2,015 research outputs found
Exhaustive generation of atomic combinatorial differential operators
Labelle and Lamathe introduced in 2009 a generalization of the standard combinatorial differential species operator D, by giving a combinatorial interpretation to âŠ(X, D)F(X), where âŠ(X, T) and F(X) are two-sort and one-sort species respectively. One can show that such operators can be decomposed as sums of products of simpler operators called atomic combinatorial differential operators. In their paper, Labelle and Lamathe presented a list of the first atomic differential operators. In this paper, we describe an algorithm that allows to generate (and enumerate) all of them, subject to available computer resources. We also give a detailed analysis of how to compute the molecular components of âŠ(X, D)F(X)
3nj Morphogenesis and Semiclassical Disentangling
Recoupling coefficients (3nj symbols) are unitary transformations between
binary coupled eigenstates of N=(n+1) mutually commuting SU(2) angular momentum
operators. They have been used in a variety of applications in spectroscopy,
quantum chemistry and nuclear physics and quite recently also in quantum
gravity and quantum computing. These coefficients, naturally associated to
cubic Yutsis graphs, share a number of intriguing combinatorial, algebraic, and
analytical features that make them fashinating objects to be studied on their
own. In this paper we develop a bottom--up, systematic procedure for the
generation of 3nj from 3(n-1)j diagrams by resorting to diagrammatical and
algebraic methods. We provide also a novel approach to the problem of
classifying various regimes of semiclassical expansions of 3nj coefficients
(asymptotic disentangling of 3nj diagrams) for n > 2 by means of combinatorial,
analytical and numerical tools
Exploration of Reaction Pathways and Chemical Transformation Networks
For the investigation of chemical reaction networks, the identification of
all relevant intermediates and elementary reactions is mandatory. Many
algorithmic approaches exist that perform explorations efficiently and
automatedly. These approaches differ in their application range, the level of
completeness of the exploration, as well as the amount of heuristics and human
intervention required. Here, we describe and compare the different approaches
based on these criteria. Future directions leveraging the strengths of chemical
heuristics, human interaction, and physical rigor are discussed.Comment: 48 pages, 4 figure
Group field theories for all loop quantum gravity
Group field theories represent a 2nd quantized reformulation of the loop
quantum gravity state space and a completion of the spin foam formalism. States
of the canonical theory, in the traditional continuum setting, have support on
graphs of arbitrary valence. On the other hand, group field theories have
usually been defined in a simplicial context, thus dealing with a restricted
set of graphs. In this paper, we generalize the combinatorics of group field
theories to cover all the loop quantum gravity state space. As an explicit
example, we describe the GFT formulation of the KKL spin foam model, as well as
a particular modified version. We show that the use of tensor model tools
allows for the most effective construction. In order to clarify the
mathematical basis of our construction and of the formalisms with which we
deal, we also give an exhaustive description of the combinatorial structures
entering spin foam models and group field theories, both at the level of the
boundary states and of the quantum amplitudes.Comment: version published in New Journal of Physic
Computational aerodynamics and artificial intelligence
The general principles of artificial intelligence are reviewed and speculations are made concerning how knowledge based systems can accelerate the process of acquiring new knowledge in aerodynamics, how computational fluid dynamics may use expert systems, and how expert systems may speed the design and development process. In addition, the anatomy of an idealized expert system called AERODYNAMICIST is discussed. Resource requirements for using artificial intelligence in computational fluid dynamics and aerodynamics are examined. Three main conclusions are presented. First, there are two related aspects of computational aerodynamics: reasoning and calculating. Second, a substantial portion of reasoning can be achieved with artificial intelligence. It offers the opportunity of using computers as reasoning machines to set the stage for efficient calculating. Third, expert systems are likely to be new assets of institutions involved in aeronautics for various tasks of computational aerodynamics
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