Commuting Flows and Conservation Laws for Noncommutative Lax Hierarchies

We discuss commuting flows and conservation laws for Lax hierarchies on noncommutative spaces in the framework of the Sato theory. On commutative spaces, the Sato theory has revealed essential aspects of the integrability for wide class of soliton equations which are derived from the Lax hierarchies in terms of pseudo-differential operators. Noncommutative extension of the Sato theory has been already studied by the author and Kouichi Toda, and the existence of various noncommutative Lax hierarchies are guaranteed. In the present paper, we present conservation laws for the noncommutative Lax hierarchies with both space-space and space-time noncommutativities and prove the existence of infinite number of conserved densities. We also give the explicit representations of them in terms of Lax operators. Our results include noncommutative versions of KP, KdV, Boussinesq, coupled KdV, Sawada-Kotera, modified KdV equations and so on.Comment: 22 pages, LaTeX, v2: typos corrected, references added, version to appear in JM

On a Lagrangian reduction and a deformation of completely integrable systems

We develop a theory of Lagrangian reduction on loop groups for completely integrable systems after having exchanged the role of the space and time variables in the multi-time interpretation of integrable hierarchies. We then insert the Sobolev norm $H^1$ in the Lagrangian and derive a deformation of the corresponding hierarchies. The integrability of the deformed equations is altered and a notion of weak integrability is introduced. We implement this scheme in the AKNS and SO(3) hierarchies and obtain known and new equations. Among them we found two important equations, the Camassa-Holm equation, viewed as a deformation of the KdV equation, and a deformation of the NLS equation

Non-Abelian coset string backgrounds from asymptotic and initial data

We describe hierarchies of exact string backgrounds obtained as non-Abelian cosets of orthogonal groups and having a space--time realization in terms of gauged WZW models. For each member in these hierarchies, the target-space backgrounds are generated by the ``boundary'' backgrounds of the next member. We explicitly demonstrate that this property holds to all orders in $\alpha'$. It is a consequence of the existence of an integrable marginal operator build on, generically, non-Abelian parafermion bilinears. These are dressed with the dilaton supported by the extra radial dimension, whose asymptotic value defines the boundary. Depending on the hierarchy, this boundary can be time-like or space-like with, in the latter case, potential cosmological applications.Comment: 26 page

On supertwistor geometry and integrability in super gauge theory

In this thesis, we report on different aspects of integrability in supersymmetric gauge theories. The main tool of investigation is twistor geometry. In trying to be self-contained, we first present a brief review about the basics of twistor geometry. We then focus on the twistor description of various gauge theories in four and three space-time dimensions. These include self-dual supersymmetric Yang-Mills (SYM) theories and relatives, non-self-dual SYM theories and supersymmetric Bogomolny models. Furthermore, we present a detailed investigation of integrability of self-dual SYM theories. In particular, the twistor construction of infinite-dimensional algebras of hidden symmetries is given and exemplified by deriving affine extensions of internal and space-time symmetries. In addition, we derive self-dual SYM hierarchies within the twistor framework. These hierarchies describe an infinite number of flows on the respective solution space, where the lowest level flows are space-time translations. We also derive infinitely many nonlocal conservation laws.Comment: Ph.D. thesi

Efficient universal pushdown cellular automata and their application to complexity

In order to obtain universal classical cellular automata an infinite space is required. Therefore, the number of required processors depends on the length of input data and, additionally, may increase during the computation. On the other hand, Turing machines are universal devices which have one processor only and additionally an infinite storage tape. Here an in some sense intermediate model is studied. The pushdown cellular automata are a stack augmented generalization of classical cellular automata. They form a massively parallel universal model where the number of processors is bounded by the length of input data. Effcient universal pushdown cellular automata and their efficiently verifiable encodings are proposed. They are applied to computational complexity, and tight time and stack-space hierarchies are shown. CR Subject Classification (1998): F.1, F.4.3, B.6.1, E.

Higher-spin current multiplets in operator-product expansions

Various formulas for currents with arbitrary spin are worked out in general space-time dimension, in the free field limit and, at the bare level, in presence of interactions. As the n-dimensional generalization of the (conformal) vector field, the (n/2-1)-form is used. The two-point functions and the higher-spin central charges are evaluated at one loop. As an application, the higher-spin hierarchies generated by the stress-tensor operator-product expansion are computed in supersymmetric theories. The results exhibit an interesting universality.Comment: 19 pages. Introductory paragraph, misprint corrected and updated references. CQG in pres

PReaCH: A Fast Lightweight Reachability Index using Pruning and Contraction Hierarchies

We develop the data structure PReaCH (for Pruned Reachability Contraction Hierarchies) which supports reachability queries in a directed graph, i.e., it supports queries that ask whether two nodes in the graph are connected by a directed path. PReaCH adapts the contraction hierarchy speedup techniques for shortest path queries to the reachability setting. The resulting approach is surprisingly simple and guarantees linear space and near linear preprocessing time. Orthogonally to that, we improve existing pruning techniques for the search by gathering more information from a single DFS-traversal of the graph. PReaCH-indices significantly outperform previous data structures with comparable preprocessing cost. Methods with faster queries need significantly more preprocessing time in particular for the most difficult instances

A Neocolonial Warp of Outmoded Hierarchies, Curricula and Disciplinary Technologies in Trinidad’s Educational System

I re-appropriate the image of a space-time warp and its notion of disorientation to argue that colonialism created a warp in Trinidad’s educational system. Through an analysis of school violence and the wider network of structural violence in which it is steeped, I focus on three outmoded aspects as evidence of this warp--hierarchies, curricula and disciplinary technologies--by using data (interviews, documents and observations) from a longitudinal case study at a secondary school in Trinidad. Colonialism was about exclusion, alienation, violence, control and order, and this functionalism persists today; I therefore contend that hierarchies, curricula and disciplinary technologies are all enforcers of these tenets of (neo)colonialism in Trinidad’s schools. I conclude with some nascent thoughts on a Systemic Restorative Praxis (SRP) model as a way of de-stabilizing the warp, by stitching together literature/approaches from systems thinking, restorative justice and Freirean notions of praxis. SRP implies that colonialism (and this modern-day warp) has rendered much psychic and material damage, and that any intervention to address structural violence has to be systemic and iterative in scope and process, include healing, be participatory, and foster an ethic of horizontalization in human relations

Fragmentation and hierarchies in Argentina’s maternal health services as barriers to access, continuity and comprehensiveness of care

This paper aims to uncover the ways in which institutional regulations of maternal care services offered by the public health system in Argentina generate various forms of fragmentation and hierarchical organization that create barriers to access, continuity, and comprehensiveness of care. The conceptual and methodological tools of institutional ethnography are used as a guide for analysis of interviews with women and health agents from a province of the country’s Western region, as well as participant observation at regional hospitals and local health centers. The barriers identified and analyzed are related to regulations of time(s), space(s), and hierarchies among the health professions involved in service provision related to maternal health.Keywords: maternal health; institutional ethnography; institutional time; institutional space; hierarchies; pregnancy; Argentina; public healthcar