On Aggregation Sets and Lower-Convex Sets Tiantian Mao∗† and Ruodu Wang† November 24, 2014 Abstract It has been a challenge to characterize the set of all possible sums of random variables

Source URL: sas.uwaterloo.ca

• Probability theory
• Generalized functions
• Convex analysis
• Convergence
• Convergence of random variables
• Convex function
• Stochastic ordering
• Expected value
• Uniform integrability
• Distribution
• Continuous game
• Fourier transform

Arithmetizing proofs in analysis Ulrich Kohlenbach Department of Mathematics University of Michigan at Ann Arbor MI 48109, USA

Source URL: www.mathematik.tu-darmstadt.de

• Mathematics
• Algebra
• Linear algebra
• Abstract algebra
• Cauchy sequence
• Convergence
• Metric geometry
• Topology
• Sequence
• Norm
• Continuous function
• FO

On the Computational Content of the Bolzano-Weierstraß Principle∗ Pavol Safarik and Ulrich Kohlenbach Department of Mathematics Technische Universität Darmstadt Schlossgartenstraße 7, 64289 Darmstadt, Germany

Source URL: www.mathematik.tu-darmstadt.de

• Proof theory
• Logic
• Mathematical logic
• Mathematics
• Computability theory
• Primitive recursive functional
• Dialectica interpretation
• Combinatory logic
• Continuous function

General logical metatheorems for functional analysis Philipp Gerhardy, Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA 15213, USA

Source URL: www.mathematik.tu-darmstadt.de

• Mathematics
• Algebra
• Metric geometry
• Topology
• Space
• Topological vector spaces
• Linear algebra
• Metric
• Continuous function
• Normed vector space
• Norm
• Topology of uniform convergence

Learning Continuous-Time Bayesian Networks in Relational Domains: A Non-Parametric Approach Shuo Yang Tushar Khot

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• Markov models
• Relational model
• Machine learning
• Probability distribution
• Bayesian network
• Reinforcement learning
• Relational data mining
• Loss function

Mathematically strong subsystems of analysis with low rate of growth of provably recursive functionals Ulrich Kohlenbach Fachbereich Mathematik J.W. Goethe–Universit¨at D–60054 Frankfurt, Germany

Source URL: www.mathematik.tu-darmstadt.de

• Computability theory
• Mathematics
• Mathematical logic
• Mathematical analysis
• Primitive recursive functional
• Symbol
• Continuous function
• Primitive recursive function
• operator
• Spectral theory of ordinary differential equations

The use of a logical principle of uniform boundedness in analysis Ulrich Kohlenbach Department of Mathematics University of Michigan Ann Arbor

Source URL: www.mathematik.tu-darmstadt.de

• Mathematical analysis
• Mathematics
• Analysis
• Functional analysis
• Approximation theory
• Constructivism
• Fourier analysis
• Modulus of continuity
• Uniform boundedness principle
• Substitution
• Continuous function

Pointwise hereditary majorization and some applications Ulrich Kohlenbach Fachbereich Mathematik, J.W.Goethe–Universit¨at Robert–Mayer–Str. 6–10, 6000 Frankfurt am Main, FRG Abstract A pointwise version of the H

Source URL: www.mathematik.tu-darmstadt.de

• Computability theory
• Primitive recursive functional
• Proof theory
• Continuous function
• Spectral theory of ordinary differential equations
• It diffusion

A LIGHTFACE ANALYSIS OF THE DIFFERENTIABILITY RANK LINDA BROWN WESTRICK Abstract. We examine the computable part of the differentiability hierarchy defined by Kechris and Woodin. In that hierarchy, the rank of a differen

Source URL: www.math.uconn.edu

• Ordinal numbers
• Proof theory
• Computability theory
• Mathematical notation
• Ordinal notation
• Continuous function
• Constructible universe
• Limit of a function
• Symbol
• NC
• Computable number
• Fast-growing hierarchy

Review of Numerical Integration The fundamental problem of numerical integration is the following: Given the function f continuous on [a, b], approximate Z I (f ) =

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