Separable time-causal and time-recursive spatio-temporal receptive fields

We present an improved model and theory for time-causal and time-recursive spatio-temporal receptive fields, obtained by a combination of Gaussian receptive fields over the spatial domain and first-order integrators or equivalently truncated exponential filters coupled in cascade over the temporal domain. Compared to previous spatio-temporal scale-space formulations in terms of non-enhancement of local extrema or scale invariance, these receptive fields are based on different scale-space axiomatics over time by ensuring non-creation of new local extrema or zero-crossings with increasing temporal scale. Specifically, extensions are presented about parameterizing the intermediate temporal scale levels, analysing the resulting temporal dynamics and transferring the theory to a discrete implementation in terms of recursive filters over time.Comment: 12 pages, 2 figures, 2 tables. arXiv admin note: substantial text overlap with arXiv:1404.203

A General Framework for Recursive Decompositions of Unitary Quantum Evolutions

Decompositions of the unitary group U(n) are useful tools in quantum information theory as they allow one to decompose unitary evolutions into local evolutions and evolutions causing entanglement. Several recursive decompositions have been proposed in the literature to express unitary operators as products of simple operators with properties relevant in entanglement dynamics. In this paper, using the concept of grading of a Lie algebra, we cast these decompositions in a unifying scheme and show how new recursive decompositions can be obtained. In particular, we propose a new recursive decomposition of the unitary operator on $N$ qubits, and we give a numerical example.Comment: 17 pages. To appear in J. Phys. A: Math. Theor. This article replaces our earlier preprint "A Recursive Decomposition of Unitary Operators on N Qubits." The current version provides a general method to generate recursive decompositions of unitary evolutions. Several decompositions obtained before are shown to be as a special case of this general procedur

Local BRST cohomology and Seiberg-Witten maps in noncommutative Yang-Mills theory

We analyze in detail the recursive construction of the Seiberg-Witten map and give an exhaustive description of its ambiguities. The local BRST cohomology for noncommutative Yang-Mills theory is investigated in the framework of the effective commutative Yang-Mills type theory. In particular, we show how some of the conformal symmetries get obstructed by the noncommutative deformation.Comment: 34 pages Latex file, 2 additional references adde

Perturbation theory and locality in the Field-Antifield formalism

The BatalinVilkovisky formalism is studied in the framework of perturbation theory by analyzing the antibracket BecchiRouetStoraTyutin (BRST) cohomology of the proper solution S0. It is concluded that the recursive equations for the complete proper solution S can be solved at any order of perturbation theory. If certain conditions on the classical action and on the gauge generators are imposed the solution can be taken local

On Renormalization Group Flows and Polymer Algebras

In this talk methods for a rigorous control of the renormalization group (RG) flow of field theories are discussed. The RG equations involve the flow of an infinite number of local partition functions. By the method of exact beta-function the RG equations are reduced to flow equations of a finite number of coupling constants. Generating functions of Greens functions are expressed by polymer activities. Polymer activities are useful for solving the large volume and large field problem in field theory. The RG flow of the polymer activities is studied by the introduction of polymer algebras. The definition of products and recursive functions replaces cluster expansion techniques. Norms of these products and recursive functions are basic tools and simplify a RG analysis for field theories. The methods will be discussed at examples of the $\Phi^4$-model, the $O(N)$ $\sigma$-model and hierarchical scalar field theory (infrared fixed points).Comment: 32 pages, LaTeX, MS-TPI-94-12, Talk presented at the conference ``Constructive Results in Field Theory, Statistical Mechanics and Condensed Matter Physics'', 25-27 July 1994, Palaiseau, Franc

Form Factors of the Elementary Field in the Bullough-Dodd Model

We derive the recursive equations for the form factors of the local hermitian operators in the Bullough-Dodd model. At the self-dual point of the theory, the form factors of the fundamental field of the Bullough-Dodd model are equal to those of the fundamental field of the Sinh-Gordon model at a specific value of the coupling constant.Comment: 14 pages, LATEX file, ISAS/EP/92/208;USP-IFQSC/TH/92-5

A model of near-rational exuberance

We study how the use of judgment or "add-factors" in forecasting may disturb the set of equilibrium outcomes when agents learn using recursive methods. We isolate conditions under which new phenomena, which we call exuberance equilibria, can exist in a standard self-referential environment. Local indeterminacy is not a requirement for existence. We construct a simple asset pricing example and find that exuberance equilibria, when they exist, can be extremely volatile relative to fundamental equilibria.Monetary policy ; Rational expectations (Economic theory)