arXiv subjects

David Hartman

Publications and source records attributed to David Hartman.

21 records · Page 2Linked to original sources

arXiv2012

Non-linear dependence and teleconnections in climate data: sources, relevance, nonstationarity

Quantification of relations between measured variables of interest by statistical measures of dependence is a common step in analysis of climate data. The term "connectivity" is used in the network context including the study of complex coupled dynamical systems. The choice of dependence measure is key for the results of the subsequent analysis and interpretation. The use of linear Pearson's correlation coefficient is widespread and convenient. On the other side, as the climate is widely acknowledged to be a nonlinear system, nonlinear connectivity quantification methods, such as those based on information-theoretical concepts, are increasingly used for this purpose. In this paper we outline an approach that enables well informed choice of connectivity method for a given type of data, improving the subsequent interpretation of the results. The presented multi-step approach includes statistical testing, quantification of the specific non-linear contribution to the interaction information, localization of nodes with strongest nonlinear contribution and assessment of the role of specific temporal patterns, including signal nonstationarities. In detail we study the consequences of the choice of a general nonlinear connectivity measure, namely mutual information, focusing on its relevance and potential alterations in the discovered dependence structure. We document the method by applying it on monthly mean temperature data from the NCEP/NCAR reanalysis dataset as well as the ERA dataset. We have been able to identify main sources of observed non-linearity in inter-node couplings. Detailed analysis suggested an important role of several sources of nonstationarity within the climate data. The quantitative role of genuine nonlinear coupling at this scale has proven to be almost negligible, providing quantitative support for the use of linear methods for this type of data.

stat.ME↗

arXiv2012

Small-world topology of functional connectivity in randomly connected dynamical systems

Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths together with high clustering of the network, is one of the most discussed and studied. When dealing with coupled dynamical systems, links among units of the system are commonly quantified by a measure of pairwise statistical dependence of observed time series (functional connectivity). We argue that the functional connectivity approach leads to upwardly biased estimates of small-world characteristics (with respect to commonly used random graph models) due to partial transitivity of the accepted functional connectivity measures such as the correlation coefficient. In particular, this may lead to observation of small-world characteristics in connectivity graphs estimated from generic randomly connected dynamical systems. The ubiquity and robustness of the phenomenon is documented by an extensive parameter study of its manifestation in a multivariate linear autoregressive process, with discussion of the potential relevance for nonlinear processes and measures.

cs.SI↗

arXiv2012

Homomorphism-homogeneous L-colored graphs

A relational structure is homomorphism-homogeneous (HH-homogeneous for short) if every homomorphism between finite induced substructures of the structure can be extended to a homomorphism over the whole domain of the structure. Similarly, a structure is monomorphism-homogeneous (MH-homogeneous for short) if every monomorphism between finite induced substructures of the structure can be extended to a homomorphism over the whole domain of the structure. In this paper we consider L-colored graphs, that is, undirected graphs without loops where sets of colors selected from L are assigned to vertices and edges. A full classification of finite MH-homogeneous L-colored graphs where L is a chain is provided, and we show that the classes MH and HH coincide. When L is a diamond, that is, a set of pairwise incomparable elements enriched with a greatest and a least element, the situation turns out to be much more involved. We show that in the general case the classes MH and HH do not coincide.

math.CO↗