Evidence functions: a compositional approach to information

The discrete case of Bayes’ formula is considered the paradigm of information acquisition. Prior and posterior probability functions, as well as likelihood functions, called evidence functions, are compositions following the Aitchison geometry of the simplex, and have thus vector character. Bayes’ formula becomes a vector addition. The Aitchison norm of an evidence function is introduced as a scalar measurement of information. A fictitious fire scenario serves as illustration. Two different inspections of affected houses are considered. Two questions are addressed: (a) which is the information provided by the outcomes of inspections, and (b) which is the most informative inspection.Peer Reviewe

Evidence functions: a compositional approach to information

The discrete case of Bayes’ formula is considered the paradigm of information acquisition. Prior and posterior probability functions, as well as likelihood functions, called evidence functions, are compositions following the Aitchison geometry of the simplex, and have thus vector character. Bayes’ formula becomes a vector addition. The Aitchison norm of an evidence function is introduced as a scalar measurement of information. A fictitious fire scenario serves as illustration. Two different inspections of affected houses are considered. Two questions are addressed: (a) which is the information provided by the outcomes of inspections, and (b) which is the most informative inspection.Peer ReviewedPostprint (author's final draft

A Sensorimotor Model for Computing Intended Reach Trajectories

The presumed role of the primate sensorimotor system is to transform reach targets from retinotopic to joint coordinates for producing motor output. However, the interpretation of neurophysiological data within this framework is ambiguous, and has led to the view that the underlying neural computation may lack a well-defined structure. Here, I consider a model of sensorimotor computation in which temporal as well as spatial transformations generate representations of desired limb trajectories, in visual coordinates. This computation is suggested by behavioral experiments, and its modular implementation makes predictions that are consistent with those observed in monkey posterior parietal cortex (PPC). In particular, the model provides a simple explanation for why PPC encodes reach targets in reference frames intermediate between the eye and hand, and further explains why these reference frames shift during movement. Representations in PPC are thus consistent with the orderly processing of information, provided we adopt the view that sensorimotor computation manipulates desired movement trajectories, and not desired movement endpoints

A Real-Time Unsupervised Neural Network for the Low-Level Control of a Mobile Robot in a Nonstationary Environment

This article introduces a real-time, unsupervised neural network that learns to control a two-degree-of-freedom mobile robot in a nonstationary environment. The neural controller, which is termed neural NETwork MObile Robot Controller (NETMORC), combines associative learning and Vector Associative Map (YAM) learning to generate transformations between spatial and velocity coordinates. As a result, the controller learns the wheel velocities required to reach a target at an arbitrary distance and angle. The transformations are learned during an unsupervised training phase, during which the robot moves as a result of randomly selected wheel velocities. The robot learns the relationship between these velocities and the resulting incremental movements. Aside form being able to reach stationary or moving targets, the NETMORC structure also enables the robot to perform successfully in spite of disturbances in the enviroment, such as wheel slippage, or changes in the robot's plant, including changes in wheel radius, changes in inter-wheel distance, or changes in the internal time step of the system. Finally, the controller is extended to include a module that learns an internal odometric transformation, allowing the robot to reach targets when visual input is sporadic or unreliable.Sloan Fellowship (BR-3122), Air Force Office of Scientific Research (F49620-92-J-0499

Open Quantum Dynamics: Complete Positivity and Entanglement

We review the standard treatment of open quantum systems in relation to quantum entanglement, analyzing, in particular, the behaviour of bipartite systems immersed in a same environment. We first focus upon the notion of complete positivity, a physically motivated algebraic constraint on the quantum dynamics, in relation to quantum entanglement, i.e. the existence of statistical correlations which can not be accounted for by classical probability. We then study the entanglement power of heat baths versus their decohering properties, a topic of increasing importance in the framework of the fast developing fields of quantum information, communication and computation. The presentation is self contained and, through several examples, it offers a detailed survey of the physics and of the most relevant and used techniques relative to both quantum open system dynamics and quantum entanglement.Comment: LaTex, 77 page