Tootfinder

Moment-like maps and real algebraic functions with prescribed preimages
Naoki Kitazawa
https://arxiv.org/abs/2506.17791 https://arxiv…

Moment-like maps and real algebraic functions with prescribed preimages
We discuss a problem on singularity theory of differentiable (smooth) or real algebraic maps which is different from knowing existence and has been difficult: constructing explcit real algebraic functions. We discuss construction of real algebraic functions with exactly one singular value, the singular points being of definite type, and prescribed preimages of single points. We discuss generalizations of the canonical projection of the unit sphere around the pole and the Morse-Bott functions …

A Simple but Accurate Approximation for Multivariate Gaussian Rate-Distortion Function and Its Application in Maximal Coding Rate Reduction
Zhenglin Huang, Qifa Yan, Bin Dai, Xiaohu Tang
https://arxiv.org/abs/2506.18613

A Simple but Accurate Approximation for Multivariate Gaussian Rate-Distortion Function and Its Application in Maximal Coding Rate Reduction
The multivariate Gaussian rate-distortion (RD) function is crucial in various applications, such as digital communications, data storage, or neural networks. However, the complex form of the multivariate Gaussian RD function prevents its application in many neural network-based scenarios that rely on its analytical properties, for example, white-box neural networks, multi-device task-oriented communication, and semantic communication. This paper proposes a simple but accurate approximation for …

Sizing Antenna Arrays for Near-field Communication and Sensing
Marcin Wachowiak, Andr\'e Bourdoux, Sofie Pollin
https://arxiv.org/abs/2506.18465 https:…

Sizing Antenna Arrays for Near-field Communication and Sensing
This paper presents key performance metrics for near-field communication and sensing systems with a focus on their scaling behavior as a function of the antenna array aperture. Analytical expressions are derived for several standard array geometries to enable the design of the large antenna arrays for given system requirements. First, the near-field beam focusing is analyzed and the minimum beamdepth is observed to rapidly saturate to a low asymptotic limit as the array aperture increases. In c…

Building Automotive Security on Internet Standards: An Integration of DNSSEC, DANE, and DANCE to Authenticate and Authorize In-Car Services
Timo Salomon, Mehmet Mueller, Philipp Meyer, Thomas C. Schmidt
https://arxiv.org/abs/2506.13261

Building Automotive Security on Internet Standards: An Integration of DNSSEC, DANE, and DANCE to Authenticate and Authorize In-Car Services
The automotive industry is undergoing a software-as-a-service transformation that enables software-defined functions and post-sale updates via cloud and vehicle-to-everything communication. Connectivity in cars introduces significant security challenges, as remote attacks on vehicles have become increasingly prevalent. Current automotive designs call for security solutions that address the entire lifetime of a vehicle. In this paper, we propose to authenticate and authorize in-vehicle services …

Canonical Partition Function on a Quantum Computer through Trotter Interpolation
Taozhi Guo, Gumaro Rendon, Rutuja Kshirsagar
https://arxiv.org/abs/2506.09318

Canonical Partition Function on a Quantum Computer through Trotter Interpolation
In this work, we present a Gibbs state observable estimation algorithm based on Trotter interpolation, which reaches a state-of-the-art quantum computational cost of $ \tilde{O}(β\log{1/ε})$. Our approach saves $\log(Γ)$ ancilla qubits compared with the qubitization-based methods for Hamiltonian with $Γ$ stages. To provide a robust assessment of our approach, we benchmark our results against state-of-the-art methodology using the SYK model as a testbed. Our method provides an efficient alte…

On Designing Modulation for Over-the-Air Computation -- Part II: Pyramid Sampling
Saeed Razavikia, Carlo Fischione
https://arxiv.org/abs/2506.16208 https:/…

On Designing Modulation for Over-the-Air Computation -- Part II: Pyramid Sampling
Over-the-air computation (OAC) harnesses the natural superposition of wireless signals to compute aggregate functions during transmission, thereby collapsing communication and computation into a single step and significantly reducing latency and resource usage. In Part I, digital OAC was formulated as a noise-aware constellation design problem by casting encoder design as a max-min optimization that aligns minimum Euclidean distances between superimposed constellation points with squared differ…

Measure and integration
Teo Banica
https://arxiv.org/abs/2506.15534 https://arxiv.org/pdf/2506.15534…

Measure and integration
This is an introduction to measure theory, integration and function spaces, with all the needed preliminaries included, and with some applications included as well. We first discuss some basic motivations, coming from discrete probability, that we develop in detail, as a preliminary to general measure theory. Then we discuss measure theory, integration and function spaces, all developed in a standard way, and with emphasis on the explicit computation of various integrals. Finally, we come back …

On Designing Modulation for Over-the-Air Computation -- Part I: Noise-Aware Design
Saeed Razavikia, Carlo Fischione
https://arxiv.org/abs/2506.15950 https:…

On Designing Modulation for Over-the-Air Computation -- Part I: Noise-Aware Design
Over-the-air computation (OAC) leverages the physical superposition property of wireless multiple access channels (MACs) to compute functions while communication occurs, enabling scalable and low-latency processing in distributed networks. While analog OAC methods suffer from noise sensitivity and hardware constraints, existing digital approaches are often limited in design complexity, which may hinder scalability and fail to exploit spectral efficiency fully. This two-part paper revisits and e…

High Probability Convergence of Distributed Clipped Stochastic Gradient Descent with Heavy-tailed Noise
Yuchen Yang, Kaihong Lu, Long Wang
https://arxiv.org/abs/2506.11647

High Probability Convergence of Distributed Clipped Stochastic Gradient Descent with Heavy-tailed Noise
In this paper, the problem of distributed optimization is studied via a network of agents. Each agent only has access to a noisy gradient of its own objective function, and can communicate with its neighbors via a network. To handle this problem, a distributed clipped stochastic gradient descent algorithm is proposed, and the high probability convergence of the algorithm is studied. Existing works on distributed algorithms involving stochastic gradients only consider the light-tailed noises. Di…

Building Automotive Security on Internet Standards: An Integration of DNSSEC, DANE, and DANCE to Authenticate and Authorize In-Car Services
Timo Salomon, Mehmet Mueller, Philipp Meyer, Thomas C. Schmidt
https://arxiv.org/abs/2506.13261

Building Automotive Security on Internet Standards: An Integration of DNSSEC, DANE, and DANCE to Authenticate and Authorize In-Car Services
The automotive industry is undergoing a software-as-a-service transformation that enables software-defined functions and post-sale updates via cloud and vehicle-to-everything communication. Connectivity in cars introduces significant security challenges, as remote attacks on vehicles have become increasingly prevalent. Current automotive designs call for security solutions that address the entire lifetime of a vehicle. In this paper, we propose to authenticate and authorize in-vehicle services …