Finite free convolutions of polynomials [PDF]
Probability Theory and Related Fields, 2022 AbstractWe study three convolutions of polynomials in the context of free probability theory. We prove that these convolutions can be written as the expected characteristic polynomials of sums and products of unitarily invariant random matrices. The symmetric additive and multiplicative convolutions were introduced by Walsh and Szegö in different ...
Daniel A Spielman, Nikhil Srivastava
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The arithmetic of distributions in free probability theory
Open Mathematics, 2011 We give an analytical approach to the definition of additive and multiplicative free convolutions which is based on the theory of Nevanlinna and of Schur functions.
Chistyakov Gennadii, Götze Friedrich
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Rank one HCIZ at high temperature: interpolating between classical and free convolutions
SciPost Physics, 2022 We study the rank one Harish-Chandra-Itzykson-Zuber integral in the limit where $\frac{N \beta}{2} \to c $, called the high temperature regime and show that it can be used to construct a promising one-parameter interpolation, with parameter $c ...
Pierre Mergny, Marc Potters
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MLCANet: Multi-Level Composite Attention-Guided Network for Non-Homogeneous Image Dehazing in Adverse Weather Conditions [PDF]
SensorsImage dehazing is a challenging ill-posed problem in low-level computer vision tasks, requiring the restoration of high-quality, haze-free images from complex and foggy conditions.
Yongsheng Qiu
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DGS-YOLO: A Detection Network for Rapid Pig Face Recognition [PDF]
AnimalsThis study addresses the practical demand for facial recognition of pigs in the food safety and insurance industries, tackling the challenge of low recognition accuracy caused by complex farming environments, occlusions, and similar textures. To this end,
Hongli Chao +9 more
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An Intelligent Ship Detection Algorithm Based on Visual Sensor Signal Processing for AIoT-Enabled Maritime Surveillance Automation [PDF]
SensorsOriented object detection constitutes a fundamental yet challenging task in Artificial Intelligence of Things (AIoT)-enabled maritime surveillance, where real-time processing of dense visual streams is imperative.
Liang Zhang +3 more
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Stability of Cauchy–Stieltjes Kernel Families by Free and Boolean Convolutions Product
MathematicsLet F(νj)={Qmjνj,mj∈(m−νj,m+νj)}, j=1,2, be two Cauchy–Stieltjes Kernel (CSK) families induced by non-degenerate compactly supported probability measures ν1 and ν2. Introduce the set of measures F=F(ν1)⊞F(ν2)={Qm1ν1⊞Qm2ν2,m1∈(m−ν1,m+ν1)andm2∈(m−ν2,m+ν2)}.
Ayed. R. A. Alanzi +2 more
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An inequality for the distance between densities of free convolutions
Annals of Probability, 2013 This paper contributes to the study of the free additive convolution of probability measures. It shows that under some conditions, if measures $\mu_i$ and $\nu_i, i=1,2$, are close to each other in terms of the L\'{e}vy metric and if the free convolution
Kargin, V.
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Discriminating single-molecule binding events from diffraction-limited fluorescence [PDF]
Nature CommunicationsSingle-molecule localization microscopy enables high-resolution imaging of molecular interactions, but discriminating molecular binding types has traditionally relied on complex strategies, such as multiple dyes, time-division techniques, or kinetic ...
Yueming Yin +9 more
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Multi-channel free space optical convolutions [PDF]
EPJ Web of Conferences, 2023 Convolutional layers are a critical feature of modern neural networks and require significant com-putational resources. In response, optical accelerators have been developed as a low-energy, high-bandwidth approach for performing large-scale convolutions.
Song Alexander +2 more
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