi-round gains in small trained nonlinear agents with a root-mean-square error of 0.45 percentage points on two synthetic tasks; tests with natural edge changes and handwritten digits extend the evaluation. Second, under community-shared bias, higher mean individual accuracy can coexist with harm to unaffected communities or lower global-vote accuracy. At fixed communication rounds, calibration constraints reduce observed community harm while retaining much of the mean benefit, but do not guarantee protection. Full direct calibration performs similarly. The results connect spectral insufficiency, task-aware prediction and the distribution of communication benefits, while leaving broad transfer and practical superiority open.

Cross-expertise technical communication (i.e., communicating about computing topics across levels of computing expertise) is important for workplace collaboration. However, students are underprepared because computing education rarely explicitly teaches communication, and available practice tends to occur among peers with similar expertise. We take a learner-centered design approach to inform technologies for developing these skills. We interviewed 12 industry professionals and conducted focus group and co-design sessions with 14 college students preparing for computing-related roles. Professionals emphasized adapting communication, negotiating expectations, building shared understanding, and using multiple modalities and artifacts. Students anticipated challenges adapting communication, navigating unfamiliar workplace dynamics, and communicating under fear of judgment, and valued rich, realistic practice environments that preserved their psychological safety. Synthesizing professional and learner perspectives with educational theory, we conclude that building self-efficacy through authentic mastery experiences and changing attitudes related to help-seeking are critical elements for educational technology design in this context.

Online controlled experiments, or A/B tests, are widely used to estimate causal effects on digital platforms. A central challenge is to improve experimental sensitivity, or statistical power, without increasing the experimental sample size. Stratified sampling is a classical variance reduction technique; however, its effectiveness depends critically on how the strata are constructed. We thus propose an optimization-based stratification framework for stratified sampling using optimal multi-way decision trees. Our method, called Optimal Multi-way Stratification Trees (OMST), formulates stratification as a path-selection problem over a feature graph. The selected paths define interpretable stratification rules and are optimized using an exact variance-minimizing binary optimization formulation under continuous proportional allocation and a Neyman-type optimal allocation. We incorporate supervised optimal binning to generate outcome-relevant candidate splits for numerical features. Furthermore, we introduce reduction procedures for redundant candidate paths and assignment constraints, substantially reducing the optimization problem size. Experiments on both a real-world and a simulated dataset demonstrate that OMST achieves comparable or superior variance reduction to existing methods while maintaining shallow and interpretable stratification trees.

This paper presents a comparative evaluation of dense embedding models for semantic candidate-job matching in high-volume staffing workflows. Incoming job descriptions are converted into structured English search text and language-specific keywords through LLM-based parsing, and candidate profiles are indexed as semantically enriched resume representations. We evaluate EmbeddingGemma (base) against EmbeddingGemma fine-tuned with Cached Multiple Negatives Ranking Loss (MNRL) within a unified hybrid retrieval pipeline that fuses vector similarity and full-text relevance via reciprocal rank fusion (RRF), and benchmark both against the MPNet model on a batch comparative evaluation dataset scored through the deployed job-candidate matching scoring pipeline. We further document, with mathematical detail, the broader set of contrastive fine-tuning objectives considered during model development (including AnglE/CoSENT-style refinement) and the empirical rationale for retaining Cached-MNRL-only adaptation as the preferred configuration. To support reproducible model selection, we define a broader evaluation framework comprising standard information retrieval metrics (Recall@K, mean reciprocal rank, nDCG) under the exact hybrid-retrieval protocol; the metrics used for the evaluation reported in this paper are fine-tuning convergence diagnostics and a batch comparative evaluation using the deployed AI-Match score and an independent LLM-as-a-Judge relevance score, and we state this scope explicitly rather than implying the full framework was measured. The paper addresses the gap between general-purpose embedding benchmarks and enterprise job-candidate matching constraints, providing a structured basis for comparing embedding strategies under realistic job-candidate retrieval conditions.

Let $\pi: X\to \mathbb P^1$ be a semistable Jacobian elliptic surface over $\mathbb C$, and set $\chi=\chi(\mathcal O_X)\ge3$, so that $\kappa(X)=1$. Assume that the Mordell-Weil group of $\pi$ is finite and that $\pi$ has at least one reducible fiber, the reducible fibers being of types $I_{n_1},\cdots, I_{n_s}$. Recently, Laface et al. proved that the zero section and the components of the reducible fibers generate $\overline{\mathrm NE}(X)$ if and only if $$\delta(\pi):=\sum_{i=1}^s\frac{\lfloor n_i^2/4\rfloor}{n_i}\le\chi.$$ In particular, the Mori cone is rational polyhedral in this range. They also proved that $N(\pi)=\sum_{i=1}^s n_i\le 2\chi+3$ implies that $X$ is a Mori dream surface. In this paper, we study the existence problem of Mori dream surfaces provided that $N(\pi)\ge 2\chi+4$. Suppose $\delta(\pi)\le \chi$. We first show that every nef isotropic divisor on $X$ is semiample, and whenever each $n_i$ is even. Furthermore, when every $n_i$ is even, we obtain criteria for $X$ to be a Mori dream surface: $X$ is a Mori dream surface provided that either (i) all $n_i=2$, or (ii) $N(\pi)\le 2\chi+4$; if some $n_j=4$, then $X$ is a Mori dream surface if and only if $N(\pi)\le 2\chi+4$. However, once some $n_i$ is odd, we construct a Jacobian elliptic surface $\pi: Y\to\mathbb P^1$ with $\delta(\pi)=\chi=3$, trivial Mordell-Weil group, and singular-fiber configuration $I_4+3I_3+23I_1$ for which none of the eight non-vertical isotropic extremal rays is semiample. In particular, $Y$ is not a Mori dream surface.