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      Fibers of maps to totally nonnegative spaces

      March 4, 2019

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      Mathematics
      Combinatorics
      Geometric Topology
      Representation Theory
      Combinatorics
      Geometric Topology
      Representation Theory
      This paper undertakes a study of the structure of the fibers of the Chevalley exponentiation maps f(i1,…,id)f_{(i_1,\dots ,i_d)}f(i1​,…,id​)​. The fibers of these maps f(i1,…,id)f_{(i_1,\dots ,i_d)}f(i1​,…,id​)​ encode the nonnegative real relations amongst exponentiated Chevalley ...

      Albatross: An optimistic consensus algorithm

      March 4, 2019

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      Computer Science
      Cryptography and Security
      Cryptography and Security
      The consensus protocol is a critical component of distributed ledgers and blockchains. Achieving consensus over a decentralized network poses challenges to transaction finality and performance. Currently, the highest-performing consensus al...

      A duality theorem for harmonic maps into inner symmetric spaces

      March 3, 2019

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      Mathematics
      Differential Geometry
      In this note, we show that for any harmonic map into a non-compact symmetric space one can find naturally a "dual" harmonic map into a compact symmetric space which can be constructed from the same basic data (called "potentials" in the loo...

      Uniform exponential mixing for congruence covers of convex cocompact hyperbolic manifolds

      March 2, 2019

      Mathematics
      Dynamical Systems
      Geometric Topology
      Spectral Theory
      Let Γ\GammaΓ be a Zariski dense convex cocompact subgroup contained in an arithmetic lattice of SO⁡(n,1)∘\operatorname{SO}(n, 1)^{\circ}SO(n,1)∘. We prove uniform exponential mixing of the geodesic flow for congruence covers of the hyperbolic manifold $\G...

      Model-Based Reinforcement Learning for Atari

      March 1, 2019

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      Computer Science
      Statistics
      Machine Learning
      Machine Learning
      Model-free reinforcement learning (RL) can be used to learn effective policies for complex tasks, such as Atari games, even from image observations. However, this typically requires very large amounts of interaction -- substantially more, i...

      Local asymptotic properties for the growth rate of a jump-type CIR process

      February 28, 2019

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      Mathematics
      Probability
      In this paper, we consider a one-dimensional jump-type Cox-Ingersoll-Ross process driven by a Brownian motion and a subordinator, whose growth rate is an unknown parameter. Considering the process observed continuously or discretely at high...

      Neutrino Quantum Kinetics in Compact Objects

      February 28, 2019

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      Physics
      High Energy Astrophysical Phenomena
      High Energy Physics - Phenomenology
      Nuclear Theory
      Neutrinos play a critical role of transporting energy and changing the lepton density within core-collapse supernovae and neutron star mergers. The quantum kinetic equations (QKEs) combine the effects of neutrino-matter interactions treated...

      Graph and String Parameters: Connections Between Pathwidth, Cutwidth and the Locality Number

      February 28, 2019

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      Computer Science
      Data Structures and Algorithms
      We investigate the locality number, a recently introduced structural parameter for strings (with applications in pattern matching with variables), and its connection to two important graph-parameters, cutwidth and pathwidth. These connectio...

      Opial's inequality in qqq-Calculus revisited

      February 27, 2019

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      Mathematics
      General Mathematics
      We have fundamentally corrected the proofs of the theorems from our paper [9] by giving an entirely different approach, using quite a simple method based on applications of some elementary inequalities, well-known H\"older's inequality, and...

      Bergman projection induced by radial weight

      February 26, 2019

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      Mathematics
      Functional Analysis
      Complex Variables
      Functional Analysis
      Complex Variables
      The question of when the Bergman projection PωP_\omegaPω​ induced by a radial weight ω\omegaω on the unit disc is a bounded operator from one space into another is of primordial importance in the theory of Bergman spaces. The long-standing pro...
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