41,439 research outputs found
Topological modular forms and conformal nets
We describe the role conformal nets, a mathematical model for conformal field
theory, could play in a geometric definition of the generalized cohomology
theory TMF of topological modular forms. Inspired by work of Segal and
Stolz-Teichner, we speculate that bundles of boundary conditions for the net of
free fermions will be the basic underlying objects representing TMF-cohomology
classes. String structures, which are the fundamental orientations for
TMF-cohomology, can be encoded by defects between free fermions, and we
construct the bundle of fermionic boundary conditions for the TMF-Euler class
of a string vector bundle. We conjecture that the free fermion net exhibits an
algebraic periodicity corresponding to the 576-fold cohomological periodicity
of TMF; using a homotopy-theoretic invariant of invertible conformal nets, we
establish a lower bound of 24 on this periodicity of the free fermions
Topological Quantum Field Theories and Operator Algebras
We review "quantum" invariants of closed oriented 3-dimensional manifolds
arising from operator algebras.Comment: For proceedings of "International Workshop on Quantum Field Theory
and Noncommutative Geometry", Sendai, November 200
Object-Oriented Dynamics Learning through Multi-Level Abstraction
Object-based approaches for learning action-conditioned dynamics has
demonstrated promise for generalization and interpretability. However, existing
approaches suffer from structural limitations and optimization difficulties for
common environments with multiple dynamic objects. In this paper, we present a
novel self-supervised learning framework, called Multi-level Abstraction
Object-oriented Predictor (MAOP), which employs a three-level learning
architecture that enables efficient object-based dynamics learning from raw
visual observations. We also design a spatial-temporal relational reasoning
mechanism for MAOP to support instance-level dynamics learning and handle
partial observability. Our results show that MAOP significantly outperforms
previous methods in terms of sample efficiency and generalization over novel
environments for learning environment models. We also demonstrate that learned
dynamics models enable efficient planning in unseen environments, comparable to
true environment models. In addition, MAOP learns semantically and visually
interpretable disentangled representations.Comment: Accepted to the Thirthy-Fourth AAAI Conference On Artificial
Intelligence (AAAI), 202
Localization and Entanglement in Relativistic Quantum Physics
The combination of quantum theory and special relativity leads to structures
that differ in several respects from non-relativistic quantum mechanics of
particles. These differences are quite familiar to practitioners of Algebraic
Quantum Field Theory but less well known outside this community. The paper is
intended as a concise survey of some selected aspects of relativistic quantum
physics, in particular regarding localization and entanglement.Comment: For the proceedings of the workshop "The Message of Quantum Science
-- Attempts Towards a Synthesis" held at ZIF, Bielefeld, February-March 201
The failure tolerance of mechatronic software systems to random and targeted attacks
This paper describes a complex networks approach to study the failure
tolerance of mechatronic software systems under various types of hardware
and/or software failures. We produce synthetic system architectures based on
evidence of modular and hierarchical modular product architectures and known
motifs for the interconnection of physical components to software. The system
architectures are then subject to various forms of attack. The attacks simulate
failure of critical hardware or software. Four types of attack are
investigated: degree centrality, betweenness centrality, closeness centrality
and random attack. Failure tolerance of the system is measured by a 'robustness
coefficient', a topological 'size' metric of the connectedness of the attacked
network. We find that the betweenness centrality attack results in the most
significant reduction in the robustness coefficient, confirming betweenness
centrality, rather than the number of connections (i.e. degree), as the most
conservative metric of component importance. A counter-intuitive finding is
that "designed" system architectures, including a bus, ring, and star
architecture, are not significantly more failure-tolerant than interconnections
with no prescribed architecture, that is, a random architecture. Our research
provides a data-driven approach to engineer the architecture of mechatronic
software systems for failure tolerance.Comment: Proceedings of the 2013 ASME International Design Engineering
Technical Conferences & Computers and Information in Engineering Conference
IDETC/CIE 2013 August 4-7, 2013, Portland, Oregon, USA (In Print
Characterization of complex networks: A survey of measurements
Each complex network (or class of networks) presents specific topological
features which characterize its connectivity and highly influence the dynamics
of processes executed on the network. The analysis, discrimination, and
synthesis of complex networks therefore rely on the use of measurements capable
of expressing the most relevant topological features. This article presents a
survey of such measurements. It includes general considerations about complex
network characterization, a brief review of the principal models, and the
presentation of the main existing measurements. Important related issues
covered in this work comprise the representation of the evolution of complex
networks in terms of trajectories in several measurement spaces, the analysis
of the correlations between some of the most traditional measurements,
perturbation analysis, as well as the use of multivariate statistics for
feature selection and network classification. Depending on the network and the
analysis task one has in mind, a specific set of features may be chosen. It is
hoped that the present survey will help the proper application and
interpretation of measurements.Comment: A working manuscript with 78 pages, 32 figures. Suggestions of
measurements for inclusion are welcomed by the author
From Operator Algebras to Superconformal Field Theory
We make a review on the recent progress in the operator algebraic approach to
(super)conformal field theory. We discuss representation theory, classification
results, full and boundary conformal field theories, relations to supervertex
operator algebras and Moonshine, connections to subfactor theory and
noncommutative geometry
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