1645542 results (page 3 of 65822)
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Graph Eigenvalues and Projection Constants
For an integer $k\ge2$, let $λ_k(G)$ denote the $k$th largest adjacency eigenvalue of a graph $G$. For every graph $G$ on $n$ vertices and every $2 \leq k \leq n$, we prove \[ λ_k(G) \le \frac{(k-2)\sqrt{k+1}+2}{2k(k-1)}\,n-1. \] Our bound is tight for $k\in\{2,3,4,8,24\}$. We obtain it by reducing the graph-eigenvalue problem to an extremal problem for orthogonal projections and then applying the…
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Caustics and Superenergy in the Quantum Bouncer
We investigate the quantum interference and energetic phenomena associated with classical caustics in the quantum bouncing ball problem, we refer to as quantum caustics. By considering an initial Gaussian wavepacket, we show that caustics associated with the underlying classical trajectory families are exhibited. We connect the associated phase singularity chains in the vicinity of the caustic wit…
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Measurement and control of the interaction frequency shift in bosonic optical lattice clocks
We report precise measurements of inter-level interactions in a bosonic optical lattice clock based on $^{88}$Sr atoms. We observe a nonlinear density dependence of the clock shift, even without reaching quantum degeneracy. In a 2D lattice, the Rabi line shape exhibits an interaction sideband consistent with a collective spin model, while in a 1D lattice the shift is modified by density-induced de…
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Deep Learning-Based Active Trim Panels for Enhanced Aircraft Interior Noise Control
Active noise control (ANC) trim panels offer an effective solution to suppress multi-tonal noise in aircraft. The selective fixed-filter ANC (SFANC) method, characterized by low computational complexity, high robustness and rapid response, is suitable to handle multi-tonal engine noise that varies in frequency due to changes in the rotational speed of the engine shaft. However, real-world conditio…
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Generalised projective integration scheme in equation-free multiscale modelling
When the spectrum of a system varies significantly over time, fixed choices of macro-, meso-, and micro-time steps, as well as burst lengths, become inadequate, necessitating adaptive and locally informed strategies. To address these challenges, this article proposes a novel and flexible generalised projective integration (GPI) scheme, designed to accommodate time-dependent spectral variation and …
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A Bismut-Elworthy-Li formula for linear stochastic evolution equations in Banach spaces
We prove a Bismut-Elworthy-Li formula for linear stochastic evolution equations in Banach spaces. The admissible directions are those for which the deterministic orbit is square integrable with values in the Hilbertian range of the noise coefficient. Under this square function condition, the derivative of the semigroup is represented by a stochastic integral against an explicit deterministic contr…
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Deep Learning-Based Estimation of Ground Reaction Forces in Parkinsonian Gait Using an Optimized Set of IMU Data
Accurate gait analysis in Parkinson's disease (PD) typically relies on laboratory-based systems to capture biomechanical data, such as ground reaction forces (GRFs). Estimating GRFs using inertial measurement units (IMUs) provides a feasible alternative. However, this approach remains challenging in pathological gait like PD due to its high variability and complexity. Moreover, existing monitoring…
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A Unified Kullback--Leibler Divergence Analysis of Generative Diffusion Models via Entropy Production Rate
We introduce a unified framework for the error analysis of generative models based on the entropy production rate of the forward-reverse diffusion process pair. For a pair of continuity equation flows, the rate admits a closed velocity form identity whose time integral decomposes the terminal Kullback--Leibler (KL) divergence into the sum of an initialization error, a score approximation error, an…
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Entanglement Generation Beyond Quantum Theory: From Product States to Popescu-Rohrlich Boxes
Entanglement generation is a fundamental dynamical capability in quantum information science and underpins many quantum advantages. While quantum theory enables it through unitary dynamics, boxworld, a generalized probabilistic theory admitting Popescu--Rohrlich boxes with supraquantum correlations, has no reversible transformation capable of generating entanglement. We show that this no-go pictur…
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Network Information Enhances Unreliable News Domain Detection
Content-based detection of unreliable news is increasingly difficult, as low-reliability sources mimic credible journalism and generative AI makes fabricated content harder to flag. We ask whether network structure can improve news reliability classification, taking a domain-level approach that shifts the focus from individual articles to source reliability. From URL-sharing patterns in Telegram c…
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A Spectral Filtering Approach to Regret Analysis of Distributed Online Control for Linear Dynamical Systems
This paper studies the distributed online control problem over a network of linear time-invariant (LTI) systems in the presence of adversarial disturbances and time-varying convex costs. The network cost is characterized by the summation of local cost functions, where each local function is sequentially revealed only to the corresponding agent. The goal of each agent is to generate a control seque…
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Subleading Asymptotic Charges in Massless Scalar QED
We study subleading asymptotic charges of a U(1) gauge field coupled to a charged massless scalar field in Minkowski spacetime. We consider a phase space for which the scalar-field initial data on null infinity have compact support, while the gauge-field initial data admit an asymptotic expansion with inverse-power tails in retarded (advanced) time, which we refer to as initial-data tails. We iden…
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A Benchmarking Case Study for Local Flexibility Markets: Network, Scenarios, and Open Inputs
