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

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

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

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