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A Point is Normal for Almost All Maps beta x+ alpha mod 1 or Generalised beta-Transformations

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We construct a measure on the thick points of a Brownian loop soup in a bounded domain D

D

of the plane with given intensity theta>0

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, which is formally obtained by exponentiating the square root of its occupation field. The measure is construct ...

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A Functional Perspective on Information Measures

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Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

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Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are ubiquitous in statistics, ...

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Examples of normal, not geometrically normal, projective Gorenstein del Pezzo surfaces with at most Du Val singularities

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Chirok is software for a post-refinement test of the absolute structure. The software allows a user to calculate a distribution of the measure of chirality based on intensity quotients and linked to the Flack parameter. The distribution is fitted by a set ...

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First passage sets of the 2D continuum Gaussian free field

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We introduce the first passage set (FPS) of constant level -a of the two-dimensional continuum Gaussian free field (GFF) on finitely connected domains. Informally, it is the set of points in the domain that can be connected to the boundary by a path on whi ...

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Although the versatility of photodynamic therapy (PDT) is well established, the technical aspects of light delivery systems vary significantly depending on the targeted organ. This article describes the optical properties of a light and drug delivery syste ...

2020

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ANNUAL REVIEWS2019

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Multiplicative chaos of the Brownian loop soup

Antoine Pierre François Jego, Titus Lupu

We construct a measure on the thick points of a Brownian loop soup in a bounded domain D

D

of the plane with given intensity theta>0

\theta >0

, which is formally obtained by exponentiating the square root of its occupation field. The measure is construct ...

WILEY2023