Partial Separability and Functional Graphical Models for Multivariate Gaussian Processes

The covariance structure of multivariate functional data can be highly complex, especially if the multivariate dimension is large, making extension of statistical methods for standard multivariate data to the functional data setting quite challenging. For example, Gaussian graphical models have recently been extended to the setting of multivariate functional data by applying multivariate methods to the coefficients of truncated basis expansions. However, a key difficulty compared to multivariate data is that the covariance operator is compact, and thus not invertible. The methodology in this paper addresses the general problem of covariance modeling for multivariate functional data, and functional Gaussian graphical models in particular. As a first step, a new notion of separability for multivariate functional data is proposed, termed partial separability, leading to a novel Karhunen-Lo\`eve-type expansion for such data. Next, the partial separability structure is shown to be particularly useful in order to provide a well-defined Gaussian graphical model that can be identified with a sequence of finite-dimensional graphical models, each of fixed dimension. This motivates a simple and efficient estimation procedure through application of the joint graphical lasso. Empirical performance of the method for graphical model estimation is assessed through simulation and analysis of functional brain connectivity during a motor task.Comment: 39 pages, 5 figure

Density-dependence and within-host competition in a semelparous parasite of leaf-cutting ants

BACKGROUND: Parasite heterogeneity and within-host competition are thought to be important factors influencing the dynamics of host-parasite relationships. Yet, while there have been many theoretical investigations of how these factors may act, empirical data is more limited. We investigated the effects of parasite density and heterogeneity on parasite virulence and fitness using four strains of the entomopathogenic fungus, Metarhizium anisopliae var. anisopliae, and its leaf-cutting ant host Acromyrmex echinatior as the model system. RESULTS: The relationship between parasite density and infection was sigmoidal, with there being an invasion threshold for an infection to occur (an Allee effect). Although spore production was positively density-dependent, parasite fitness decreased with increasing parasite density, indicating within-host scramble competition. The dynamics differed little between the four strains tested. In mixed infections of three strains the infection-growth dynamics were unaffected by parasite heterogeneity. CONCLUSIONS: The strength of within-host competition makes dispersal the best strategy for the parasite. Parasite heterogeneity may not have effected virulence or the infection dynamics either because the most virulent strain outcompeted the others, or because the interaction involved scramble competition that was impervious to parasite heterogeneity. The dynamics observed may be common for virulent parasites, such as Metarhizium, that produce aggregated transmission stages. Such parasites make useful models for investigating infection dynamics and the impact of parasite competition

All-fibre supercontinuum laser for in vivo multispectral photoacoustic microscopy of lipids in the extended near-infrared region

Among the numerous endogenous biological molecules, information on lipids is highly coveted for understanding both aspects of developmental biology and research in fatal chronic diseases. Due to the pronounced absorption features of lipids in the extended near-infrared region (1650−1850 nm), visualisation and identification of lipids become possible using multi-spectral photoacoustic (optoacoustic) microscopy. However, the spectroscopic studies in this spectral region require lasers that can produce high pulse energies over a broad spectral bandwidth to efficiently excite strong photoacoustic signals. The most well-known laser sources capable of satisfying the multi-spectral photoacoustic microscopy requirements (tunability and pulse energy) are tunable nanosecond optical parametric oscillators. However, these lasers have an inherently large footprint, thus preventing their use in compact microscopy systems. Besides, they exhibit low-repetition rates. Here, we demonstrate a compact all-fibre, high pulse energy supercontinuum laser that covers a spectral range from 1440 to 1870 nm with a 7 ns pulse duration and total energy of 18.3 μJ at a repetition rate of 100 kHz. Using the developed high-pulse energy source, we perform multi-spectral photoacoustic microscopy imaging of lipids, both ex vivo on adipose tissue and in vivo to study the development of Xenopus laevis tadpoles, using six different excitation bands over the first overtone transition of C–H vibration bonds (1650−1850 nm)

Stability of sub-surface oxygen at Rh(111)

Using density-functional theory (DFT) we investigate the incorporation of oxygen directly below the Rh(111) surface. We show that oxygen incorporation will only commence after nearly completion of a dense O adlayer (\theta_tot = 1.0 monolayer) with O in the fcc on-surface sites. The experimentally suggested octahedral sub-surface site occupancy, inducing a site-switch of the on-surface species from fcc to hcp sites, is indeed found to be a rather low energy structure. Our results indicate that at even higher coverages oxygen incorporation is followed by oxygen agglomeration in two-dimensional sub-surface islands directly below the first metal layer. Inside these islands, the metastable hcp/octahedral (on-surface/sub-surface) site combination will undergo a barrierless displacement, introducing a stacking fault of the first metal layer with respect to the underlying substrate and leading to a stable fcc/tetrahedral site occupation. We suggest that these elementary steps, namely, oxygen incorporation, aggregation into sub-surface islands and destabilization of the metal surface may be more general and precede the formation of a surface oxide at close-packed late transition metal surfaces.Comment: 9 pages including 9 figure files. Submitted to Phys. Rev. B. Related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Defects in muscarinic receptor-coupled signal transduction in isolated parotid gland cells after in vivo irradiation: evidence for a non-DNA target of radiation

Radiation-induced dysfunction of normal tissue, an unwanted side effect of radiotherapeutic treatment of cancer, is usually considered to be caused by impaired loss of cell renewal due to sterilisation of stem cells. This implies that the onset of normal tissue damage is usually determined by tissue turnover rate. Salivary glands are a clear exception to this rule: they have slow turnover rates (>60 days), yet develop radiation-induced dysfunction within hours to days. We showed that this could not be explained by a hypersensitivity to radiation-induced apoptosis or necrosis of the differentiated cells. In fact, salivary cells are still capable of amylase secretion shortly after irradiation while at the same time water secretion seems specifically and severely impaired. Here, we demonstrate that salivary gland cells isolated after in vivo irradiation are impaired in their ability to mobilise calcium from intracellular stores (Ca2+i), the driving force for water secretion, after exposure to muscarinic acetylcholine receptor agonists. Using radioligand-receptor-binding assays it is shown that radiation caused no changes in receptor density, receptor affinity nor in receptor-G-protein coupling. However, muscarinic acetylcholine agonist-induced activation of protein kinase C alpha (PKCα), measured as translocation to the plasma membrane, was severely affected in irradiated cells. Also, the phorbol ester PMA could no longer induce PKCα translocation in irradiated cells. Our data hence indicate that irradiation specifically interferes with PKCα association with membranes, leading to impairment of intracellular signalling. To the best of our knowledge, these data for the first time suggest that, the cells' capacity to respond to a receptor agonist is impaired after irradiation