1645542 results (page 7 of 65822)
-
Divisive Normalization Shapes Low-Rank Slow Manifolds for Continuous Working Memory
The ability to robustly maintain and update continuous variables is a hallmark of working memory. While classical continuous attractor networks suffer from severe fine-tuning fragility, standard artificial recurrent neural networks (RNNs) like GRUs and LSTMs typically fail to stably learn continuous manifolds, instead shattering the state space into discretized point attractors. To bridge this gap…
-
Oraqle: An Empirical Analysis of Qubit Readout and Discriminators in Quantum Error Correction
Quantum error correction (QEC) is the most promising route toward fault-tolerant quantum computing and, thus, useful quantum computers. QEC operates as a continuous measure-decode-correct cycle: ancilla qubits are read out, a decoder infers errors from the resulting syndromes, and corrections are applied before the next round begins. Within this loop, readout occupies a uniquely critical role, as …
-
Semantic Networks as Clues: A Theoretical Foundation and Process Optimization for Semantic Network Construction
The subject matter of this paper is twofold. One is to review the theoretical foundation of a specific type of Semantic Networks (SNs) representing textual non-propositional knowledge. The other involves proposing a framework (ClueNetwork) for ranking candidate SNs generated through various Semantic Network Construction (SNC) processes for the type. In the first fold, it is clarified that the type…
-
Numerical approximation of fractional diffusion equations on metric graphs
We study fractional diffusion equations on compact metric graphs, where the nonlocal dynamics is governed by fractional powers of the shifted Kirchhoff-Laplacian. Building on recent advances in the analysis of fractional operators on metric graphs, we establish a rigorous mathematical framework and propose a fully discrete scheme based on backward Euler time-stepping and finite element discretizat…
-
Markov and lattice bases for Forman-Ricci curvature of graphs
Discrete Forman-Ricci curvature is a quantity associated to each edge of a graph that describes its local geometry. It has proven to be a useful tool in network analysis in a variety of applications. Recent work by Roost et al.\ (2024) proposed the use of Markov bases to sample from the space of graphs with prescribed vertex degrees and curvatures. In the present work, we further develop the algeb…
-
PHY-Layer Modeling and Throughput-Driven Adaptation for Batteryless V2X Networks
Passive overlay communication for batteryless devices is an important enabling capability for next-generation vehicle-to-everything (V2X) networks. However, enabling reliable passive payload delivery without occupying additional spectrum remains challenging, since overlay signaling must be embedded into short and time-varying vehicular packets while preserving the decodability of the legacy host t…
-
New upper bound for the Ramsey number of odd cycles
The \emph{$k$-color Ramsey number} $R_k(C_{2\ell+1})$ is the least integer $n$ such that any $k$-edge-coloring of a complete graph $K_n$ has a monochromatic odd cycle $C_{2\ell+1}$. Axenovich, Cames van Batenburg, Janzer, Michel, and Rundström~(JCT-B, 2026) recently proved \[ R_k(C_{2\ell+1})\le (4\ell-2)^k k^{k/\ell}+1, \] and Miyazaki, Mulrenin, Pohoata, and Zheng further improved the factor $k^…
-
Interspecies clock comparison below $5 \times 10^{-18}$ uncertainty with a transportable clock
We report a measurement of the optical frequency ratio between the $^2\mathrm{S}_{1/2}(F=0)$--${^2\mathrm{F}_{7/2}(F=3)}$ electric-octupole (E3) transition of $^{171}$Yb$^{+}$ and the $^1\mathrm{S}_0$--${^3\mathrm{P}_0}$ transition of $^{87}$Sr, $ν_{\mathrm{Yb}^{+}}/ν_\mathrm{Sr} = 1.495\,991\,618\,544\,900\,588\,1(65)$. Reaching a fractional uncertainty of $4.3 \times 10^{-18}$, this result impro…
-
A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization
This paper studies smoothed matrix-polar spectral gradient flows for unconstrained matrix-valued optimization.The canonical polar-factor map loses smoothness at rank-deficient matrices and becomes ill-conditioned as singular values approach zero, creating analytical difficulties.We therefore introduce a spectral feedback law generated by a smooth spectral potential and establish the regularity, mo…
-
Optimality of Gaussian Entanglement of Formation
We prove that the entanglement of formation of every two-mode Gaussian state coincides with its Gaussian restriction, solving a longstanding open problem in continuous variable quantum information theory. The key result is a sharp affine relation between entanglement and a generalized Einstein-Podolsky-Rosen observable, valid for arbitrary pure two-mode states, including non-Gaussian ones. Our res…
-
A Time-Dependent Canonical Transformation between Bateman and Doubled Caldirola--Kanai Systems for a Homogeneous Massive Scalar Field on a Prescribed FLRW Background
Dissipative equations admit distinct variational descriptions in the Bateman and Caldirola--Kanai (CK) formalisms. The classical correspondence between them is extended to a homogeneous canonical scalar field on a prescribed spatially flat Friedmann--Lemaître--Robertson--Walker (FLRW) background, where the expansion produces the time-dependent damping coefficient $3H(t)$. A multiplier action yield…
-
The Pangaea Architecture: Fault-Tolerant Heterogeneous Topological Codes via a Quantum Bus
We introduce Pangaea, a fault-tolerant quantum architecture that uses a quantum bus to mediate logical operations between remote patches of two-dimensional topological codes. The bus is an auxiliary gauge-code strip whose measurements reconstruct joint logical operators while preserving nearest-neighbor physical connectivity. Enabling native heterogeneous topological codes and multi-qubit Pauli op…
