1612191 results (page 1 of 64488)
-
Pushing the Primordial Frontier: Exact Linear Solutions in Multifield Inflation
We present exact analytic solutions for the linear dynamics of a two-field inflationary system in which the primordial curvature perturbation $ζ$ is coupled to an isocurvature perturbation $σ$ of entropy mass $μ$. The solutions are valid for arbitrary values of $μ$ and the dimensionless interaction strength $λ$, within a quasi-de Sitter background. They therefore provide analytic control over the …
-
A Joint Optimal Search for Gravitational Waves from Resolved and Unresolved Supermassive Binary Black Holes with Pulsar Timing Arrays
We introduce, from first principles, a joint model of the gravitational wave background (GWB) and brightest supermassive black hole binary (SMBHB) sources that may be individually resolvable in Pulsar Timing Array (PTA) searches for gravitational waves. We propose the characteristic number of SMBHB sources, $N_{\rm c}$, as a detection statistic for the astrophysical origin of the GWB. We then demo…
-
Impulse Decoding of Quantum LDPC Codes: Equivalence of Degeneracy and Code-Shortening
Quantum error correction is essential for building scalable quantum computers. Within the stabilizer formalism, the Calderbank-Shor-Steane framework constructs quantum codes from pairs of classical linear codes. A distinctive feature in this setting is degeneracy, where multiple equivalent error estimates exist-a phenomenon that has no classical counterpart, and the lack of a meaningful classical …
-
On zero-sum problems of two new types
In this paper, we mainly investigate zero-sum problems over $\mathbb Z/n\mathbb Z$ (with $n>1$) of two new types. Let $s_1(n)$ (resp. $t_1(n)$) be the least positive integer $k$ such that for any integers $a_1,\ldots,a_k$ not divisible by $n$ (resp., relatively prime to $n$), there is an $I\subseteq\{1,\ldots,k\}$ with $|I|=n$ for which the sum $\sum_{i\in I}a_i$ is divisible by $n$ but not divisi…
-
Field-level vs summaries: convergence of information in non-Gaussian density fields
We elucidate the sources of information gain in weakly non-Gaussian cosmological fields at the field- vs. summary-statistic-level in a controlled setting. Specifically, we compare field-level inference (FLI) with the standard power spectrum plus bispectrum (P${+}$B), and a family of composite-operator correlators (OCs) built from auto- and cross-spectra of local powers of the galaxy density field.…
-
Learning Red Agent Policy from Observations for Neurosymbolic Autonomous Cyber Agents
With sophisticated cyber-attacks becoming increasingly prevalent, modern networks require intelligent autonomous cyber-defense agents trained via Reinforcement Learning (RL). These agents employ neurosymbolic approaches such as behavior trees with learning-enabled components (LECs) to learn, reason, adapt, and implement security rules while maintaining critical operations. However, these autonomou…
-
LGNO: A Local-Global Neural Operator for Hyperbolic Conservation Laws
Solutions of hyperbolic conservation laws exhibit both smooth structures across large scales and sharp localized features such as shocks and contact discontinuities, making them difficult to approximate accurately with existing neural operators. The Fourier Neural Operator (FNO) captures long-range interactions well but tends to smear localized structures through excessive numerical dissipation. T…
-
Ice Giants Revisited: Uranus and Neptune as Magma Ocean Worlds
Uranus and Neptune are commonly interpreted as volatile-rich "ice giants", an assumption that underpins most interior models. Here we show that their observed radii, bulk densities, gravitational harmonics, normalized moments of inertia, intrinsic luminosities, and key features of their atmospheric compositions are consistent with interiors comprising supercritical, hydrogen-rich magma oceans over…
-
Finite-Time Queue Peak Laws in Stochastic Networks: Logarithmic Scaling After Geometric Thresholds
We study finite-horizon queue peaks in generalized switches, a standard stochastic-network model in which many queues share constrained service resources. Arrivals may be dependent, time-varying, and adapted to the past; the standing load condition is uniform interior slack, meaning the conditional mean arrival vector stays in a fixed contraction of the capacity region. We show that this slack res…
-
Time and Killed Resolvents in Reflected Optimal Stopping with a Max Payoff
We study infinite-horizon optimal stopping for normally reflected two-dimensional diffusions in the positive quadrant with max payoff \(G(x_1,x_2)=x_1\veeαx_2\). The non-smooth payoff produces a singular stopping-gain measure on the kink set \(Δ=\{x_1=αx_2\}\). We prove $\displaystyle Γ^Δ(dx) = -\frac{n^\top a(x)n}{2\sqrt{1+α^2}}\,σ_Δ(dx)$, with $n=(1,-α)$, so the diagonal component is non-pos…
-
Einstein-Podolsky-Rosen correlations between mechanical oscillators revealed through SU(1,1) interferometry
Quantum correlations are essential for achieving quantum advantage in computing, communication and sensing. Moreover, their observation challenges and constrains our fundamental understanding of nature. Mechanical oscillators in the quantum regime provide an appealing platform for preparing and investigating quantum correlations at macroscopic scales. Despite substantial progress, however, continu…
-
A Diagnostic Software Suite for Auditing Learned PDE Simulators
Learned PDE simulators are increasingly used as low-cost replacements for expensive numerical solvers, but standard relative $L^2$ error does not determine whether a learned model behaves as a coherent numerical time propagator. This paper presents a diagnostic software suite for auditing learned PDE simulators as approximate evolution operators. The suite provides architecture-independent, post h…
-
Conformal Prediction Intervals with Tail-Specific Guarantees
This paper extends classical conformal frameworks for constructing prediction intervals with global marginal coverage $1-α$ to intervals that provide explicitly calibrated guarantees for the upper and lower tails separately. Focusing on split conformal prediction, we first construct lower and upper one-sided conformal intervals that achieve marginal validity, and then derive the induced two-sided …
