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Related Articles from SNS
Theta phase and theta-gamma coupling organise the spoken language network
Speech production requires rapid coordination of conceptual and lexical processes across distributed cortical networks, yet the neurophysiological mechanisms enabling this coordination remain poorly understood. Oscillatory coupling has emerged as a candidate mechanism for coordinating neural activity across spatial scales. Here, we used whole-head magnetoencephalography during overt picture naming to test how phase and phase-amplitude coupling organise neural dynamics preceding articulation.
Theta gates and routes information in the frontal cortex
Theta (4-10 Hz) oscillations seem well-suited for coordinating neural activity. Many studies have focused on theta's role in long-range coordination across brain regions (e.g., connectivity between the prefrontal cortex and the hippocampus). It remains unclear how theta coordinates neural activity more locally within prefrontal subareas.
Weak order one convergence of structure-preserving stochastic theta methods for stochastic differential algebraic equations with time-dependent singular matrices
new Abstract: This paper studies the weak convergence order of structure-preserving stochastic theta methods for a class of index-$1$ stochastic differential algebraic equations with time-dependent singular matrices. The singular matrix is allowed to vary in time but preserves a fixed differential-algebraic splitting, thereby extending the constant singular-matrix setting while retaining the projector structure required for constraint preservation. By exploiting the index-$1$...
Symmetry-based selection rules for higher-order interactions in coupled oscillators
Announce Type: cross Abstract: Pairwise interactions among general nonlinear oscillators can be reduced, via phase reduction, to a Kuramoto-type phase coupling $\sin(- \theta_j+\theta_k )$. For higher-order interactions, multiple phase couplings exist -- such as $\sin(-2\theta_j+\theta_k+\theta_l )$ and $\sin(-\theta_j+2\theta_k-\theta_l)$. Since different nonpairwise coupling functions produce qualitatively different dynamics, it is important to understand which phase couplings should be...
A remark on the majorizing measures theorem for general processes
Announce Type: replace-cross Abstract: We show that the lower bound in the majorizing measures theorem holds for a large class of random vectors. Specifically, suppose $X \sim \mu$ is a centered random vector in $\mathbf{R}^n$ with \[ C_{\mathrm{KL}}(\mu) = \sup_{\substack{\theta \neq \eta \\ \theta, \eta \in \mathbf{R}^n}} \frac{\mathrm{KL}(\mu_\theta \| \mu_\eta)}{\|\theta - \eta\|_2^2} <
A remark on the majorizing measures theorem for general processes
arXiv:2606.03973v1 Announce Type: cross Abstract: We show that the lower bound in the majorizing measures theorem holds for a large class of random vectors. Specifically, suppose $X \sim \mu$ is a centered random vector in $\mathbf{R}^n$ with \[ C_{\mathrm{KL}}(\mu) = \sup_{\substack{\theta \neq \eta \\ \theta, \eta \in \mathbf{R}^n}} \frac{\mathrm{KL}(\mu_\theta \| \mu_\eta)}{\|\theta - \eta\|_2^2} <
Characterization of Gaussian Universality Breakdown in High-Dimensional Empirical Risk Minimization
arXiv:2604.03146v2 Announce Type: replace-cross Abstract: We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs. By heuristically extending the Convex Gaussian Min-Max Theorem (CGMT) to non-Gaussian settings, we derive an asymptotic min-max characterization of key statistics, enabling approximation of the mean $\mu_{\hat{\theta}}$ and covariance $C_{\hat{\theta}}$ of the ERM estimator $\hat{\theta}$. Specifically, under a concentration...
Closed-form linear moments of the two-dimensional angular central Gaussian distribution
arXiv:2605.31536v1 Announce Type: cross Abstract: The polar-angle marginal of a centred bivariate Gaussian distribution, obtained after integrating out the radial coordinate, gives the two-dimensional angular central Gaussian (ACG) distribution of Tyler. While its trigonometric and vector-valued moments have been studied in detail, to our knowledge there are no explicit closed-form expressions for the \emph{linear} moments $\mathbf{E}[\theta]$ and $\mathbf{E}[\theta^{2}]$ on the natural...
Revenue Guarantees of No-Swap-Regret Dynamics in First Price Auctions
arXiv:2606.06085v1 Announce Type: new Abstract: We study the revenue of approximate correlated equilibrium in discrete first price auctions - the set of allowable bids is $\mathcal{B} = \{0, 1/k, \dots, 1 - 1/k, 1\}$ for some $k \in \mathbb{N}$. We show that the revenue of any $\epsilon$-approximate correlated equilibrium is at least $v_2 - \Theta(1/k)- \Theta(\epsilon k^2)$, where $v_2 \geq 0$ is the second-highest valuation. Our results establish the first polynomial convergence rates on...
Constraint residuals, graph posteriors, and determinant-corrected full-space targets in Bayesian inverse problems
Announce Type: cross Abstract: Bayesian inverse problems constrained by state equations are often sampled in a full parameter-state space by penalising the residual, rather than in a reduced space where the state is eliminated. We show that these formulations are not automatically equivalent as posterior measures. For finite-dimensional discretisations of equality-constrained inverse problems, assume the state equation \(c(\theta,u)=0\) has a unique solution \(u=G(\theta)\) and nonsingular...