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We extend Fine's selection method to the setting of intuitionistic modal logic and use it to provide a model-theoretic proof that Fischer Servi-style intuitionistic $\sf K4$ has the finite model property.
Guo, Fang, and Lu recently proved the Komlós conjecture: for vectors $v_1,\ldots,v_n\in\mathbb R^d$ of Euclidean norm at most one, there are signs $\varepsilon_j\in\{-1,1\}$ with $\|\sum_j\varepsilon_jv_j\|_\infty\le3\sqrt{2π}$. We give a short proof of the bound $3π$ that keeps the geometric lifting framework of (Guo, Fang, and Lu 2026a) while replacing the analytic core by a quadratic Dirichlet energy. Moreover, using a more fine-grained analysis of the stability of the product-cosine function of (Smirnov and Vershynin 2026) under translations, we further sharpen the bound to below $6.9013$. On the algorithmic side, based on the polynomial-time construction of (Guo, Fang, and Lu 2026b) we give a deterministic algorithm that finds a coloring of discrepancy at most $37.54$ using at most $\widetilde O(mn+n^4)$ arithmetic operations.
Let H be a linear group. We show that if there is an invertible matrix x such that all the elements of xH share the same characteristic polynomial then H is virtually solvable. There are plenty of applications that will be presented in future paper. Here, we discuss some applications to the generalized Weigold conjecture and present an alternative straightforward proof of the Formanek--Procesi nonlinearity theorem for Aut(F_n), n>2, over every field. When n>4 our non-linearity proof gives a stronger result than the original Formanek--Procesi theorem.
We investigate the low Mach number limit of the three-dimensional full compressible Navier-Stokes-Fourier (NSF) equations on \(\mathbb{R}\times\mathbb{T}^2\) for two different classes of initial data, corresponding respectively to a well-prepared regime and an ill-prepared regime. The density and temperature are allowed to approach different asymptotic states at infinity. For the well-prepared regime, the solutions of compressible NSF equations converge to a planar diffusion wave solution globally in time as the Mach number tends to zero, where the difference between the states at the far fields is small independently of the Mach number and the non-zero modes of the initial perturbations are exponentially small. Moreover, the optimal time-decay rate can be obtained. It can be viewed as the first global-in-time result on the low Mach number limit of three-dimensional NSF equations with large temperature variations. The corresponding local-in-time result is proved while the difference between the states at the far fields can be arbitrarily large for the ill-prepared data.
In this paper, we generalize the covariant phase space formalism conjugate to field dependent vectors to include internal gauge transformations when gauge fields are present. In our formalism, the symmetry generators are combination of diffeomorphisms plus internal gauge transformations and depend on the field configuration. When the field dependence of the symmetry generators is considered in the covariant phase space formalism, the first law of black hole thermodynamics is a direct result for generally invariant gravitational theories. To check the validity of our formalism, we investigate the conserved charges and the first laws of thermodynamics for a torus-like black hole in Einstein-Maxwell theory and a charged Einstein-Euler-Heisenberg AdS black hole in Einstein-Euler-Heisenberg nonlinear electrodynamics.
Fixed roadside cameras repeatedly observe a stable scene overlaid by sparse moving traffic. Temporal memory can recover weak observations, but reusing moving evidence at stale locations can corrupt occupancy predictions. Motion compensation addresses displacement, while reliance on the resulting history remains a separate learning problem. We introduce RoadOcc, which learns soft routing among fixed-coordinate history (\emph{Persist}), velocity-addressed history (\emph{Transport}), and current evidence (\emph{Refresh}). Motion state and class-consistent historical support supervise these source choices. Dynamic-aware cross-attention (DCA) updates candidate locations, multi-scale voxel velocity estimation (VVE) constructs transport addresses from multi-scale current--history correspondence, and velocity-guided dynamic sparse fusion (VDSF) combines routed evidence under fixed sparse-token budgets. On InfraOcc, RoadOcc reaches 65.29 mIoU and 32.37 dynamic mIoU, gains of 4.44 and 4.71 over STCOcc. Controlled address experiments show that VVE raises dynamic mIoU by 0.87 over fixed-coordinate reading. Across three seeds, supervised P/T/R adds 1.40 dynamic points over motion-corrected retrieval, while removing Refresh costs 0.32 points. Results from two transfer models, Occ3D-nuScenes, and longer intervals provide additional support. Code will be released.
