128,665 research outputs found
Monodromic vs geodesic computation of Virasoro classical conformal blocks
We compute 5-point classical conformal blocks with two heavy, two light, and
one superlight operator using the monodromy approach up to third order in the
superlight expansion. By virtue of the AdS/CFT correspondence we show the
equivalence of the resulting expressions to those obtained in the bulk
computation for the corresponding geodesic configuration.Comment: 20 pages, v2: more comments, refs added, NPB versio
Answer Set Planning Under Action Costs
Recently, planning based on answer set programming has been proposed as an
approach towards realizing declarative planning systems. In this paper, we
present the language Kc, which extends the declarative planning language K by
action costs. Kc provides the notion of admissible and optimal plans, which are
plans whose overall action costs are within a given limit resp. minimum over
all plans (i.e., cheapest plans). As we demonstrate, this novel language allows
for expressing some nontrivial planning tasks in a declarative way.
Furthermore, it can be utilized for representing planning problems under other
optimality criteria, such as computing ``shortest'' plans (with the least
number of steps), and refinement combinations of cheapest and fastest plans. We
study complexity aspects of the language Kc and provide a transformation to
logic programs, such that planning problems are solved via answer set
programming. Furthermore, we report experimental results on selected problems.
Our experience is encouraging that answer set planning may be a valuable
approach to expressive planning systems in which intricate planning problems
can be naturally specified and solved
A mathematical theory of semantic development in deep neural networks
An extensive body of empirical research has revealed remarkable regularities
in the acquisition, organization, deployment, and neural representation of
human semantic knowledge, thereby raising a fundamental conceptual question:
what are the theoretical principles governing the ability of neural networks to
acquire, organize, and deploy abstract knowledge by integrating across many
individual experiences? We address this question by mathematically analyzing
the nonlinear dynamics of learning in deep linear networks. We find exact
solutions to this learning dynamics that yield a conceptual explanation for the
prevalence of many disparate phenomena in semantic cognition, including the
hierarchical differentiation of concepts through rapid developmental
transitions, the ubiquity of semantic illusions between such transitions, the
emergence of item typicality and category coherence as factors controlling the
speed of semantic processing, changing patterns of inductive projection over
development, and the conservation of semantic similarity in neural
representations across species. Thus, surprisingly, our simple neural model
qualitatively recapitulates many diverse regularities underlying semantic
development, while providing analytic insight into how the statistical
structure of an environment can interact with nonlinear deep learning dynamics
to give rise to these regularities
Using ACL2 to Verify Loop Pipelining in Behavioral Synthesis
Behavioral synthesis involves compiling an Electronic System-Level (ESL)
design into its Register-Transfer Level (RTL) implementation. Loop pipelining
is one of the most critical and complex transformations employed in behavioral
synthesis. Certifying the loop pipelining algorithm is challenging because
there is a huge semantic gap between the input sequential design and the output
pipelined implementation making it infeasible to verify their equivalence with
automated sequential equivalence checking techniques. We discuss our ongoing
effort using ACL2 to certify loop pipelining transformation. The completion of
the proof is work in progress. However, some of the insights developed so far
may already be of value to the ACL2 community. In particular, we discuss the
key invariant we formalized, which is very different from that used in most
pipeline proofs. We discuss the needs for this invariant, its formalization in
ACL2, and our envisioned proof using the invariant. We also discuss some
trade-offs, challenges, and insights developed in course of the project.Comment: In Proceedings ACL2 2014, arXiv:1406.123
Intertwining technique for a system of difference Schroedinger equations and new exactly solvable multichannel potentials
The intertwining operator technique is applied to difference Schroedinger
equations with operator-valued coefficients. It is shown that these equations
appear naturally when a discrete basis is used for solving a multichannel
Schroedinger equation. New families of exactly solvable multichannel
Hamiltonians are found
Zamolodchikov relations and Liouville hierarchy in SL(2,R)_k WZNW model
We study the connection between Zamolodchikov operator-valued relations in
Liouville field theory and in the SL(2,R)_k WZNW model. In particular, the
classical relations in SL(2,R)_k can be formulated as a classical Liouville
hierarchy in terms of the isotopic coordinates, and their covariance is easily
understood in the framework of the AdS_3/CFT_2 correspondence. Conversely, we
find a closed expression for the classical Liouville decoupling operators in
terms of the so called uniformizing Schwarzian operators and show that the
associated uniformizing parameter plays the same role as the isotopic
coordinates in SL(2,R)_k. The solutions of the j-th classical decoupling
equation in the WZNW model span a spin j reducible representation of SL(2,R).
Likewise, we show that in Liouville theory solutions of the classical
decoupling equations span spin j representations of SL(2,R), which is
interpreted as the isometry group of the hyperbolic upper half-plane. We also
discuss the connection with the Hamiltonian reduction of SL(2,R)_k WZNW model
to Liouville theory.Comment: 49 p
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