DRUM Community: Computer Science Department Technical Reportshttp://hdl.handle.net/1903/22252014-04-25T08:55:54Z2014-04-25T08:55:54ZRecursive computation of spherical harmonic rotation coefficients of large degreeGumerov, Nail A.Duraiswami, Ramanihttp://hdl.handle.net/1903/150132014-03-31T02:30:30Z2014-03-28T00:00:00ZTitle: Recursive computation of spherical harmonic rotation coefficients of large degree
Authors: Gumerov, Nail A.; Duraiswami, Ramani
Abstract: Computation of the spherical harmonic rotation coefficients or elements
of Wigner's d-matrix is important in a number of quantum mechanics and
mathematical physics applications. Particularly, this is important for
the Fast Multipole Methods in three dimensions for the Helmholtz,
Laplace and related equations, if rotation-based decomposition of
translation operators are used. In these and related problems related to
representation of functions on a sphere via spherical harmonic
expansions computation of the rotation coefficients of large degree n
(of the order of thousands and more) may be necessary. Existing
algorithms for their computation, based on recursions, are usually
unstable, and do not extend to n. We develop a new recursion and study
its behavior for large degrees, via computational and asymptotic
analyses. Stability of this recursion was studied based on a novel
application of the Courant-Friedrichs-Lewy condition and the von Neumann
method for stability of finite-difference schemes for solution of PDEs.
A recursive algorithm of minimal complexity O(n^2) for degree n and
FFT-based algorithms of complexity O(n^2 log n) suitable for computation
of rotation coefficients of large degrees are proposed, studied
numerically, and cross-validated. It is shown that the latter algorithm
can be used for n <~ 10^3 in double precision, while the former
algorithm was tested for large n (up to 10^4 in our experiments) and
demonstrated better performance and accuracy compared to the FFT-based
algorithm.2014-03-28T00:00:00ZA Block Preconditioner for an Exact Penalty Formulation for Stationary MHDPhillips, Edward G.Elman, Howard C.Cyr, Eric C.Shadid, John N.Pawlowski, Roger P.http://hdl.handle.net/1903/149702014-02-13T03:32:08Z2014-02-04T00:00:00ZTitle: A Block Preconditioner for an Exact Penalty Formulation for Stationary MHD
Authors: Phillips, Edward G.; Elman, Howard C.; Cyr, Eric C.; Shadid, John N.; Pawlowski, Roger P.
Abstract: The magnetohydrodynamics (MHD) equations are used to model the flow of electrically conducting fluids in such applications as liquid metals and plasmas. This system of non-self adjoint, nonlinear PDEs couples the Navier-Stokes equations for fluids and Maxwell's equations for electromagnetics. There has been recent interest in fully coupled solvers for the MHD system because they allow for fast steady-state solutions that do not require pseudo-time stepping. When the fully coupled system is discretized, the strong coupling can make the resulting algebraic systems difficult to solve, requiring effective preconditioning of iterative methods for efficiency. In this work, we consider a finite element discretization of an exact penalty formulation for the stationary MHD equations. This formulation has the benefit of implicitly enforcing the divergence free condition on the magnetic field without requiring a Lagrange multiplier. We consider extending block preconditioning techniques developed for the Navier-Stokes equations to the full MHD system. We analyze operators arising in block decompositions from a continuous perspective and apply arguments based on the existence of approximate commutators to develop new preconditioners that account for the physical coupling. This results in a family of parameterized block preconditioners for both Picard and Newton linearizations.
We develop an automated method for choosing the relevant parameters and demonstrate the robustness of these preconditioners for a range of the physical non-dimensional parameters and with respect to mesh refinement.2014-02-04T00:00:00ZProceedings of the 2013 Annual Conference on Advances in Cognitive Systems: Workshop on Metacognition about Artificial Situated AgentsJosyula, DarsanaRobertson, PaulCox, Michael T.http://hdl.handle.net/1903/147442014-01-23T03:30:48Z2013-12-14T00:00:00ZTitle: Proceedings of the 2013 Annual Conference on Advances in Cognitive Systems: Workshop on Metacognition about Artificial Situated Agents
Authors: Josyula, Darsana; Robertson, Paul; Cox, Michael T.