In this paper, we prove that on a smooth complex projective curve of positive genus, the Deligne--Hitchin twistor spaces for the structure groups $\mathrm{GL}(n,\mathbb{C})\ (n\geq1)$ and $\mathrm{SL}(n,\mathbb{C})\ (n\geq2)$ admit no algebraization by a complex scheme locally of finite type. When the genus is at least two, the same holds for their stable loci and hence for the corresponding Hitchin twistor spaces. Nevertheless, the Deligne--Hitchin twistor spaces admit $\mathbb{R}_{\mathrm{alg}}$-definable complex analytic structures when the rank or the genus is one.
We compare the superconformal index of three-dimensional ADHM theory in fixed monopole sectors with the index of the BMN matrix model around fuzzy-sphere vacua. The monopole charges determine the sizes of the fuzzy-sphere blocks, and their multiplicities determine how many identical blocks occur. At a fixed number of fundamental hypermultiplets, we increase all positive monopole charges by the same amount while keeping their differences and multiplicities fixed. After dividing the ADHM index by the contribution of the bare monopole, it agrees order by order with the BMN index in the corresponding limit of large blocks. Fundamental excitations move to arbitrarily high orders in the index expansion, while the upper angular-momentum cutoffs of the BMN harmonics diverge, leaving the same vector and adjoint contribution.
Social simulation studies how individual behavior and social interaction produce collective outcomes. In social media marketing, campaign actions shape which consumers encounter the content and how they respond; these responses then spread through the population. We propose OranSim, a social simulation framework that connects creative, creator, targeting, and budget choices to this process. Heterogeneous consumers receive exposure according to content matching and platform allocation and generate initial responses, which propagate among 60 population segments. Candidate campaigns share the initial population and aligned random numbers, making their response trajectories comparable under action changes. In a controlled synthetic campaign, doubling the budget approximately doubles reach while lowering mean content match and engagement probability among the reached consumers; mean 14-day cumulative simulated response mass rises to 1.96 times the baseline. LightGBM predictors fitted to 39,000 historical RedNote notes estimate platform engagement with log-scale $R^2$ of 0.56--0.62 in five-fold cross-validation; a separate 12,154-note corpus supplies temporal, unseen-creator, and held-out-niche test splits. Public-data experiments evaluate policy-value estimation and audience ranking, and paired synthetic outcomes test counterfactual scoring. Together, scenario trajectories and engagement estimates support campaign selection according to a prespecified marketing objective. Code is available at https://github.com/OranAi-Ltd/oransim.
The Baringhaus-Henze-Epps-Pulley (BHEP) tests for multivariate normality are affine-invariant goodness-of-fit tests based on a Gaussian-weighted $L^2$ distance between empirical and Gaussian characteristic functions. In 1990, Henze and Zirkler expressed the limiting null distribution through the eigenvalues of an integral operator on the standard Gaussian space. In 1997, Henze and Wagner obtained a simpler covariance kernel and raised the problem of calculating the eigenvalues of the resulting operator on a Gaussian-weighted space. Although subsequent work treated the univariate case and numerical approximations in a few low dimensions, the complete all-dimensional spectral problem remained open. This paper determines both complete spectra for every dimension $d \in \mathbb{N}$ and every smoothing parameter $β> 0$. The two operators are shown to have the forms $\mathcal{X}_{β,d}^*\mathcal{X}_{β,d}$ and $\mathcal{X}_{β,d}\mathcal{X}_{β,d}^*$ for the same Hilbert-Schmidt operator $\mathcal{X}_{β,d}$. Consequently, their nonzero eigenvalues agree, including multiplicities, while the null space of the Henze-Zirkler operator is identified exactly. The Gaussian integral operator in the Henze-Wagner decomposition is diagonalized by Mehler's formula, and rotational symmetry confines the finite-rank correction to the sectors associated with spherical harmonics of degrees $0$, $1$, and $2$. The degree-$1$ and degree-$2$ eigenvalues are characterized by scalar transcendental equations, and the radial eigenvalues by an explicit pole-safe Fredholm determinant. The paper establishes nonnegativity, multiplicities, eigenfunction reconstruction, completeness, the trace identity, and a complete characterization of all exceptional pole cases.
