Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1605.00451

Towards a characterization of the uncertainty curve for graphs

Bastien Pasdeloup·Vincent Gripon·Grégoire Mercier·Dominique Pastor
View original source ↗Read source document ↗Export metadata ↓

Abstract

Signal processing on graphs is a recent research domain that aims at generalizing classical tools in signal processing, in order to analyze signals evolving on complex domains. Such domains are represented by graphs, for which one can compute a particular matrix, called the normalized Laplacian. It was shown that the eigenvalues of this Laplacian correspond to the frequencies of the Fourier domain in classical signal processing. Therefore, the frequency domain is not the same for every support graph. A consequence of this is that there is no non-trivial generalization of Heisenberg's uncertainty principle, that states that a signal cannot be fully localized both in the time domain and in the frequency domain. A way to generalize this principle, introduced by Agaskar and Lu, consists in determining a curve that represents a lower bound on the compromise between precision in the graph domain and precision in the spectral domain. The aim of this paper is to propose a characterization of the signals achieving this curve, for a larger class of graphs than the one studied by Agaskar and Lu.

Explore related subjects

cs.OHcs.SYeess.SY

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Bastien Pasdeloup, Vincent Gripon, Grégoire Mercier, Dominique Pastor. 2016-04-27. Towards a characterization of the uncertainty curve for graphs. https://doi.org/10.1109/icassp.2016.7472540

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Bidirectional Temporal Dynamics Modeling for EEG-based Driving Fatigue Recognition

Driving fatigue is a major contributor to traffic accidents and poses a serious threat to road safety. Electroencephalography (EEG) provides a direct measurement of neural activity, yet EEG-based fatigue recognition is hindered by strong non-stationarity and asymmetric neural dynamics. To address these challenges, we propose DeltaGateNet, a novel framework that explicitly captures Bidirectional temporal dynamics for EEG-based driving fatigue recognition. Our key idea is to introduce a Bidirectional Delta module that decomposes first-order temporal differences into positive and negative components, enabling explicit modeling of asymmetric neural activation and suppression patterns. Furthermore, we design a Gated Temporal Convolution module to capture long-term temporal dependencies for each EEG channel using depthwise temporal convolutions and residual learning, preserving channel-wise specificity while enhancing temporal representation robustness. Extensive experiments conducted under both intra-subject and inter-subject evaluation settings on the public SEED-VIG and SADT driving fatigue datasets demonstrate that DeltaGateNet consistently outperforms existing methods. On SEED-VIG, DeltaGateNet achieves an intra-subject accuracy of 81.89% and an inter-subject accuracy of 55.55%. On the balanced SADT 2022 dataset, it attains intra-subject and inter-subject accuracies of 96.81% and 83.21%, respectively, while on the unbalanced SADT 2952 dataset, it achieves 96.84% intra-subject and 84.49% inter-subject accuracy. These results indicate that explicitly modeling Bidirectional temporal dynamics yields robust and generalizable performance under varying subject and class-distribution conditions.

cs.OH↗
arXiv2026

Fixing ill-formed UTF-16 strings with SIMD instructions

UTF-16 is a widely used Unicode encoding representing characters with one or two 16-bit code units. The format relies on surrogate pairs to encode characters beyond the Basic Multilingual Plane, requiring a high surrogate followed by a low surrogate. Ill-formed UTF-16 strings -- where surrogates are mismatched -- can arise from data corruption or improper encoding, posing security and reliability risks. Consequently, programming languages such as JavaScript include functions to fix ill-formed UTF-16 strings by replacing mismatched surrogates with the Unicode replacement character (U+FFFD). We propose using Single Instruction, Multiple Data (SIMD) instructions to handle multiple code units in parallel, enabling faster and more efficient execution. Our software is part of the Google JavaScript engine (V8) and thus part of several major Web browsers.

cs.OH↗
arXiv2026

MRSeqStudio: MRI Sequence Design and Simulation as a Service in a Free and Open-Source Web Platform

MRI sequence prototyping increasingly relies on graphical design environments and numerical simulators to accelerate development and validation. While several platforms support interactive sequence construction, fully web-based solutions that combine integrated phantom management, high-fidelity Bloch simulation, and scalable multi-user deployment remain limited. We present MRSeqStudio, a web-based platform for interactive MR sequence design and simulation. The tool adopts a block-based representation model with real-time visualization and native JSON/Pulseq export. Simulations are performed using the GPU-enabled Bloch simulator KomaMRI, which enables accurate modeling of arbitrary pulse sequences and phantoms within an installation-free architecture. The system separates front-end interaction from back-end simulation services to support concurrent multi-user access. Sequence validity was assessed by comparing GRE and bSSFP implementations against equivalent sequences designed in mtrk and gammaSTAR. The resulting images showed minimal absolute differences and high mean structural similarity indices (SSIM). Stress testing under burst-request conditions demonstrated stable performance with up to 100 concurrent users on a high-performance desktop deployment. A comparative workflow analysis with mtrk and gammaSTAR further examined differences in representation models, parameter propagation strategies, and integration levels across platforms, highlighting the relative strengths and limitations of each tool. Results indicate that MRSeqStudio provides a reliable and accessible environment for MR sequence prototyping, combining web-native deployment with Bloch-level simulation fidelity and integrated phantom visualization.

cs.OH↗