Infinitesimal moduli for the Strominger system and Killing spinors in generalized geometry

We construct the space of infinitesimal variations for the Strominger system and an obstruction space to integrability, using elliptic operator theory. We initiate the study of the geometry of the moduli space, describing the infinitesimal structure of a natural foliation on this space. The associated leaves are related to generalized geometry and correspond to moduli spaces of solutions of suitable Killing spinor equations on a Courant algebroid. As an application, we propose a unifying framework for metrics with holonomy \SU(3) and solutions of the Strominger system.Comment: 48 pages. Section 5 and Appendix A from previous version have been suppressed and will appear elsewhere. Title slightly changed, references added, presentation improved. To appear in Math. Anna

Pedagogical Possibilities for the N-Puzzle Problem

In this paper we present work on a project funded by the National Science Foundation with a goal of unifying the Artificial Intelligence (AI) course around the theme of machine learning. Our work involves the development and testing of an adaptable framework for the presentation of core AI topics that emphasizes the relationship between AI and computer science. Several hands-on laboratory projects that can be closely integrated into an introductory AI course have been developed. We present an overview of one of the projects and describe the associated curricular materials that have been developed. The project uses machine learning as a theme to unify core AI topics in the context of the N-puzzle game. Games provide a rich framework to introduce students to search fundamentals and other core AI concepts. The paper presents several pedagogical possibilities for the N-puzzle game, the rich challenge it offers, and summarizes our experiences using it

Enhancing Undergraduate AI Courses through Machine Learning Projects

It is generally recognized that an undergraduate introductory Artificial Intelligence course is challenging to teach. This is, in part, due to the diverse and seemingly disconnected core topics that are typically covered. The paper presents work funded by the National Science Foundation to address this problem and to enhance the student learning experience in the course. Our work involves the development of an adaptable framework for the presentation of core AI topics through a unifying theme of machine learning. A suite of hands-on semester-long projects are developed, each involving the design and implementation of a learning system that enhances a commonly-deployed application. The projects use machine learning as a unifying theme to tie together the core AI topics. In this paper, we will first provide an overview of our model and the projects being developed and will then present in some detail our experiences with one of the projects – Web User Profiling which we have used in our AI class

Unifying an Introduction to Artificial Intelligence Course through Machine Learning Laboratory Experiences

This paper presents work on a collaborative project funded by the National Science Foundation that incorporates machine learning as a unifying theme to teach fundamental concepts typically covered in the introductory Artificial Intelligence courses. The project involves the development of an adaptable framework for the presentation of core AI topics. This is accomplished through the development, implementation, and testing of a suite of adaptable, hands-on laboratory projects that can be closely integrated into the AI course. Through the design and implementation of learning systems that enhance commonly-deployed applications, our model acknowledges that intelligent systems are best taught through their application to challenging problems. The goals of the project are to (1) enhance the student learning experience in the AI course, (2) increase student interest and motivation to learn AI by providing a framework for the presentation of the major AI topics that emphasizes the strong connection between AI and computer science and engineering, and (3) highlight the bridge that machine learning provides between AI technology and modern software engineering

Incompatible Multiple Consistent Sets of Histories and Measures of Quantumness

In the consistent histories (CH) approach to quantum theory probabilities are assigned to histories subject to a consistency condition of negligible interference. The approach has the feature that a given physical situation admits multiple sets of consistent histories that cannot in general be united into a single consistent set, leading to a number of counter-intuitive or contrary properties if propositions from different consistent sets are combined indiscriminately. An alternative viewpoint is proposed in which multiple consistent sets are classified according to whether or not there exists any unifying probability for combinations of incompatible sets which replicates the consistent histories result when restricted to a single consistent set. A number of examples are exhibited in which this classification can be made, in some cases with the assistance of the Bell, CHSH or Leggett-Garg inequalities together with Fine's theorem. When a unifying probability exists logical deductions in different consistent sets can in fact be combined, an extension of the "single framework rule". It is argued that this classification coincides with intuitive notions of the boundary between classical and quantum regimes and in particular, the absence of a unifying probability for certain combinations of consistent sets is regarded as a measure of the "quantumness" of the system. The proposed approach and results are closely related to recent work on the classification of quasi-probabilities and this connection is discussed.Comment: 29 pages. Second revised version with discussion of the sample space and non-uniqueness of the unifying probability and small errors correcte

How far does the analogy between causal horizon-induced thermalization with the standard heat bath situation go?

After a short presentation of KMS states and modular theory as the unifying description of thermalizing systems we propose the absence of transverse vacuum fluctuations in the holographic projections as the mechanism for an area behavior (the transverse area) of localization entropy as opposed to the volume dependence of ordinary heat bath entropy. Thermalization through causal localization is not a property of QM, but results from the omnipresent vacuum polarization in QFT and does not require a Gibbs type ensemble avaraging (coupling to a heat bath).Comment: 10 pages, based on talk given at the 2002 Londrina Winter Schoo

Yang-Baxter Equations, Computational Methods and Applications

Computational methods are an important tool for solving the Yang-Baxter equations(in small dimensions), for classifying (unifying) structures, and for solving related problems. This paper is an account of some of the latest developments on the Yang-Baxter equation, its set-theoretical version, and its applications. We construct new set-theoretical solutions for the Yang-Baxter equation. Unification theories and other results are proposed or proved.Comment: 12 page

Unifying R-symmetry in M-theory

In this contribution we address the following question: Is there a group with a fermionic presentation which unifies all the physical gravitini and dilatini of the maximal supergravity theories in D=10 and D=11 (without introducing new degrees of freedom)? The affirmative answer relies on a new mathematical object derived from the theory of Kac--Moody algebras, notably E10. It can also be shown that in this way not only the spectrum but also dynamical aspects of all supergravity theories can be treated uniformly.Comment: 17 pages. Proceedings of ICMP 200