arXiv preprints from January 1, 2026 through September 10, 2026 — 09:44:14 EST
For every constant $2<p<\infty$ and every constant \[ 0<\varepsilon< \min\left\{\frac{p-2}{4p},\frac18\right\}, \] we give a deterministic polynomial-time reduction from 3SAT to $M^\varepsilon$-GapSVP$_p$, where $M$ is the lattice rank. For $p=\infty$, the same holds for every constant $0<\varepsilon<1/8$. The reduction builds on...
This study investigates the methodological and theoretical properties of session handover in applications that use large language models. A task may continue in a new session when the context reaches the model's input limit, when the application restarts, or when another agent is asked to finish the task. The application must then...
Large language model (LLM) agents are increasingly used to modernize the legacy Fortran underlying production scientific software, but validation of these transformations emphasizes nominal executions and may not test whether a modernization preserves the original code's response to faults, perturbations, and reduced precision. We...
We study a general class of gradient interface models with Hamiltonian $H=β\sum V(\nablaφ)$, $β>0$, assuming essentially that the potential $V$ is even, $V'(s)\ge αs$ on $[0,\infty)$ for some $α>0$, and $-M\leq V''\le C$. We establish a Helffer-Sjöstrand representation for these models, and use it to prove that their scaling limits...
In this paper, a quantitative condition for optimality for distributed optimal control problems with box-constraints that are subject to a semilinear elliptic equation is considered. An important property of the investigated optimal control problems is the absence of a Tikhonov regularization. It is well known that at a given control,...
We develop bootstrap-assisted robust binary segmentation (BARBS), a recursive binary segmentation method for multiple change point detection under general nonstationary temporal dynamics. A novel Gaussian multiplier bootstrap for the CUSUM statistics is proposed, offering robustness to complex dependence structures. Through meticulous...
We propose a distributed selective inference framework tailored for high-dimensional quantile regression. To enable valid post-selection inference in this context, we address the computational challenge posed by the non-smooth quantile loss via a response-surrogation strategy. This strategy transforms the problem into a penalized...
Estimating the distribution of relaxation times (DRT) fromelectrochemical impedance spectroscopy (EIS) is an ill-posed inverse problem that is highly sensitive to regularisation choices. We propose a physics-informed convolutional autoencoder that estimates DRT directly from EIS data without spectrum-specific tuning. A discretised...
Causal mediation analysis is typically formulated under no interference, an assumption often violated in networked populations. We develop a nonparametric framework for a single large observed network that allows simultaneous treatment and mediator spillovers and high-dimensional network confounding. Exposure and mediator mappings...
We present the mathematical foundations of linear independent component analysis (ICA) models based on standard literature in a self-contained note. It is aimed at readers with a background in measure-theoretic probability theory. We first develop the theory of the characteristic functions of probability measures on $\mathbb{R}^d$,...
Many operational decisions are sequences of interventions under a cumulative resource limit, such as a maintenance schedule within a crew-hour budget. Choosing among them calls for the outcome and the cumulative cost each would produce, counterfactual quantities identified from observational data. Two strategies with the same expected...
We develop the statistical and algorithmic theory of inverse optimal transport (IOT) under the feature-parameterized cost C_theta(i,j) = -theta^T phi(i,j). The core technical contribution is the Sinkhorn linearization -- the implicit-function sensitivity of the entropic OT plan to the cost -- together with its spectral proxy, a...
Socioeconomic indicators in England exhibit complex spatial patterns that are not well captured by standard approaches based on averages or broad geographic classifications. We propose a method for comparing areas based on their internal spatial structure, using a multiresolution representation derived from the discrete wavelet...
To avoid missing important variables and their connections in networks, more and more variables are included in network analysis. Here we show that in a setting with many more parameters than observations (high-dimensional) it is possible to get a conservative (i.e., low false positive rate) estimate of the neighbourhood for each node...
In the linear regression model, we construct a nonparametric estimate of the regression parameter vector $\boldgreekβ$ that is insensitive to a possible nuisance autoregression in the model errors. The main tool for estimating $\boldgreekβ$ is based on the autoregression rank scores of the model. The resulting estimator is invariant...
Distributional shifts arise when the target deployment environment differs from the source environment that generated the training data. Robust learning frameworks such as Distributionally Robust Optimization (DRO) and Robust Satisficing (RS) aim to address this challenge, yet their finite-sample guarantees under such shifts, and...
We propose a robust barycenter for distribution-valued data by incorporating the Huber loss directly into the optimal transport cost. In contrast to metric-space Huber means, which apply the Huber loss to the Wasserstein distance after optimization, our construction acts on individual transport displacements, preserving quadratic...
In organized crime, membership moves fastest, deterrence capacity moves more slowly, and division norms move slowest. We model this as a three-stage game: division norms fix how every possible coalition divides its proceeds; the authority then attaches deterrence capacity to named members, before knowing which coalition will form;...
I consider an AR($p$) process that is observed every $q$ periods, either as a snapshot (stock variable) or as a sum over the sampling interval (flow variable). Under fairly mild assumptions, I derive the identified set for general lag lengths $p \in \mathbb{N}$ and sampling frequencies $q \in \mathbb{N}$, I bound its cardinality, and...
We consider the classical additive measurement-error model $X=Y+Z$, where the latent random variable $Y$ has unknown distribution $F_Y$ and the error $Z$ has a known distribution. We develop direct estimators for three functionals of $F_Y$: (i) $F_Y(x)$ at continuity points; (ii) interval probabilities $F_Y(y)-F_Y(x)$ when $x<y$ are...
We solve a natural bimatrix game related to graphs. We consider a finite directed graph $G=(V,E),$ where the strategy set of Player I is the set of vertices $V$ and that of Player II is the set of edges $E.$ There are two sets of positive weights ${\{α_e\}}_{e\in E}$ and ${\{β_e\}}_{e\in E}.$ If Player I chooses a vertex $v$ and...
This paper studies imperfect competition in general equilibrium when households and firms choose price-contingent schedules. Market clearing selects the price generated by those schedules, and each agent accounts for how its own behavior changes equilibrium prices. We derive household and firm optimality conditions, establish...
The dispersion of self-reported life satisfaction has been proposed and used as a comprehensive measure of societal inequality. A negative cross-country association between mean life satisfaction and its standard deviation has been read as evidence that this inequality is itself welfare-relevant, but critics have pointed to the...
Factor-MIDAS regressions forecast a low-frequency target by extracting common factors from a large panel of high-frequency predictors via principal component analysis (PCA). While PCA mitigates the curse of dimensionality, it relies on factor pervasiveness, an assumption often violated when factors are weak, as is common in...
We study a platform that prefers to sell the more profitable of two products. It designs an algorithm that determines the product the consumer encounters first, conditional on her best match. The algorithm simultaneously manipulates consumer attention (steers) and communicates information about match quality (informs). When the...