Concept
Moment-generating function
Related publications (71)
On the number of regions of piecewise linear neural networks
Michaël Unser, Alexis Marie Frederic Goujon
Many feedforward neural networks (NNs) generate continuous and piecewise-linear (CPWL) mappings. Specifically, they partition the input domain into regions on which the mapping is affine. The number of these so-called linear regions offers a natural metric ...
2024Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds
Le Chen, Cheuk Yin Lee, David Jean-Michel Candil
We consider nonlinear parabolic stochastic PDEs on a bounded Lipschitz domain driven by a Gaussian noise that is white in time and colored in space, with Dirichlet or Neumann boundary condition. We establish existence, uniqueness and moment bounds of the r ...
New York2023DATED: GUIDELINES FOR CREATING SYNTHETIC DATASETS FOR ENGINEERING DESIGN APPLICATIONS
Jürg Alexander Schiffmann, Cyril Picard, Faez Ahmed
Exploiting the recent advancements in artificial intelligence, showcased by ChatGPT and DALL-E, in real-world applications necessitates vast, domain-specific, and publicly accessible datasets. Unfortunately, the scarcity of such datasets poses a significan ...
Amer Soc Mechanical Engineers2023A DONALDSON-THOMAS CREPANT RESOLUTION CONJECTURE ON CALABI-YAU 4-FOLDS
Let G be a finite subgroup of SU(4) such that its elements have age at most one. In the first part of this paper, we define K-theoretic stable pair invariants on a crepant resolution of the affine quotient C4/G, and conjecture a closed formula for their ge ...
Providence2023Surface roughness and shear resistance in cracked concrete
Guillaume Anciaux, Mohit Pundir
In concrete structures, opened cracks contribute significantly to the transfer of shear and normal stresses through the contact forces acting on fractured surfaces. Such contact forces are due to protruding asperities, engaged by interlocking and friction ...
2022Strong Subconvexity for Self-Dual GL(3) L-Functions
Yongxiao Lin, Ramon Moreira Nunes, Zhi Qi
In this paper, we prove strong subconvexity bounds for self-dual GL(3) L-functions in the t-aspect and for GL(3) x GL(2) L-functions in the GL(2)-spectral aspect. The bounds are strong in the sense that they are the natural limit of the moment method pione ...
OXFORD UNIV PRESS2022Dual Approach for Two-Stage Robust Nonlinear Optimization
Adjustable robust minimization problems where the objective or constraints depend in a convex way on the adjustable variables are generally difficult to solve. In this paper, we reformulate the original adjustable robust nonlinear problem with a polyhedral ...
INFORMS2022CFD Simulation of Particle-Laden Flow in a 3D Differentially Heated Cavity Using Coarse Large Eddy Simulation
Konstantin Mikityuk, Abdelouahab Dehbi
Particulate flow in closed space is involved in many engineering applications. In this paper, the prediction of particle removal is investigated in a thermally driven 3D cavity at turbulent Rayleigh number Ra = 1E9 using Coarse Large Eddy Simulation (CLES) ...
2022Scattering Map for the Vlasov–Poisson System
We construct (modified) scattering operators for the Vlasov–Poisson system in three dimensions, mapping small asymptotic dynamics as t→−∞ to asymptotic dynamics as t→+∞. The main novelty is the construction of modified wave operators, but we also obtain a ...
2021Distributionally Robust Mechanism Design
Daniel Kuhn, Cagil Kocyigit, Wolfram Wiesemann
We study a mechanism design problem where an indivisible good is auctioned to multiple bidders, for each of whom it has a private value that is unknown to the seller and the other bidders. The agents perceive the ensemble of all bidder values as a random v ...
2020