Claims data can show that provider behavior changed but cannot by itself explain why. Fraud, waste, and abuse (FWA) review requires identifying material behavior, locating the codes and dollars driving it, and testing plausible explanations. Forecast residuals conflate growth, service-line shifts, code maintenance, and incomplete observation with potentially concerning behavior. We instead formulate provider review as a descriptive representation problem: observed amount $y_{ijt}=s_{it}p_{ijt}$, where $s_{it}$ is provider scale and $p_{ijt}$ is procedure composition. The profile records scale history, effective-dated code lineage, clinical-family shares, first-use events, billing context, and Medicare-versus-client differences. An optional rank-32 nonnegative factorization of procedure co-occurrence adds a fixed semantic geometry for similarity and retrieval. The profile surfaces evidence for review without inferring intent or adjudicating FWA, and is one engine within Falcon's broader review system. In a ten-quarter proprietary Medicare Carrier and DME build (1.27 million providers; 9.2 million provider-quarter profiles through 2026~Q2), the semantic dictionary covers 3,641 procedures and raises recall at 10 from 36.0\% to 44.4\%; for high-cost rare events, recall at 50 is 56.1\% versus zero for popularity. Under the governed eligibility contract, 414,093 providers enter the national review population, with 81.8\% and 90.8\% remaining eligible across adjacent quarters. Replication across eight client panels preserves 86.9--95.2\% amount-weighted semantic coverage. Transparent descriptions thus form the core, with learned representations adding optional semantic context.
A weak form of the Hellinger conjecture of Anantharam, Bogdanov, Chakrabarti, Jayram, and Nair for the binary symmetric channel is proved: dictator functions maximize Hellinger $Φ$-entropy among all Boolean functions of the input and all one-bit statistics of the output of a noisy channel. The technical heart of the matter is an explicit inequality in three real parameters, which is proved using explicit polynomial approximations and computer-assisted positivity checks. The results are also formally verified in Lean 4.
Intermittent time series are common in spare-parts demand and retail sales. Since the cost of forecast errors is typically asymmetric, decisions such as inventory control require the full predictive distribution rather than a point forecast. Many probabilistic forecasting methods have been proposed; their implementations, however, are scattered across different software frameworks, making it difficult to compare them systematically. We introduce $\textbf{fable.intermittent}$, an R package that implements several probabilistic forecasting methods for intermittent series within the $\textbf{fable}$ framework. The package allows several models to be fitted and evaluated on a collection of time series through a single, simple forecasting pipeline. We also introduce TWEES, a new exponential smoothing model with a Tweedie predictive distribution. Fitting TWEES requires repeated evaluation of the computationally demanding Tweedie density. We also release the R package $\textbf{tweedieDistr}$, whose implementation of the Tweedie distribution is substantially faster than the existing one while preserving the same numerical accuracy. We evaluate the methods implemented in $\textbf{fable.intermittent}$ on four datasets, also released in the package.
Scientific tasks specify a desired capability, but realizing it often requires building a computational system tailored to the task---acquiring data, designing representations, training models, implementing tools, and deciding how they are used at inference. We present, a framework in which an AI builder turns a scientific brief into an executable AI lab: a task-specific solver that integrates models, knowledge resources, tools, and a controller behind a fixed interface. The builder develops and packages the lab in a metered workspace; a separate host then executes the delivered artifact on held-out inputs, with reference labels kept outside the solver's input interface, and scores its outputs under the task's protocol. This makes the delivered system, rather than the builder's account of its progress, the object of evaluation. We document 10 selected constructions across six scientific task categories---from molecular and genomic prediction to medical imaging, clinical decision support, and biomedical text---whose delivered labs exceeded their configured reference values on all 12 subtests under host-side execution. Four contain predictive models fitted during construction; the others assemble executable analysis environments, knowledge resources, and tool-driven workflows around a fixed platform LLM. Together they show that an AI agent can carry a scientific brief all the way to a working lab that can still be invoked, inspected, and checked after construction ends.
