Algorithmic Integrability Tests for Nonlinear Differential and Lattice Equations

Three symbolic algorithms for testing the integrability of polynomial systems of partial differential and differential-difference equations are presented. The first algorithm is the well-known Painlev\'e test, which is applicable to polynomial systems of ordinary and partial differential equations. The second and third algorithms allow one to explicitly compute polynomial conserved densities and higher-order symmetries of nonlinear evolution and lattice equations. The first algorithm is implemented in the symbolic syntax of both Macsyma and Mathematica. The second and third algorithms are available in Mathematica. The codes can be used for computer-aided integrability testing of nonlinear differential and lattice equations as they occur in various branches of the sciences and engineering. Applied to systems with parameters, the codes can determine the conditions on the parameters so that the systems pass the Painlev\'e test, or admit a sequence of conserved densities or higher-order symmetries.Comment: Submitted to: Computer Physics Communications, Latex, uses the style files elsart.sty and elsart12.st

Intelligent Broadcasting in Mobile Ad Hoc Networks: Three Classes of Adaptive Protocols

<p/> <p>Because adaptability greatly improves the performance of a broadcast protocol, we identify three ways in which machine learning can be applied to broadcasting in a mobile ad hoc network (MANET). We chose broadcasting because it functions as a foundation of MANET communication. Unicast, multicast, and geocast protocols utilize broadcasting as a building block, providing important control and route establishment functionality. Therefore, any improvements to the process of broadcasting can be immediately realized by higher-level MANET functionality and applications. While efficient broadcast protocols have been proposed, no single broadcasting protocol works well in all possible MANET conditions. Furthermore, protocols tend to fail catastrophically in severe network environments. Our three classes of adaptive protocols are pure machine learning, intra-protocol learning, and inter-protocol learning. In the pure machine learning approach, we exhibit a new approach to the design of a broadcast protocol: the decision of whether to rebroadcast a packet is cast as a classification problem. Each mobile node (MN) builds a classifier and trains it on data collected from the network environment. Using intra-protocol learning, each MN consults a simple machine model for the optimal value of one of its free parameters. Lastly, in inter-protocol learning, MNs learn to switch between different broadcasting protocols based on network conditions. For each class of learning method, we create a prototypical protocol and examine its performance in simulation.</p

Theories of Access Consciousness

Theories of access consciousness address how it is that some mental states but not others are available for evaluation, choice behavior, and verbal report. Farah, O&apos;Reilly, and Vecera (1994) argue that quality of representation is critical; Dehaene, Sergent, and Changeux (2003) argue that the ability to communicate representations is critical. We present a probabilistic information transmission or PIT model that suggests both of these conditions are essential for access consciousness

A Rational Analysis of Cognitive Control in a Speeded Discrimination Task

We are interested in the mechanisms by which individuals monitor and adjust their performance of simple cognitive tasks. We model a speeded discrimination task in which individuals are asked to classify a sequence of stimuli (Jones &amp; Braver, 2001). Response conflict arises when one stimulus class is infrequent relative to another, resulting in more errors and slower reaction times for the infrequent class. How do control processes modulate behavior based on the relative class frequencies? We explain performance from a rational perspective that casts the goal of individuals as minimizing a cost that depends both on error rate and reaction time. With two additional assumptions of rationality---that class prior probabilities are accurately estimated and that inference is optimal subject to limitations on rate of information transmission---we obtain a good fit to overall RT and error data, as well as trial-by-trial variations in performance

A

of long-term repetition priming and skill refinement

Prodding the ROC Curve: Constrained Optimization of Classifier Performance

When designing a two-alternative classifier, one ordinarily aims to maximize the classifier&apos;s ability to discriminate between members of the two classes. We describe a situation in a real-world business application of machine-learning prediction in which an additional constraint is placed on the nature of the solution: that the classifier achieve a specified correct acceptance or correct rejection rate (i.e., that it achieve a fixed accuracy on members of one class or the other)

A Rational Analysis of Cognitive Control

We are interested in the mechanisms by which individuals monitor and adjust their performance of simple cognitive tasks. We model a speeded discrimination task in which individuals are asked to classify a sequence of stimuli (Jones &amp; Braver, 2001). Response conflict arises when one stimulus class is infrequent relative to another, resulting in more errors and slower reaction times for the infrequent class. How do control processes modulate behavior based on the relative class frequencies? We explain performance from a rational perspective that casts the goal of individuals as minimizing a cost that depends both on error rate and reaction time. With two additional assumptions of rationality---that class prior probabilities are accurately estimated and that inference is optimal subject to limitations on rate of information transmission---we obtain a good fit to overall RT and error data, as well as trial-by-trial variations in performance