A Measure of Synergy Based on Union Information.

The partial information decomposition (PID) framework is concerned with decomposing the information that a set of (two or more) random variables (the sources) has about another variable (the target) into three types of information: unique, redundant, and synergistic. Classical information theory alone does not provide a unique way to decompose information in this manner and additional assumptions have to be made. One often overlooked way to achieve this decomposition is using a so-called measure of union information-which quantifies the information that is present in at least one of the sources-from which a synergy measure stems. In this paper, we introduce a new measure of union information based on adopting a communication channel perspective, compare it with existing measures, and study some of its properties. We also include a comprehensive critical review of characterizations of union information and synergy measures that have been proposed in the literature.

Orders between Channels and Implications for Partial Information Decomposition.

The partial information decomposition (PID) framework is concerned with decomposing the information that a set of random variables has with respect to a target variable into three types of components: redundant, synergistic, and unique. Classical information theory alone does not provide a unique way to decompose information in this manner, and additional assumptions have to be made. Recently, Kolchinsky proposed a new general axiomatic approach to obtain measures of redundant information based on choosing an order relation between information sources (equivalently, order between communication channels). In this paper, we exploit this approach to introduce three new measures of redundant information (and the resulting decompositions) based on well-known preorders between channels, contributing to the enrichment of the PID landscape. We relate the new decompositions to existing ones, study several of their properties, and provide examples illustrating their novelty. As a side result, we prove that any preorder that satisfies Kolchinsky's axioms yields a decomposition that meets the axioms originally introduced by Williams and Beer when they first proposed PID.

Adult cerebellar medulloblastoma: CT and MRI findings in eight cases.

Medulloblastoma is a brain tumor of neuroepithelial origin, which represents 15 to 30% of all pediatric brain tumors, and less than 1% of CNS adult neoplasms. We report the imaging findings of 8 adult patients with medulloblastoma. The mean age was 35 years, ranging from 20 to 65 years, and the male:female rate was 3:5. The tumors were predominantly lateral (63%), hyperdense on CT scans (83%), and on the MRI, hypointense on T1 (100%) and hyperintense on T2 (80%) weighted images. It was seen intratumoral necrosis and cysts in six cases and calcifications in three. Hydrocephalus was observed in 5 cases and brain stem invasion in four. The imaging findings of medulloblastomas in adults are different of those in child, and also nonspecific. Although these tumors are uncommon in adults, they must be considered in the differential diagnosis of cerebellar masses in the posterior fossa of this age group.

Adult cerebellar medulloblastoma: CT and MRI findings in eight cases

Medulloblastoma is a brain tumor of neuroepithelial origin, which represents 15 to 30 percent of all pediatric brain tumors, and less than 1 percent of CNS adult neoplasms. We report the imaging findings of 8 adult patients with medulloblastoma. The mean age was 35 years, ranging from 20 to 65 years, and the male:female rate was 3:5. The tumors were predominantly lateral (63 percent), hyperdense on CT scans (83 percent), and on the MRI, hypointense on T1 (100 percent) and hyperintense on T2 (80 percent) weighted images. It was seen intratumoral necrosis and cysts in six cases and calcifications in three. Hydrocephalus was observed in 5 cases and brain stem invasion in four. The imaging findings of medulloblastomas in adults are different of those in child, and also nonspecific. Although these tumors are uncommon in adults, they must be considered in the differential diagnosis of cerebellar masses in the posterior fossa of this age group