1645542 results (page 1 of 65822)
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Nearly tight lower bounds for estimating quantum functionals: Uhlmann fidelity, trace distance, and von Neumann entropy
In this paper, we present a unified framework for proving lower bounds for estimating functionals of quantum states. We therefore resolve several open problems by establishing lower bounds that match known upper bounds: we show that it requires $\widetildeΩ(N^2)$ samples to estimate the Uhlmann fidelity, trace distance, and von Neumann entropy. Moreover, they immediately imply matching query lower…
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Bridging Artificial Intelligence and Power Systems Education Using a Hands-On Executable Framework
Artificial intelligence (AI) is increasingly central to power and energy systems, supporting modeling, forecasting, optimization, and control. Yet most existing works emphasize specialized applications and offer little reusable material for newcomers or interdisciplinary learners, who increasingly rely on large language models rather than building their own. This gap points to a need for engineeri…
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An Argmax Principle for Sum-of-Squares Relaxations on the Sphere
We develop an argmax principle for analyzing sum-of-squares relaxations of optimization problems over the unit sphere. Given a feasible pseudo-expectation, we form a polynomial of high-order pseudo-moments, such as $Φ_k(u)=\widetilde{\mathbb E}\langle x,u\rangle^{2k}$. Our guiding principle is that its maximizers are rounding candidates: their local and global optimality conditions reveal the rewe…
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Exact Likelihood and Sampling for Riemannian Gaussian Distributions on Correlation Matrices
Correlation matrices arise when marginal scales are removed from covariance matrices, yet a normalized likelihood must account for both quotient distance and quotient volume. We propose a Riemannian Gaussian model for full-rank correlation matrices under quotient-affine geometry. The distribution is proper and has finite radial moments. We derive exact score and profiled-scale equations and recove…
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Testing for subgroup treatment effect consistency in the Cox model
An overall treatment effect in a clinical trial may inadequately represent particular patient subgroups, creating uncertainty about whether a population-level efficacy conclusion can legitimately be transferred to them. Conventional interaction tests only investigate whether subgroup-specific treatment effects are exactly equal or not, but cannot detect whether the differences are small enough to …
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Optimal Quantum de Finetti Theorems via Argmax Rounding
We prove optimal finite quantum de Finetti upper bounds. Given a bosonic state $ρ_N\in D(\mathrm{Sym}^N(\mathbb C^d))$, there is a probability measure $ν$ on the unit sphere such that \[ \left\| ρ_N^{(2)}-\int |u\rangle\langle u|^{\otimes 2}\,dν(u) \right\|_1 \le \frac{\sqrt{d-1}}{N-1}. \] By purification, the bosonic theorem also gives the optimal $O(d/N)$ upper bound for arbitrary exchan…
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Entanglement of flower states
The mysterious nature of entanglement, one of the most prominent exquisitely quantum phenomena, is reflected in its intricate operational structure, with a hierarchy of classes of free operations that enable its manipulation at different levels of effectiveness. Here we use the class of 'flower states', parametrised by their (even) local dimension $2k$, to shine light on some aspects of this varie…
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Pseudorandom Streams within Diffusion Models Act as Learnable Inputs That Affect Generation Quality
Diffusion models rely on stochastic inputs, yet on finite-precision hardware, the "randomness" they consume is realized as deterministic numerical orbits generated by pseudorandom rules. Accessible orbit structure can become a learnable input and affect both training and generation because the realized loss and its gradient depend on the concrete pseudorandom values consumed at each optimization s…
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Performance-based Adaptation Termination for Preventing Parameter Drift in Adaptive Vibration Suppression
Parameter drift remains a practical limitation of adaptive vibration control systems, particularly when persistence of excitation diminishes after disturbance attenuation or when measurement disturbances render the adaptation problem ill-conditioned. This issue is especially relevant in flexible structures, where adaptive controllers may continue updating parameters even after satisfactory vibrati…
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Additive decompositions of multiplicative subgroups in prime fields: a self-contained approach
Sárközy conjectured that the nonzero quadratic residues modulo a sufficiently large prime have no nontrivial additive decomposition. Hanson and Petridis proved the conjecture for almost all primes, and Kalmynin completed the proof. Kalmynin also developed a general framework for additive decompositions of multiplicative subgroups. More recently, Rudnev and Tyrrell used this framework to classify a…
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On (1,1,2,3)- and (1,1,3,3,3)-Packing Colorings of Claw-Free Subcubic Graphs
For a non-decreasing sequence $S=(a_1,a_2,\ldots,a_r)$ of positive integers, an $S$-packing coloring of a graph $G$ is a partition of $V(G)$ into sets $A_1,\ldots,A_r$ such that any two distinct vertices in $A_i$ are at distance greater than $a_i$, for every $i\in\{1,\ldots,r\}$. Gastineau and Togni [\emph{Discrete Math.} 339 (2016), 2461--2470] asked whether every subcubic graph, except the Peter…
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A curvature-based criterion for harmonic circadian waveforms
Experimental and theoretical studies of circadian rhythms have focused largely on the period, on mutants that alter it and on phase shifts, and this focus has driven the identification of clock genes and clarified how clocks entrain to light--dark cycles. The waveform of the oscillation itself, by contrast, has attracted little attention as an indicator of the properties of the underlying oscillat…
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House-monotone multi-level apportionment has logarithmic quota discrepancy
