36 research outputs found
Learning Language from a Large (Unannotated) Corpus
A novel approach to the fully automated, unsupervised extraction of
dependency grammars and associated syntax-to-semantic-relationship mappings
from large text corpora is described. The suggested approach builds on the
authors' prior work with the Link Grammar, RelEx and OpenCog systems, as well
as on a number of prior papers and approaches from the statistical language
learning literature. If successful, this approach would enable the mining of
all the information needed to power a natural language comprehension and
generation system, directly from a large, unannotated corpus.Comment: 29 pages, 5 figures, research proposa
On the Minkowski Measure
The Minkowski Question Mark function relates the continued-fraction
representation of the real numbers, to their binary expansion. This function is
peculiar in many ways; one is that its derivative is 'singular'. One can show
by classical techniques that its derivative must vanish on all rationals. Since
the Question Mark itself is continuous, one concludes that the derivative must
be non-zero on the irrationals, and is thus a discontinuous-everywhere
function. This derivative is the subject of this essay.
Various results are presented here: First, a simple but formal
measure-theoretic construction of the derivative is given, making it clear that
it has a very concrete existence as a Lebesgue-Stieltjes measure, and thus is
safe to manipulate in various familiar ways. Next, an exact result is given,
expressing the measure as an infinite product of piece-wise continuous
functions, with each piece being a Mobius transform of the form (ax+b)/(cx+d).
This construction is then shown to be the Haar measure of a certain transfer
operator. A general proof is given that any transfer operator can be understood
to be nothing more nor less than a push-forward on a Banach space; such
push-forwards induce an invariant measure, the Haar measure, of which the
Minkowski measure can serve as a prototypical example. Some minor notes
pertaining to it's relation to the Gauss-Kuzmin-Wirsing operator are made.Comment: 27 pages, 5 figures, corrections, added remark
On Differences of Zeta Values
Finite differences of values of the Riemann zeta function at the integers are
explored. Such quantities, which occur as coefficients in Newton series
representations, have surfaced in works of Maslanka, Coffey, Baez-Duarte, Voros
and others. We apply the theory of Norlund-Rice integrals in conjunction with
the saddle point method and derive precise asymptotic estimates. The method
extends to Dirichlet L-functions and our estimates appear to be partly related
to earlier investigations surrounding Li's criterion for the Riemann
hypothesis.Comment: 18 page
Calculation of Ground State Energy for Confined Fermion Fields
A method for renormalization of the Casimir energy of confined fermion fields
in (1+1)D is proposed. It is based on the extraction of singularities which
appear as poles at the point of physical value of the regularization parameter,
and subsequent compensation of them by means of redefinition of the "bare"
constants. A finite ground state energy of the two-phase hybrid model of
fermion bag with chiral boson-fermion interaction is calculated as the function
of the bag's size.Comment: 10 pages, LaTeX; no figures. Version to appear in Phys. Lett. B
(2001
Casimir Energy For a Massive Dirac Field in One Spatial Dimension: A Direct Approach
In this paper we calculate the Casimir energy for a massive fermionic field
confined between two points in one spatial dimension, with the MIT Bag Model
boundary condition. We compute the Casimir energy directly by summing over the
allowed modes. The method that we use is based on the Boyer's method, and there
will be no need to resort to any analytic continuation techniques. We
explicitly show the graph of the Casimir energy as a function of the distance
between the points and the mass of the fermionic field. We also present a
rigorous derivation of the MIT Bag Model boundary condition.Comment: 8 Pages, 4 Figure
Cheshire Cat Scenario in a 3+1 dimensional Hybrid Chiral Bag
The total energy in the two-phase chiral bag model is studied, including the
contribution due to the bag (Casimir energy plus energy of the valence quarks),
as well as the one coming from the Skyrmion in the external sector. A
consistent determination of the parameters of the model and the renormalization
constants in the energy is performed. The total energy shows an approximate
independence with the bag radius (separation limit between the phases), in
agreement with the Cheshire Cat Principle.Comment: 16 pages, 3 uuencoded postscript figures, typing error correcte
Response of nucleons to external probes in hedgehog models: II. General formalism
Linear response theory for SU(2) hedgehog soliton models is developed.Comment: 25 pages, DOE/ER/40322-163, U. of MD PP \#92-225, (ReVTeX