Alistair Windsor

Livsic theorems for non-commutdative groups including diffeomorphism groups and results on the existence of conformal structures for Anosov systems

The celebrated Livsic theorem states that given M a manifold, a Lie group G, a transitive Anosov diffeomorphism f on M and a Holder function \eta: M \mapsto G whose range is sufficiently close to the identity, it is sufficient for the existence of \phi :M \mapsto G satisfying \eta(x) = \phi(f(x)) \phi(x)^{-1} that a condition -- obviously necessary -- on the cocycle generated by \eta restricted to periodic orbits is satisfied. In this paper we present a new proof of the main result. These methods allow us to treat cocycles taking values in the group of diffeomorphisms of a compact manifold. This has applications to rigidity theory. The localization procedure we develop can be applied to obtain some new results on the existence of conformal structures for Anosov systems.

Non-standard smooth realizations of Liouville rotations

We augment the C-infinity conjugation approximation method with explicit estimates on the conjugacy map. This allows us to construct ergodic volume-preserving diffeomorphisms measure-theoretically isomorphic to any a priori given Liouville rotation on a variety of manifolds. In the special case of tori the maps can be made uniquely ergodic.

Smoothness is not an obstruction to realizability

A sequence of non-negative integers (φn)∞n=1 is said to be realizable if there is a map T of a set X such that φn = #{x : T n x = x}. We prove that any realizable sequence can be realized by a C diffeomorphism of T2.

SKOPE-IT (Shareable Knowledge Objects as Portable Intelligent Tutors): overlaying natural language tutoring on an adaptive learning system for mathematics

BackgroundThis study investigated learning outcomes and user perceptions from interactions with a hybrid intelligent tutoring system created by combining the AutoTutor conversational tutoring system with the Assessment and Learning in Knowledge Spaces (ALEKS) adaptive learning system for mathematics. This hybrid intelligent tutoring system (ITS) uses a service-oriented architecture to combine these two web-based systems. Self-explanation tutoring dialogs were used to talk students through step-by-step worked examples to algebra problems. These worked examples presented an isomorphic problem to the preceding algebra problem that the student could not solve in the adaptive learning system.ResultsDue to crossover issues between conditions, experimental versus control condition assignment did not show significant differences in learning gains. However, strong dose-dependent learning gains were observed that could not be otherwise explained by either initial mastery or time-on-task. User perceptions of the dialog-based tutoring were mixed, and survey results indicate that this may be due to the pacing of dialog-based tutoring using voice, students judging the agents based on their own performance (i.e., the quality of their answers to agent questions), and the students’ expectations about mathematics pedagogy (i.e., expecting to solving problems rather than talking about concepts). Across all users, learning was most strongly influenced by time spent studying, which correlated with students’ self-reported tendencies toward effort avoidance, effective study habits, and beliefs about their ability to improve in mathematics with effort.ConclusionsIntegrating multiple adaptive tutoring systems with complementary strengths shows some potential to improve learning. However, managing learner expectations during transitions between systems remains an open research area. Finally, while personalized adaptation can improve learning efficiency, effort and time-on-task for learning remains a dominant factor that must be considered by interventions.

Evaluating the Effectiveness of Integrating Natural Language Tutoring into an Existing Adaptive Learning System

This paper reports initial results of an evaluation for an ITS that follows service-oriented principles to integrate natural language tutoring into an existing adaptive learning system for mathematics. Self-explanation tutoring dialogs were used to talk students through step-by-step worked solutions to Algebra problems. These worked solutions presented an isomorphic problem to a preceding Algebra problem that the student could not solve in an adaptive learning system. Due to crossover issues between conditions, experimental versus control condition assignment did not show significant differences in learning gains. However, strong dose-dependent learning gains were observed that could not be otherwise explained by either initial mastery or time-on-task.

Leader Language and Political Survival Strategies

ABSTRACT Authoritarian leaders’ language provides clues to their survival strategies for remaining in office. This line of inquiry fits within an emerging literature that refocuses attention from state-level features to the dynamic role that individual heads of state and government play in international relations, especially in authoritarian regimes. The burgeoning text-as-data field can be used to deepen our understanding of the nuances of leader survival and political choices; for example, language can serve as a leading indicator of leader approval, which itself is a good predictor of leader survival. In this paper, we apply computational linguistics tools to an authoritarian leader corpus consisting of 102 speeches from nine leaders of countries across the Middle East and North Africa between 2009 and 2012. We find systematic differences in the language of these leaders, which help advance a more broadly applicable theory of authoritarian leader language and tenure.

Independence and Alpern multitowers

ABSTRACT Let T be any invertible, ergodic, aperiodic measure-preserving transformation of a Lebesgue probability space , and P  any finite measurable partition of X. We show that a (finite) Alpern multitower may always be constructed whose base is independent of P.