Raman preprocessing and enhancement methods are often assessed by comparing their output with a clean reference spectrum using measures such as mean squared error (MSE). Whether these spectral quality measures reflect downstream analytical performance is rarely tested. We propose a controlled-perturbation framework for this test. Five perturbation types (baseline distortion, independent noise, correlated noise, global wavenumber shift, and nonlinear axis warping) at eight strengths produce paired changes in a quality measure (metric harm) and in downstream performance (task harm). The alignment gap (AG) quantifies how much a single monotone metric-to-task relationship, fitted by isotonic regression, improves when each perturbation type receives its own relationship. Ordering concordance (OC), a clustered Kendall-type index, measures how often a measure ranks conditions of different perturbation types in the same order as their task harm. Cluster-bootstrap intervals and Holm-adjusted sign-flip tests compare twelve candidate measures with MSE. Three public datasets are used: bacterial classification by principal component analysis and logistic regression, sugar-mixture quantification by partial least squares regression, and mineral identification by cosine library matching. Models are fitted to unperturbed or to correspondingly perturbed training spectra. For bacterial classifiers fitted to unperturbed spectra, Wasserstein distance improved both statistics relative to MSE (Holm-adjusted p < 0.05), also after axis perturbations were removed or spectra were compared on a common grid; refitting to perturbed spectra reversed this advantage. Peak-based measures and a structure-to-noise ratio improved both statistics only for refitted sugar calibrations, and no candidate did so for mineral identification. Open code supports testing new measures.
Physical changes or sensing errors can invalidate embodied agents' task-relevant beliefs. AquaMend compares re-probing, rollback, and supported continuation on a probe-belief-action graph under an expected-loss objective covering sensing, physical recovery, and uncorrected failures. A joint posterior guides a one-step policy with conditional detection-power screening. The per-belief three-way optimum requires independence, separability, and fully resolving probes; the general policy has no global optimality guarantee. Across 32 paired scenarios in a self-constructed simulation benchmark, AquaMend recovers in 28/32 cases and reduces mean complete loss by 21.6% versus restart. Its paired loss difference from decision-theoretic troubleshooting (DTT) is not statistically significant after Holm correction. Against the all-candidate ablation, online decision time decreases by 12.3% overall but increases by 3.4% in the uncovered late stage.
Atmospheric observations are sparse, heterogeneous, and unevenly distributed, whereas many generative atmospheric models learn distributions over regularly gridded multivariate states. Once pretrained, diffusion models can supply atmospheric priors that can be combined with observation-derived likelihood factors in a Bayesian formulation. However, these observation sources differ substantially in geometry and sampling density, complicating the consistent use of their observations within a common inference framework. Here, we formulate this reconstruction problem as generative atmospheric super-resolution and introduce composable observation interfaces for conditioning a single pretrained 13-variable atmospheric diffusion model. The interfaces convert sparse radiosonde (R), clustered aircraft (A), and dense irregular surface-station (S) observations into source-specific likelihood factors that specify where observations constrain the gridded state, how residuals are counted under uneven sampling, and how strongly each source guides posterior sampling. We developed the aircraft and surface observation interfaces using 2019 observations and evaluated the selected interfaces throughout 2020 without further tuning. Compared with reconstructions conditioned only on radiosonde observations, the composed R+A+S interface reduces RMSE evaluated against ERA5 by $9.24\%$ across all 13 state variables over the CONUS domain. The aircraft and surface factors provide complementary improvements in upper-air and surface variables. The R+A+S combination also lowers the Continuous Ranked Probability Score (CRPS), while evaluations at held-out aircraft and surface-station observations show reduced prediction errors. Together, these results demonstrate a modular route for conditioning a pretrained atmospheric generative prior on heterogeneous in situ observations without retraining the underlying model.
Links in projective space $\mathbb{R}P^3$ can be represented by diagrams in $\mathbb{R}P^2$ where the projective plane $\mathbb{R}P^2$ is represented by a disk with antipodal identifications on the boundary. In this context if we place an $n-$strand braid $β$ on this disk keeping its end points on the boundary then due to the identification of antipodal points it naturally represents a link diagram in $\mathbb{R}P^3$. We call this the projective closure of the braid $β$. In this paper we show that not all links in $\mathbb{R}P^3$ possess a diagram represented by projective closure of some braid.