Multi-level apportionment allocates integer seats through a hierarchy of groups. Schmidt-Kraepelin, Suksompong, and Wijaya proved that, at every fixed house size, lower and upper quota can be satisfied simultaneously; they also constructed house-monotone rules satisfying either quota separately. They left open whether one rule can satisfy lower quota, upper quota, and house monotonicity together, …
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A Joint Bayesian Boolean Matrix Factorization with Application to Chromosomal Copy Number Alterations in Multiple Myeloma
Boolean matrix factorization provides an interpretable framework for discovering latent binary patterns in high-dimensional data, yet existing methods typically analyze a single binary matrix or factorize multiple matrices independently, failing to exploit shared latent structure across related datasets. We propose Joint Bayesian Boolean Matrix Factorization (JBBMF), a model that simultaneously fa…
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On the local conformal structure of Imaginary Liouville theory
Imaginary Liouville theory was recently proposed as a path integral construction of a non-rational conformal field theory (CFT) with central charge less than one (Usciati et al. 2026). In the present work, we establish Ward identities and Belavin-Polyakov-Zamolodchikov differential equations in this framework, assuming a precise conjecture on the decay of the Laplace transform of Imaginary Gaussia…
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Gauge and Metaphysics of Spacetime
Some authors have argued that spacetime in general relativity should be given a radically different interpretation from the ones given to spacetime in other theories in virtue of it being a gauge theory. In this article I review this sort of argument and argue against this view. That is, I argue that spacetime in general relativity can be understood analogously to spacetime in other models and tha…
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A Simple Approximation to the Distribution of the Ridge Regression Estimator
We present a simple Gaussian approximation to the finite-sample distribution of the classical ridge regression estimator. Our approximation captures the fact that, in finite samples, the ridge regression estimator trades off bias and variance to reduce estimation and prediction error. Our approximation is based on nonstandard asymptotics where $i)$ we let the estimator's regularization parameter g…
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Interaction Is Not Necessary for Order-Optimal 1-Bit Mean Estimation
This paper is concerned with one-bit mean estimation, where each independent sample is represented by a single binary message. We consider distributions on $\mathbb{R}$ with mean in $[-λ,λ]$ and absolute $k$-th central moment at most $σ^k$, where $k>1$ is fixed. For this class, previous work attained the optimal sample complexity for general queries using a two-stage protocol. The first stage loca…
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Multicolor Ramsey numbers of odd cycles are superexponential
In a recent breakthrough, OpenAI proved that the $k$-color Ramsey number of the triangle $C_3$ grows super-exponentially, more precisely, they proved that $R_k(C_3)\ge k^{k/3-o(k)}$. In this short note, we present a modification of their recursive construction that works for multicolor Ramsey numbers of fixed odd cycles. More precisely, for $p\ge 1$, let $\mathcal{O}_p=\{C_3,C_5,\ldots,C_{2p+1}\}$…
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Do I Even Need a Multilevel Model? Negligible Effect Significance Testing for Intraclass Correlation Coefficients
In applied research, the decision to utilize multilevel modeling (MLM) is commonly guided by comparing a point estimate of the unconditional intraclass correlation coefficient (ICC) against some recommended threshold (e.g., 0.05). This naive approach, however, fails to account for sampling uncertainty and provides no formal inferential justification for a decision. The current work introduces negl…
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Safe and robust tube-based path-following for robot navigation
In this paper, we propose a new robust navigation framework for path following tasks in robots operating within unknown, cluttered environments. Our approach ensures reactive safety through obstacle avoidance and guaranteed convergence to a target path, while simultaneously mitigating the impact of unknown-but-bounded disturbances using a tube-based control strategy. The methodology integrates key…
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Cyclic Sources of Strong Domination in Graph Norms
Conlon and Lee asked for strongly dominating graphs beyond norming graphs and even paths. We construct a two-parameter family of pairwise non-isomorphic $2$-connected strongly dominating graphs that are not seminorming, and hence lie outside the two classes of examples previously identified for signed strong domination. The construction uses cyclic amalgamation of two-rooted blocks. For root-rever…
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On calculating polar solvation energy of nonrigid proteins in the Poisson-Boltzmann theory
The Poisson-Boltzmann (PB) theory is a cornerstone of implicit solvent models for electrostatic analysis, and has found a great success in various biomolecular applications. However, in calculating polar solvation energy, one should consider that the structure of the protein changes upon transition from vacuum to water phases. To address this, here we report for the first time a generalized PB fra…
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The Erdős-Hajnal conjecture for odd-girth
A famous conjecture of Erdős and Hajnal from 1969 states that for every integer $g\ge 4$ there exists a (smallest) function $f_g:\mathbb{N}\rightarrow \mathbb{N}$ such that every graph of chromatic number at least $f_g(k)$ contains a subgraph with chromatic number at least $k$ and girth at least $g$. So far, this has only been proved for $g=4$ by Rödl in 1977 and remains open for every $g\ge 5$.…
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Squeezing-Fueled Quantum Otto Engine via Measurement-Induced Cooling: The Two-Qubit Quantum Rabi Model
We investigate a quantum Otto engine (QOE) constructed from the two-qubit quantum Rabi model, operating within a cavity quantum electrodynamics (QED) architecture. The engine operates with two qubits as the working substance and a single non-Markovian hot thermal bath, modeled via the hierarchical equations of motion (HEOM) formalism. In place of a conventional cold thermal reservoir, the cooling …