-
Gap distributions between successive personal bests in cricket: Data and Models
Successive personal best performances provide a natural measure of progression in an athlete's career. Classical record theory predicts a universal gap distribution, $P(g)\sim 1/g$, for independent and identically distributed (i.i.d.) sequences. However, sporting careers are shaped by learning, aging, changes in ability, and external influences that violate these assumptions. We investigate the st…
-
The maximum index and spectral radius of unbalanced signed multipartite graphs
Let $Γ=(G,σ)$ be a signed graph, where $G$ is the underlying graph with vertex set $V(G)$ and edge set $E(G)$ such that $σ: E(G)\to \{-1,1\}$ is the sign function. For $U\subset V(G)$, the operation that changes the sign of all edges between $U$ and $V(G)\setminus U$ is called switching. Two signed graphs with the same underlying graph are switching equivalent if one is obtainable from the other o…
-
Bipartite Turán Numbers of Trees and Star Forests
The bipartite Turán number of a graph $H$, denoted $\text{ex}(m, n; H)$, is the maximum number of edges in any $H$-free bipartite graph $G = (A, B; E)$ with parts of size $|A| = m$ and $|B| = n$. We study this problem for two families. For a tree $T = T(r, s)$ with parts $R$ and $S$ of sizes $|R| = r \le s = |S|$, we prove \[ (r - 1) n \;\le\; \text{ex}(m, n; T(r, s)) \;\le\; (r - 1) n + O(m…
-
Safe screening rules for portfolio optimization with linear and cardinality constraints
In portfolio optimization, a cardinality constraint, which limits the number of assets held, plays a key role in cutting down monitoring and transaction costs. However, the resulting problem is NP-hard and becomes computationally difficult to solve globally as the number of candidate assets grows. Safe screening addresses this difficulty by fixing decision variables before optimization without exc…
-
$0/1$-Polytopes with Exponentially Small Edge Expansion
We present a construction of a family of $0/1$-polytopes whose edge expansion decreases exponentially with the dimension, which disproves the Mihail-Vazirani conjecture that the graph of every $0/1$-polytope has edge expansion at least one.
-
Analytically Approximate Black Hole Solution to Higher Curvature Gravity
Higher-curvature gravity usually leads to very complicated field equations, which makes it hard to find analytical solutions. In this work, we obtain analytical charged black hole solutions in higher-curvature gravity by using black hole thermodynamics and the continued fraction expansion. We study the thermodynamics of static black holes using the first law of thermodynamics and the Smarr formula…
-
Probabilistic Deep Learning for Drought Forecasting: Role of Internal Climate Variability
Predicting drought risk is essential for anticipating impacts on water resources, agriculture, ecosystems, and climate adaptation planning. Yet drought forecasts remain uncertain because variability can substantially alter regional precipitation and evaporative demand. Treating this variability as unstructured noise ignores the fact that internal variability has spatial, seasonal, and temporal str…
-
Exponential mixing for Korteweg-de Vries equation with localized noise
We establish exponential mixing for the randomly forced and weakly damped KdV equation in $L^2(\mathbb{T})$. The noise is bounded, localized, and degenerate in high frequencies. Our proof relies on a general probabilistic framework in [11,33], nonlinear smoothing for KdV and its linearization via normal form transformation, and stabilization of the system by localized force. This paper continues a…
-
A Variational Characterization of a Gibbs Measure related to the Aviles-Giga Functional
We derive explicit characterizations of Gibbs-measures related to the Aviles-Giga functional. We build on the variational approach presented by Barashkov and Gubinelli (2020) in the context of the $Φ^4_3$-model.
-
Sparse Linear Surrogates for Interpretable Budget Allocation
To address the demand for inherently interpretable optimization methods, we introduce novel linear surrogates for budget allocation problems. These surrogates consist of sparse linear rules that map instances to feature-based representations of solutions. We present an exact approach based on mixed-integer programming as well as a heuristic for their computation. The performance of both approaches…
-
RADAR Perception for Dynamic Obstacle Avoidance onboard small-scale Quadrotor UAVs
Fast dynamic obstacle avoidance (DOA) on uncrewed aerial vehicles (UAVs) demands not only low-latency control and actuation but also reliable perception with sufficient sensing range for accurate obstacle detection and speed estimation. This letter presents, to the best of our knowledge, the first mmWave RADAR-based perception-and-control system for fast onboard DOA. We derive and analyze latency …
-
Movable Subarray-Aided ISAC in Hybrid Near-Far Field Channels
This letter investigates an integrated sensing and communication (ISAC) system aided by movable subarrays (MSAs) using a hybrid near-far field channel model. The sensing target and communication users are assumed to lie in the near field of the overall MSA aperture but in the far-field region of each subarray. Accordingly, a hybrid near-far field channel model is established, and the equivalent Fi…
-
Local network growth: How simple rules drive network complexity
The Internet, a living cell, a circle of friends, a billion-dollar construction project: these systems share almost nothing -- yet, drawn as networks, they look astonishingly alike. Each has a few giant hubs among a multitude of sparsely connected nodes, short paths between any two parts, dense local clustering, communities, and many redundant routes. For two decades such patterns have been credit…