Construction of Neural Network Classification Expert Systems Using Switching Theory Algorithms

A new family of neural network architectures is presented. This family of architectures solves the problem of constructing and training minimal neural network classification expert systems by using switching theory. The primary insight that leads to the use of switching theory is that the problem of minimizing the number of rules and the number of IF statements (antecedents) per rule in a neural network expert system can be recast into the problem of minimizing the number of digital gates and the number of connections between digital gates in a Very Large Scale Integrated (VLSI) circuit. The rules that the neural network generates to perform a task are readily extractable from the network's weights and topology. Analysis and simulations on the Mushroom database illustrate the system's performance

Non-critical string, Liouville theory and geometric bootstrap hypothesis

The applications of the existing Liouville theories for the description of the longitudinal dynamics of non-critical Nambu-Goto string are analyzed. We show that the recently developed DOZZ solution to the Liouville theory leads to the cut singularities in tree string amplitudes. We propose a new version of the Polyakov geometric approach to Liouville theory and formulate its basic consistency condition - the geometric bootstrap equation. Also in this approach the tree amplitudes develop cut singularieties.Comment: 16 pages; revised versio

Super-Liouville - Double Liouville correspondence

The AGT motivated relation between the tensor product of the N = 1 super-Liouville field theory with the imaginary free fermion (SL) and a certain projected tensor product of the real and the imaginary Liouville field theories (LL) is analyzed. Using conformal field theory techniques we give a complete proof of the equivalence in the NS sector. It is shown that the SL-LL correspondence is based on the equivalence of chiral objects including suitably chosen chiral structure constants of all the three Liouville theories involved.Comment: The Introduction expanded, main points of the paper clarified. Misprints corrected and references added. Published in JHE

Braiding properties of the N=1 super-conformal blocks (Ramond sector)

Using a super scalar field representation of the chiral vertex operators we develop a general method of calculating braiding matrices for all types of N=1 super-conformal 4-point blocks involving Ramond external weights. We give explicit analytic formulae in a number of cases.Comment: LaTeX, 42+1 pages, typo correcte

Divacancy-induced Ferromagnetism in Graphene Nanoribbons

Zigzag graphene nanoribb ons have spin-polarized edges, anti-ferromagnetically coupled in the ground state with total spin zero. Customarily, these ribbons are made ferromagnetic by producing an imbalance between the two sublattices. Here we show that zigzag ribbons can be ferromagnetic due to the presence of reconstructed divacancies near one edge. This effect takes place despite the divacancies are produced by removing two atoms from opposite sublattices, being balanced before reconstruction to 5-8-5 defects. We demonstrate that there is a strong interaction between the defect-localized and edge bands which mix and split away from the Fermi level. This splitting is asymmetric, yielding a net edge spin-polarization. Therefore, the formation of reconstructed divacancies close to the edges of the nanoribbons can be a practical way to make them partially ferromagnetic

Elliptic recurrence representation of the N=1 superconformal blocks in the Ramond sector

The structure of the 4-point N=1 super-conformal blocks in the Ramond sector is analyzed. The elliptic recursion relations for these blocks are derived.Comment: 21 pages, no figures. An error in the description of the R-NS block of the Ramond field and all its consequences correcte

Gapless states and current control in strongly distorted gated trilayer graphene

We investigate gated trilayer graphene partially devoid of outer layers and forming a system of two trilayers connected by a single layer of graphene. A difference in the stacking order of trilayers leads to the appearance of gapless states, one of which is mainly localized in the single graphene layer. We demonstrate that by changing the value of the gate voltage applied to the outer layers one can change the slope of E(k) of this state. As a consequence the direction of current flowing in the single layer graphene can also be changed, the effect that could be useful in practical applications