Article history: Received 22 May 2014 Accepted 8 November 2014 Available online 25 November 2014 Submitted by J.M. Landsberg MSC: 15B99 13P25 20G20

One of the themes in algebraic geometry is the study of the relation between the “topology” of a smooth projective variety and a (“general”) hyperplane section. Recent results of Nori produce cohomological evidence for a conjecture that a general hypersurface of sufficently large degree should have no “interesting” cycles. We compute precise bounds for these results and show by example that the...

It is well-known that the Plücker relations generate the ideal of relations of the maximal minors of a generic m× n matrix. In this paper we discuss the relations of t-minors for t < min(m,n). We will exhibit minimal relations in degrees 2 (non-Plücker in general) and 3, and give some evidence for our conjecture that we have found the generating system of the ideal of relations. The approach is...

We generalize the traditional concept of temporal optical interferometry to any degree of freedom of a coherent optical field. By identifying the structure of a unitary optical transformation that we designate the generalized phase operator, we enable optical interferometry to be carried out in any modal basis describing a degree of freedom. The structure of the generalized phase operator is th...

We show that all levels of the jump hierarchy are first order definable in the local structure of the enumeration degrees.

We discuss the fragmentation of a heavy quark to a baryon containing two heavy quarks of mass mQ ≫ ΛQCD. In this limit the heavy quarks first combine perturbatively into a compact diquark with a radius small compared to 1/ΛQCD, which interacts with the light hadronic degrees of freedom exactly as does a heavy antiquark. The subsequent evolution of this QQ diquark to a QQq baryon is identical to...

The brain constructs representations of what is sensed and thought about in the form of nerve impulses that propagate in circuits and network assemblies (Circuit Impulse Patterns, CIPs). CIP representations of which humans are consciously aware occur in the context of a sense of self. Thus, research on mechanisms of consciousness might benefit from a focus on how a conscious sense of self is re...

Encoding and manipulation of quantum information by means of topological degrees of freedom provides a promising way to achieve natural fault tolerance that is built in at the physical level. We show that this topological approach to quantum information processing is a particular instance of the notion of computation in a noiseless quantum subsystem. The latter then provides the most general co...

A set A of nonnegative integers is computably enumerable (c.e.), also called recursively enumerable (r.e.), if there is a computable method to list its elements. The class of sets B which contain the same information as A under Turing computability (</=T) is the (Turing) degree of A, and a degree is c.e. if it contains a c.e. set. The extension of embedding problem for the c.e. degrees R = (R, ...