Order-Invariant Types and their Applications

Our goal is to show that the standard model-theoretic concept of types can be applied in the study of order-invariant properties, i.e., properties definable in a logic in the presence of an auxiliary order relation, but not actually dependent on that order relation. This is somewhat surprising since order-invariant properties are more of a combinatorial rather than a logical object. We provide two applications of this notion. One is a proof, from the basic principles, of a theorem by Courcelle stating that over trees, order-invariant MSO properties are expressible in MSO with counting quantifiers. The other is an analog of the Feferman-Vaught theorem for order-invariant properties

Deformations of the fermion realization of the sp(4) algebra and its subalgebras

With a view towards future applications in nuclear physics, the fermion realization of the compact symplectic sp(4) algebra and its q-deformed versions are investigated. Three important reduction chains of the sp(4) algebra are explored in both the classical and deformed cases. The deformed realizations are based on distinct deformations of the fermion creation and annihilation operators. For the primary reduction, the su(2) sub-structure can be interpreted as either the spin, isospin or angular momentum algebra, whereas for the other two reductions su(2) can be associated with pairing between fermions of the same type or pairing between two distinct fermion types. Each reduction provides for a complete classification of the basis states. The deformed induced u(2) representations are reducible in the action spaces of sp(4) and are decomposed into irreducible representations.Comment: 28 pages, LaTeX 12pt article styl

Basic Types of Coarse-Graining

We consider two basic types of coarse-graining: the Ehrenfests' coarse-graining and its extension to a general principle of non-equilibrium thermodynamics, and the coarse-graining based on uncertainty of dynamical models and Epsilon-motions (orbits). Non-technical discussion of basic notions and main coarse-graining theorems are presented: the theorem about entropy overproduction for the Ehrenfests' coarse-graining and its generalizations, both for conservative and for dissipative systems, and the theorems about stable properties and the Smale order for Epsilon-motions of general dynamical systems including structurally unstable systems. Computational kinetic models of macroscopic dynamics are considered. We construct a theoretical basis for these kinetic models using generalizations of the Ehrenfests' coarse-graining. General theory of reversible regularization and filtering semigroups in kinetics is presented, both for linear and non-linear filters. We obtain explicit expressions and entropic stability conditions for filtered equations. A brief discussion of coarse-graining by rounding and by small noise is also presented.Comment: 60 pgs, 11 figs., includes new analysis of coarse-graining by filtering. A talk given at the research workshop: "Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena," University of Leicester, UK, August 24-26, 200

Rapid Online Analysis of Local Feature Detectors and Their Complementarity

A vision system that can assess its own performance and take appropriate actions online to maximize its effectiveness would be a step towards achieving the long-cherished goal of imitating humans. This paper proposes a method for performing an online performance analysis of local feature detectors, the primary stage of many practical vision systems. It advocates the spatial distribution of local image features as a good performance indicator and presents a metric that can be calculated rapidly, concurs with human visual assessments and is complementary to existing offline measures such as repeatability. The metric is shown to provide a measure of complementarity for combinations of detectors, correctly reflecting the underlying principles of individual detectors. Qualitative results on well-established datasets for several state-of-the-art detectors are presented based on the proposed measure. Using a hypothesis testing approach and a newly-acquired, larger image database, statistically-significant performance differences are identified. Different detector pairs and triplets are examined quantitatively and the results provide a useful guideline for combining detectors in applications that require a reasonable spatial distribution of image features. A principled framework for combining feature detectors in these applications is also presented. Timing results reveal the potential of the metric for online applications. © 2013 by the authors; licensee MDPI, Basel, Switzerland

Working memory networks for learning multiple groupings of temporally ordered events: applications to 3-D visual object recognition

Working memory neural networks are characterized which encode the invariant temporal order of sequential events that may be presented at widely differing speeds, durations, and interstimulus intervals. This temporal order code is designed to enable all possible groupings of sequential events to be stably learned and remembered in real time, even as new events perturb the system. Such a competence is needed in neural architectures which self-organize learned codes for variable-rate speech perception, sensory-motor planning, or 3-D visual object recognition. Using such a working memory, a self-organizing architecture for invariant 3-D visual object recognition is described that is based on the model of Seibert and Waxman [1].Air Force Office of Scientific Research (90-128, 90-0175); British Petroleum (89-A-1204); Defense Advanced Research Projects Agency (90-0083); National Science Foundation (IRI 90-00530, IRI 87-16960