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Measure theory

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Extensions of Peer Prediction Incentive Mechanisms

As large, data-driven artificial intelligence models become ubiquitous, guaranteeing high data quality is imperative for constructing models. Crowdsourcing, community sensing, and data filtering have long been the standard approaches to guaranteeing or imp ...

EPFL2024

Stability of the Faber-Krahn inequality for the short-time Fourier transform

Joao Pedro Gonçalves Ramos

We prove a sharp quantitative version of the Faber–Krahn inequality for the short-time Fourier transform (STFT). To do so, we consider a deficit which measures by how much the STFT of a function fails to be optimally concentrated on an arbitrary set of pos ...

Springer Heidelberg2024

Resolving the vicinity of supermassive black holes with gravitational microlensing

Georgios Vernardos

Upcoming wide-field surveys will discover thousands of new strongly lensed quasars which will be monitored with unprecedented cadence by the Legacy Survey of Space and Time (LSST). Many of these quasars will undergo caustic-crossing events over the 10-yr L ...

Oxford Univ Press2024

Small-amplitude Red Giants Elucidate the Nature of the Tip of the Red Giant Branch as a Standard Candle

Richard Irving Anderson, Nolan Wayne Koblischke

The tip of the red giant branch (TRGB) is an important standard candle for determining luminosity distances. Although several 105 small-amplitude red giant stars (SARGs) have been discovered, variability was previously considered irrelevant for the TRGB as ...

Iop Publishing Ltd2024

Generalization of Scaled Deep ResNets in the Mean-Field Regime

Volkan Cevher, Grigorios Chrysos, Fanghui Liu

Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of wh ...

2024

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

Impact of Redundancy on Resilience in Distributed Optimization and Learning

Nirupam Gupta, Shuo Liu

This paper considers the problem of resilient distributed optimization and stochastic learning in a server-based architecture. The system comprises a server and multiple agents, where each agent has its own local cost function. The agents collaborate with ...

Assoc Computing Machinery2023

Appropriations and Uses of Travel Time

Ludy Juliana González Villamizar

Time has always been a central factor in understanding the challenges of daily mobility. For a long time, and still today, methods of economic evaluation of transport projects have monetized time savings so that they can be included in the cost–benefit ana ...

ISTE Wiley2023

IMPROVED REGULARITY OF SECOND DERIVATIVES FOR SUBHARMONIC FUNCTIONS

Xavier Fernandez-Real Girona, Riccardo Tione

In this note, we prove that if a subharmonic function Delta u >= 0 has pure second derivatives partial derivative(ii)u that are signed measures, then their negative part (partial derivative(ii)u)- belongs to L-1 (in particular, it is not singular). We then ...

Amer Mathematical Soc2023

Measurement of the 171Tm beta spectrum

Lesya Shchutska, Alexey Boyarsky

The beta spectrum of the main transition of the 171Tm was measured using a double focalizing spectrometer. The instrument was lately improved in order to reduce its low energy threshold to 34 keV. We used the spectrometer to measure the energy end-point of ...

2023

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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