External inputs to local flexibility markets, network models, demand scenarios, flexibility offers, and asset thermal, economic parameters do not change the clearing methodology, yet they are routinely defined under heterogeneous assumptions, which hinders reproducible benchmarking. This paper provides a complete, methodology-agnostic input set built around a modified CIGRE MV network with prescri…
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Joint Retrieval of Radial Wind, Terminal Fall Velocity, and Median Diameter From Single-Polarization Fast-Scanning Weather Radar
The inverse problem of precipitation retrieval from Doppler power spectral density measurements of a fast-scanning single-polarization X-band weather radar is addressed. The formulation is developed around quantities that remain interpretable and stable across short coherent processing intervals: radial-wind mean, radial-wind spectral width, reflectivity-weighted terminal fall velocity, and median…
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Aerodynamic Drag and Heat Transfer Corrections for Dehydrated Pollen Particles: CFD-Based Modeling of Airborne Allergen Transport in Smart Urban Environments
Airborne pollen transport is a key concern for urban air-quality assessment, allergy-risk forecasting, and smart-city planning. However, conventional dispersion models generally assume smooth spherical particles, neglecting how pollen dehydration alters particle morphology and impacts aerodynamic and thermal behavior. To address this gap, this study presents, for the first time, advanced CFD simul…
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The half interlacing property among the types A, B and D Eulerian polynomials
A famous result in the theory of combinatorial polynomials is the real-rootedness of the type $D$ Eulerian polynomial $D_n(x)$, which was originally conjectured by Brenti in 1994. By constructing a set of compatible polynomials over $s$-inversion sequences, Savage and Visontai proved this conjecture in 2013. Using matrices preserving interlacing properties of nonnegative polynomial sequences, Brän…
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Revealing and reducing growth-induced interfacial disorder in preferentially aligned nitrogen-vacancy centers in diamond
Nitrogen-vacancy (NV) centers in chemical-vapor-deposition (CVD) diamond can form preferentially oriented ensembles with high sensing performance and low densities of lattice defects. Thin films of this material are a cornerstone of various imaging modalities. However, nitrogen injection needed to produce such films can transiently drive growth out of equilibrium, generating interfacial strain and…
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On Hamilton cycles in connected vertex-transitive graphs of order $2pq$
The existence of Hamilton cycles in connected vertex-transitive graphs is a core open problem in algebraic graph theory, originating from Lovász's 1969 conjecture. All connected vertex-transitive graphs of order $pq$ are known to be Hamiltonian except the Petersen graph, and primitive graph of order $2pq$ are resolved except the Coxeter graph. This paper considers connected vertex-transitive graph…
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Can AI Agents Simulate A/B Test Outcomes? A Validation Framework for Agentic Experimentation
A/B testing remains the standard for rolling out new features in the technology industry. Each experiment, however, consumes real traffic, engineering effort, and weeks of wall-clock time. Can AI agents---conditioned on behavioral profiles and contextual descriptions of the intervention---simulate outcomes accurately enough to vet candidate treatments before committing live traffic? We formalize t…
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Bounds on Odd and Odd-Even Induced Subgraphs
Let $G$ be an $n$-vertex graph and let $\ell:V(G)\to\mathbb{F}_2$ prescribe degree parities. A set $S\subseteq V(G)$ is $\ell$-admissible if every $v\in S$ has degree congruent to $\ell(v)$ modulo $2$ in $G[S]$. Let $h_\ell(G)$ be the maximum order of an $\ell$-admissible set, set $f_{\mathrm{oe}}(G):=\min_\ell h_\ell(G)$, and write $f_o(G):=h_{\mathbf{1}}(G)$, where $\mathbf{1}(v)=1$ for every $v…
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The DP Color Function of Bipartite Graphs
DP-coloring (or correspondence coloring) is a generalization of list coloring that has been widely studied since its introduction by Dvořák and Postle in 2015. As the analogue of $P(G,q)$, the chromatic polynomial of a graph $G$, the DP color function of $G$, denoted by $P_{DP}(G,q)$, counts the minimum number of DP-colorings over all $q$-fold covers of $G$. It follows that $P_{DP}(G,q) \leq P(G,q…
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Finite-Syndrome Compression of Quantum Fisher Information
Readable error records can protect quantum sensing because they prevent physically distinct noise trajectories from being irreversibly mixed. A finite detector or ancilla, however, can retain only finitely many syndrome values, and a general criterion for deciding which records may be merged without losing metrological information is absent. We formulate the problem for a fixed fine-grained classi…
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Diffusion Policy with Behavioral Advantage Correction for Offline Reinforcement Learning
In offline reinforcement learning (RL), the distribution shift between behavioral data and the learned policy can lead to erroneous \emph{Q}-value estimation, thereby misguiding the direction of policy optimization. To address this issue, we develop a behavioral advantage corrected policy evaluation (BAC-PE) approach, which utilizes the \emph{Q}-function of the behavior policy to correct the learn…
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Learnable yet not simulable: a quantum resource theory of learning models
Quantum resource theory has sharpened our understanding of the intrinsic complexity of quantum systems, particularly their classical simulability. However, it remains unclear which quantum resource governs the classical learnability of quantum circuits, especially beyond the regime of efficient classical simulation. Here we close this knowledge gap by studying the expectation-value functions of fa…
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Averaging Principle for Ordinary Differential Equations in a Multiscale Random Environment
We study slow-fast stochastic systems in which a fast process, evolving within several ergodic components, drives the transition rates of a slow jump process switching between these components. Considering a differential equation whose vector field depends on both processes, we show that, under suitable ergodicity and regularity conditions, its solutions converge in law in $D([0,T],\mathbb R^d)$ t…