Abstract: Metacognition is the process of thinking about thinking. It provides cognitive systems the ability to note and deal with anomalies, changes, opportunities, surprises and uncertainty. It includes both monitoring of cognitive activities and control of such activities. Monitoring helps to evaluate and explain the cognitive activities, while control helps to adapt or modify the cognitive activities. Situated agents are agents embedded in a dynamic environment that they can sense or perceive and manipulate or change through their actions. Similarly, they can act in order to manipulate other agents among which they are situated. Examples might include robots, natural language dialog interfaces, web-based agents or virtual-reality bots. An agent can leverage metacognition of its own thinking about other agents in its situated environment. It can equally benefit from metacognition of the thinking of other agents towards itself. Metacognitive monitoring can help situated agents in negotiations, conflict resolution and norm-awareness. Metacognitive control can help coordination and coalition formations of situated social agents. In this workshop, we investigate the monitoring and control aspects of metacognition about self and other agents, and their application to situated artificial agents. The papers in this report cover some of the current work related to metacognition in the areas of meta-knowledge representation, meta-reasoning and meta-cognitive architecture. Perlis et al. outlines a high-level view of architectures for real-time situated agents and the reliance of such agents on metacognition. Mbale, K. and Josyula, D. present a generic metacognitive component based on preserving the homeostasis of a host agent. Pickett, M. presents a framework for representing, learning, and processing meta-knowledge. Riddle, P. et al. discuss meta-level search through a problem representation space for problemâ€“reformulation. Caro, M et al. use metamemory to adapt to changes in memory retrieval constraints. Langley, P. et al. abstract general problem specific abilities into strategic problem solving knowledge in an architecture for flexible problem solving across various domains. Samsonovich, A. examines metacognition as a means to improve fluid intelligence in a cognitive architecture. Perlis, D. and Cox, M. discuss the application of metacognitive monitoring to anomaly detection and goal generation.2013-12-14T00:00:00ZGoal Reasoning: Papers from the ACS workshopAha, David W.Cox, Michael T.Munoz-Avila, Hectorhttp://hdl.handle.net/1903/147402013-12-05T03:30:14Z2013-12-14T00:00:00ZTitle: Goal Reasoning: Papers from the ACS workshop
Authors: Aha, David W.; Cox, Michael T.; Munoz-Avila, Hector
Abstract: This technical report contains the 11 accepted papers presented at the Workshop on Goal Reasoning,
which was held as part of the 2013 Conference on Advances in Cognitive Systems (ACS-13) in
Baltimore, Maryland on 14 December 2013. This is the third in a series of workshops related to this
topic, the first of which was the AAAI-10 Workshop on Goal-Directed Autonomy while the second was
the Self-Motivated Agents (SeMoA) Workshop, held at Lehigh University in November 2012.
Our objective for holding this meeting was to encourage researchers to share information on the study,
development, integration, evaluation, and application of techniques related to goal reasoning, which
concerns the ability of an intelligent agent to reason about, formulate, select, and manage its
goals/objectives. Goal reasoning differs from frameworks in which agents are told what goals to
achieve, and possibly how goals can be decomposed into subgoals, but not how to dynamically and
autonomously decide what goals they should pursue. This constraint can be limiting for agents that solve
tasks in complex environments when it is not feasible to manually engineer/encode complete knowledge
of what goal(s) should be pursued for every conceivable state. Yet, in such environments, states can be
reached in which actions can fail, opportunities can arise, and events can otherwise take place that
strongly motivate changing the goal(s) that the agent is currently trying to achieve.
This topic is not new; researchers in several areas have studied goal reasoning (e.g., in the context of
cognitive architectures, automated planning, game AI, and robotics). However, it has infrequently been
the focus of intensive study, and (to our knowledge) no other series of meetings has focused specifically
on goal reasoning. As shown in these papers, providing an agent with the ability to reason about its goals
can increase performance measures for some tasks. Recent advances in hardware and software platforms
(involving the availability of interesting/complex simulators or databases) have increasingly permitted
the application of intelligent agents to tasks that involve partially observable and dynamically-updated
states (e.g., due to unpredictable exogenous events), stochastic actions, multiple (cooperating, neutral, or
adversarial) agents, and other complexities. Thus, this is an appropriate time to foster dialogue among
researchers with interests in goal reasoning.
Research on goal reasoning is still in its early stages; no mature application of it yet exists (e.g., for
controlling autonomous unmanned vehicles or in a deployed decision aid). However, it appears to have a
bright future. For example, leaders in the automated planning community have specifically
acknowledged that goal reasoning has a prominent role among intelligent agents that act on their own
plans, and it is gathering increasing attention from roboticists and cognitive systems researchers.
In addition to a survey, the papers in this workshop relate to, among other topics, cognitive architectures
and models, environment modeling, game AI, machine learning, meta-reasoning, planning, selfmotivated
systems, simulation, and vehicle control. The authors discuss a wide range of issues
pertaining to goal reasoning, including representations and reasoning methods for dynamically revising
goal priorities. We hope that readers will find that this theme for enhancing agent autonomy to be
appealing and relevant to their own interests, and that these papers will spur further investigations on
this important yet (mostly) understudied topic.2013-12-14T00:00:00Z