Rescuing Quartic and Natural Inflation in the Palatini Formalism

When considered in the Palatini formalism, the Starobinsky model does not provide us with a mechanism for inflation due to the absence of a propagating scalar degree of freedom. By (non)--minimally coupling scalar fields to the Starobinsky model in the Palatini formalism we can in principle describe the inflationary epoch. In this article, we focus on the minimally coupled quartic and natural inflation models. Both theories are excluded in their simplest realization since they predict values for the inflationary observables that are outside the limits set by the Planck data. However, with the addition of the $R^2$ term and the use of the Palatini formalism, we show that these models can be rendered viable.Comment: JCAP accepted version, 16 pages, 7 figure

Distributed Algorithms for Stochastic Source Seeking With Mobile Robot Networks

Autonomous robot networks are an effective tool for monitoring large-scale environmental fields. This paper proposes distributed control strategies for localizing the source of a noisy signal, which could represent a physical quantity of interest such as magnetic force, heat, radio signal, or chemical concentration. We develop algorithms specific to two scenarios: one in which the sensors have a precise model of the signal formation process and one in which a signal model is not available. In the model-free scenario, a team of sensors is used to follow a stochastic gradient of the signal field. Our approach is distributed, robust to deformations in the group geometry, does not necessitate global localization, and is guaranteed to lead the sensors to a neighborhood of a local maximum of the field. In the model-based scenario, the sensors follow a stochastic gradient of the mutual information (MI) between their expected measurements and the expected source location in a distributed manner. The performance is demonstrated in simulation using a robot sensor network to localize the source of a wireless radio signal

The accuracy of a Bayesian Network

A Bayesian network is a construct that represents a joint probability distribution, and can be used in order to model a given joint probability distribution. A principal characteristic of a Bayesian network is the degree to which it models the given joint probability distribution accurately; the accuracy of a Bayesian network. Although the accuracy of a Bayesian network can be well defined in theory, it is rarely possible to determine the accuracy of a Bayesian network in practice for real-world applications. Instead, alternative characteristics of a Bayesian network, which relate to and reflect the accuracy, are used to model the accuracy of a Bayesian network, and appropriate measures are devised. A popular formalism that adopts such methods to study the accuracy of a Bayesian network is the Minimum Description Length (MDL) formalism, which models the accuracy of a Bayesian network as the probability of the Bayesian network given the data set that describes the joint probability distribution the Bayesian network models. However, in the context of Bayesian Networks, the MDL formalism is flawed, exhibiting several shortcomings, and thus inappropriate for examining the accuracy of a Bayesian network. An alternative framework for Bayesian Networks is proposed, which models the accuracy of a Bayesian network as the accuracy of the conditional independencies implied by the structure of the Bayesian network, and specifies an appropriate measure called the Network Conditional Independencies Mutual Information (NCIMI) measure. The proposed framework is inspired by the principles governing the field of Bayesian Networks, and is based on formal theoretical foundations. Experiments have been conducted, using real-world problems, that evaluate both the MDL formalism and the proposed framework for Bayesian Networks. The experimental results support the theoretical claims, and confirm the significance of the proposed framework