840 research outputs found
Learning Task Specifications from Demonstrations
Real world applications often naturally decompose into several sub-tasks. In
many settings (e.g., robotics) demonstrations provide a natural way to specify
the sub-tasks. However, most methods for learning from demonstrations either do
not provide guarantees that the artifacts learned for the sub-tasks can be
safely recombined or limit the types of composition available. Motivated by
this deficit, we consider the problem of inferring Boolean non-Markovian
rewards (also known as logical trace properties or specifications) from
demonstrations provided by an agent operating in an uncertain, stochastic
environment. Crucially, specifications admit well-defined composition rules
that are typically easy to interpret. In this paper, we formulate the
specification inference task as a maximum a posteriori (MAP) probability
inference problem, apply the principle of maximum entropy to derive an analytic
demonstration likelihood model and give an efficient approach to search for the
most likely specification in a large candidate pool of specifications. In our
experiments, we demonstrate how learning specifications can help avoid common
problems that often arise due to ad-hoc reward composition.Comment: NIPS 201
Structure and enumeration of (3+1)-free posets
A poset is (3+1)-free if it does not contain the disjoint union of chains of
length 3 and 1 as an induced subposet. These posets play a central role in the
(3+1)-free conjecture of Stanley and Stembridge. Lewis and Zhang have
enumerated (3+1)-free posets in the graded case by decomposing them into
bipartite graphs, but until now the general enumeration problem has remained
open. We give a finer decomposition into bipartite graphs which applies to all
(3+1)-free posets and obtain generating functions which count (3+1)-free posets
with labelled or unlabelled vertices. Using this decomposition, we obtain a
decomposition of the automorphism group and asymptotics for the number of
(3+1)-free posets.Comment: 28 pages, 5 figures. New version includes substantial changes to
clarify the construction of skeleta and the enumeration. An extended abstract
of this paper appears as arXiv:1212.535
Higgs branch RG-flows via Decay and Fission
Magnetic quivers have been an instrumental technique for advancing our
understanding of Higgs branches of supersymmetric theories with 8 supercharges.
In this work, we present the decay and fission algorithm for unitary magnetic
quivers. It enables the derivation of the complete phase (Hasse) diagram and is
characterised by the following key attributes: First and foremost, the
algorithm is inherently simple; just relying on convex linear algebra. Second,
any magnetic quiver can only undergo decay or fission processes; these reflect
the possible Higgs branch RG-flows (Higgsings), and the quivers thereby
generated are the magnetic quivers of the new RG fixed points. Third, the
geometry of the decay or fission transition (i.e. the transverse slice) is
simply read off. As a consequence, the algorithm does not rely on a complete
list of minimal transitions, but rather outputs the transverse slice geometry
automatically. As a proof of concept, its efficacy is showcased across various
scenarios, encompassing SCFTs from dimensions 3 to 6, instanton moduli spaces,
and little string theories.Comment: 55 pages; v.2 added clarifications for sec 3.
Poset topology and homological invariants of algebras arising in algebraic combinatorics
We present a beautiful interplay between combinatorial topology and
homological algebra for a class of monoids that arise naturally in algebraic
combinatorics. We explore several applications of this interplay. For instance,
we provide a new interpretation of the Leray number of a clique complex in
terms of non-commutative algebra.
R\'esum\'e. Nous pr\'esentons une magnifique interaction entre la topologie
combinatoire et l'alg\`ebre homologique d'une classe de mono\"ides qui figurent
naturellement dans la combinatoire alg\'ebrique. Nous explorons plusieurs
applications de cette interaction. Par exemple, nous introduisons une nouvelle
interpr\'etation du nombre de Leray d'un complexe de clique en termes de la
dimension globale d'une certaine alg\`ebre non commutative.Comment: This is an extended abstract surveying the results of arXiv:1205.1159
and an article in preparation. 12 pages, 3 Figure
Quiver Theories and Formulae for Nilpotent Orbits of Exceptional Algebras
We treat the topic of the closures of the nilpotent orbits of the Lie
algebras of Exceptional groups through their descriptions as moduli spaces, in
terms of Hilbert series and the highest weight generating functions for their
representation content. We extend the set of known Coulomb branch quiver theory
constructions for Exceptional group minimal nilpotent orbits, or reduced single
instanton moduli spaces, to include all orbits of Characteristic Height 2,
drawing on extended Dynkin diagrams and the unitary monopole formula. We also
present a representation theoretic formula, based on localisation methods, for
the normal nilpotent orbits of the Lie algebras of any Classical or Exceptional
group. We analyse lower dimensioned Exceptional group nilpotent orbits in terms
of Hilbert series and the Highest Weight Generating functions for their
decompositions into characters of irreducible representations and/or Hall
Littlewood polynomials. We investigate the relationships between the moduli
spaces describing different nilpotent orbits and propose candidates for the
constructions of some non-normal nilpotent orbits of Exceptional algebras.Comment: 87 pages, 4 figure
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