Symplectic matrices with predetermined left eigenvalues

We prove that given four arbitrary quaternion numbers of norm 1 there always exists a $2\times 2$ symplectic matrix for which those numbers are left eigenvalues. The proof is constructive. An application to the LS category of Lie groups is given.Comment: 7 page

Probabilistic change detection and visualization methods for the assessment of temporal stability in biomedical data quality

The final publication is available at Springer via http://dx.doi.org/DOI 10.1007/s10618-014-0378-6. Published online.Knowledge discovery on biomedical data can be based on on-line, data-stream analyses, or using retrospective, timestamped, off-line datasets. In both cases, changes in the processes that generate data or in their quality features through time may hinder either the knowledge discovery process or the generalization of past knowledge. These problems can be seen as a lack of data temporal stability. This work establishes the temporal stability as a data quality dimension and proposes new methods for its assessment based on a probabilistic framework. Concretely, methods are proposed for (1) monitoring changes, and (2) characterizing changes, trends and detecting temporal subgroups. First, a probabilistic change detection algorithm is proposed based on the Statistical Process Control of the posterior Beta distribution of the Jensen–Shannon distance, with a memoryless forgetting mechanism. This algorithm (PDF-SPC) classifies the degree of current change in three states: In-Control, Warning, and Out-of-Control. Second, a novel method is proposed to visualize and characterize the temporal changes of data based on the projection of a non-parametric information-geometric statistical manifold of time windows. This projection facilitates the exploration of temporal trends using the proposed IGT-plot and, by means of unsupervised learning methods, discovering conceptually-related temporal subgroups. Methods are evaluated using real and simulated data based on the National Hospital Discharge Survey (NHDS) dataset.The work by C Saez has been supported by an Erasmus Lifelong Learning Programme 2013 Grant. This work has been supported by own IBIME funds. The authors thank Dr. Gregor Stiglic, from the Univeristy of Maribor, Slovenia, for his support on the NHDS data.Sáez Silvestre, C.; Pereira Rodrigues, P.; Gama, J.; Robles Viejo, M.; García Gómez, JM. (2014). Probabilistic change detection and visualization methods for the assessment of temporal stability in biomedical data quality. Data Mining and Knowledge Discovery. 28:1-1. doi:10.1007/s10618-014-0378-6S1128Aggarwal C (2003) A framework for diagnosing changes in evolving data streams. In Proceedings of the International Conference on Management of Data ACM SIGMOD, pp 575–586Amari SI, Nagaoka H (2007) Methods of information geometry. American Mathematical Society, Providence, RIArias E (2014) United states life tables, 2009. Natl Vital Statist Rep 62(7): 1–63Aspden P, Corrigan JM, Wolcott J, Erickson SM (2004) Patient safety: achieving a new standard for care. Committee on data standards for patient safety. 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Climate change facilitated the early colonization of the Azores Archipelago during medieval times

Humans have made such dramatic and permanent changes to Earth's landscapes that much of it is now substantially and irreversibly altered from its preanthropogenic state. Remote islands, until recently isolated from humans, offer insights into how these landscapes evolved in response to human-induced perturbations. However, little is known about when and how remote systems were colonized because archaeological data and historical records are scarce and incomplete. Here, we use a multiproxy approach to reconstruct the initial colonization and subsequent environmental impacts on the Azores Archipelago. Our reconstructions provide unambiguous evidence for widespread human disturbance of this archipelago starting between 700 -60/+50 and 850 -60/+60 Common Era (CE), ca. 700 y earlier than historical records suggest the onset of Portuguese settlement of the islands. Settlement proceeded in three phases, during which human pressure on the terrestrial and aquatic ecosystems grew steadily (i.e., through livestock introductions, logging, and fire), resulting in irreversible changes. Our climate models suggest that the initial colonization at the end of the early Middle Ages (500 to 900 CE) occurred in conjunction with anomalous northeasterly winds and warmer Northern Hemisphere temperatures. These climate conditions likelyinhibited exploration from southern Europe and facilitated human settlers from the northeast Atlantic. These results are consistent with recent archaeological and genetic data suggesting that the Norse were most likely the earliest settlers on the islands