-
A Sensitivity Framework for Identifying Contagion under Latent Homophily for Fixed-in-Time Network Analyses, with an Application to U.S. House Congressional Voting
Whether connected units are similar because influence spreads across ties or because similar units form ties, is a long-standing problem. Contagion or influence is generically unidentified from observational network data. We consider the minimal and common setting of a single network, fixed over time, with two waves of a binary nodal outcome. Rather than positing a parametric model for network for…
-
Receiver-Aware Analysis and Verification of the Spectral Separation Coefficient Under Interference-Induced Degradation
Interference poses a significant challenge to satellite-based positioning systems, making it essential to accurately quantify the effects of specific interference types on receiver performance and the resulting reliability of position computation. In current practice, interference effects are often quantified using receiver-independent metrics, with receiver-specific front-end characteristics eith…
-
Ergodic Deviation-Robust Equilibrium under Mirror Descent Learning in Finite Games
We introduce Ergodic Deviation-Robust Equilibrium (EDRE), a dynamics-relative equilibrium concept for repeated finite games in which agents learn via entropic mirror descent (EMD). EDRE requires three properties to hold simultaneously for the same profile and learning run: (E1) the limit profile is an $\varepsilon$-Nash equilibrium at a product distribution; (E2) along the entire learning trajecto…
-
Learning Arbitrary Lindbladians with Quantum Error Correction
We study ansatz-free Lindbladian learning, the problem of reconstructing the generator of an open quantum system without prior knowledge of its Hamiltonian or dissipator structures. This problem exhibits two distinct information-theoretic precision limits: Hamiltonian components unmasked by dissipation are Heisenberg-limited, while the remaining Lindbladian components are subject to the quadratica…
-
An Encoder-Transformer Architecture for Recognition of the Jordan Structure of a Matrix
We propose a machine-learning framework for detecting whether a given matrix is a perturbation of a matrix with a large Jordan block. The proposed model achieves high classification accuracy on synthetically generated, robustly perturbed data and outperforms a classical numerical baseline. Moreover, we demonstrate that the learned model generalizes to several classes of matrices not seen during tr…
-
Beyond Plane Waves: Coherent Network Response to Collimated Gravitational-Wave Wavepackets
We present a paraxial wavepacket model for collimated gravitational-wave bursts and derive the coherent response of detector networks to these structured signals. For current LIGO-Virgo baselines, analytic mismatch estimates and overlaps show that PWM waveforms are effectively indistinguishable from standard sine-Gaussian bursts, validating the plane-wave approximation. We then identify a regime r…
-
A Diffusion Approximation for Temporal-Difference Learning with Linear Features under Markovian Noise
Temporal difference (TD) learning with linear function approximation is a core method for policy evaluation. Its classical continuous-time description is an ordinary differential equation (ODE), which captures the asymptotic mean dynamics but neglects stochastic fluctuations determining the error floor. We introduce a stochastic differential equation (SDE) approximation for linear TD(0) under Mark…
-
A minimizing-movement framework for geometric gradient flows with admissible tangential motion
We develop a minimizing-movement framework for parametric finite element approximations of geometric gradient flows with admissible tangential motion. At each time step, the discrete variational problem combines a metric dissipation term for the normal displacement with a surface Dirichlet energy. The metric determines the normal geometric evolution: the $L^2(Γ)$ metric gives mean curvature flow, …
-
A Convex Quasilinearization Method for Solving Nonlinear PDEs with Physics-Informed Neural Networks
We present a numerical method for the forward solution of nonlinear partial differential equations (PDEs) in which Bellman-Kalaba quasilinearization reduces the nonlinear problem to a sequence of linear subproblems, each discretized by collocation onto a trial space that is linear in its parameters and solved by a single direct linear least-squares QR factorization. The trial space, which we term …
-
Universal probability bounds for partial Latin squares
This paper studies the probability of substructures occurring in random Latin squares. Our main result states that if $α,β>0$ are such that $2α+β<1$, then there are positive constants $δ= δ(α, β)$ and $Δ= Δ(α, β)$ such that if $P$ is a partial Latin square of order $n$ with $k = k(n)$ non-empty cells occupying at most $αn$ rows and $βn$ columns, the probability that a random Latin square of order …
-
An algorithm to exactly compute minimal upper bounds in the Loewner order
The Loewner order on Hermitian matrices is a partial order that compares matrices in terms of positive semidefiniteness. The Loewner order plays a key role in many fields such as optimization, numerical linear algebra, control theory, operator theory, and quantum information. A fundamental difficulty is that two or more Hermitian matrices do not necessarily have a unique minimal upper bound (or ma…
-
On independent sets in uncrowded uniform hypergraphs
We prove an average-degree lower bound on the independence number of uncrowded uniform hypergraphs. For every fixed integer $r\geq 2$ and every $η>0$, there exists $d_*=d_*(r,η)$ such that for every $d\geq d_*$, any uncrowded $(r+1)$-uniform hypergraph $G$ with $n$ vertices and average degree $d$ satisfies \[ α(G)\geq (1-η)r^{-1/r}\left(\frac{\log d}{d}\right)^{1/r}n. \] The proof combines a c…