Statistical Properties of Avalanches in Networks

We characterize the distributions of size and duration of avalanches propagating in complex networks. By an avalanche we mean the sequence of events initiated by the externally stimulated `excitation' of a network node, which may, with some probability, then stimulate subsequent firings of the nodes to which it is connected, resulting in a cascade of firings. This type of process is relevant to a wide variety of situations, including neuroscience, cascading failures on electrical power grids, and epidemology. We find that the statistics of avalanches can be characterized in terms of the largest eigenvalue and corresponding eigenvector of an appropriate adjacency matrix which encodes the structure of the network. By using mean-field analyses, previous studies of avalanches in networks have not considered the effect of network structure on the distribution of size and duration of avalanches. Our results apply to individual networks (rather than network ensembles) and provide expressions for the distributions of size and duration of avalanches starting at particular nodes in the network. These findings might find application in the analysis of branching processes in networks, such as cascading power grid failures and critical brain dynamics. In particular, our results show that some experimental signatures of critical brain dynamics (i.e., power-law distributions of size and duration of neuronal avalanches), are robust to complex underlying network topologies.Comment: 11 pages, 7 figure

Phosphorus Dynamics in Cultures and Natural Populations of Trichodesmium spp

Trichodesmium spp. fix atmospheric N2 and so an element other than N limits production by these species in the oligotrophic ocean. Because dissolved inorganic phosphorus (DIP) is in short supply in many marine systems, it has been hypothesized that P is a growth-limiting nutrient for these species in nature. However, Trichodesmium is capable of hydrolyzing dissolved organic P (DOP) compounds and the inorganic products from hydrolysis may provide an additional source of P for growth. We investigated P dynamics and alkaline phosphatase activity in cultures and natural populations of Trichodesmium from the Atlantic Ocean and the north coast of Australia to determine whether hydrolysis of DOP could supply enough P to fuel growth. During the Atlantic cruise, concentrations of DIP were lower and chlorophyll (chl a)-specific rates of alkaline phosphatase activity by Trichodesmium were higher than during the Australian transect. However, because Trichodesmium were much more abundant during the Australian transect, where they represented the bulk of the surface chl a biomass, total water column rates of alkaline phosphatase activity were higher along the Australian transect than in the Atlantic. In both systems, DOP could potentially supply a significant portion of the cellular P necessary for growth. In cultures and natural populations, alkaline phosphatase activity was inhibited when DIP was present and increased in the presence of DOP. Cultures of Trichodesmium IMS101 grew equally well on media enriched with DOP or DIP at all but the highest enrichment levels. From these studies, we conclude that if the supply of appropriate DOP substrates is adequate, DOP can represent an important P source for Trichodesmium growth which should be included in estimates of P availability in surface waters

Species-specific phytoplankton growth rates via diel DNA synthesis cycles. III. Accuracy of growth rate measurements in the dinoflagellate Prorocentrum minimum.

The accuracy of species-specific phytoplankton growth rates estimated by cell cycle analysis was tested with the dinoflagellate Prorocentrum minimum (Pav.) Sch. under conditions of altered nitrogen and phosphorus availability. Reduced nutrient availability caused major changes in the duration of cell cycle phases. At the nutrient level of complete f/2 media, the length of the combination of S, G2, and M phases was about 8 h at growth rates of 0.53 to 0.56 d-' A decrease in ~ 0 ,o~r N-O3 concentration extended the S+G2+M phase to about 15.5 to 17.7 h at growth rates ranging from 0.41 to 0.30 d-' Changes in phase durations dld not significantly affect growth rate estimates. In addition, a minimum growth rate, calculated from the maximum values on phase fraction curves, was shown to be usable as an error detector in some cases. Results support the validity of cell cycle analysis to measure in situ growth rates

Bio-optical properties of the marine diazotrophic cyanobacteria Trichodesmium spp. II. A reflectance model for remote sensing

The spatial and temporal distribution of Trichodesmium in the world's oceans is highly variable and can potentially be assessed using satellite imagery. Distinguishing these organisms from other phytoplankton in the upper ocean using remotely sensed information, however, requires an optical model that uniquely characterizes Trichodesmium. Here, we parameterize a standard remote-sensing reflectance model using measured values of Trichodesmium's inherent optical properties, namely the spectral dependence of the chlorophyll-specific optical absorption cross-sections and the spectral dependence of the chlorophyll-specific backscatter cross-sections. Values for the chlorophyll-specific absorption cross sections are described in the previous paper. We calculated the spectral chlorophyll-specific backscattering cross-section (b*b) from measurements of the chlorophyll-specific volume-scattering function and the spectral backscatter coefficients. b*b was 0.0027 m² (mg chlorophyll a [Chl a])⁻¹ at 436 nm and 0.002 m² (mg Chl a)⁻¹ at 546 nm; these cross-sections are approximately one order of magnitude higher than those for "typical" phytoplankton. The optical model revealed that the combination of high backscatter, absorption, and fluorescence could be used to distinguish moderate to high concentrations (>1 mg Chl m⁻³)of Trichodesmium from other phytoplankton. The model also predicted that surface scum blooms of Trichodesmium would have high reflectance in the near infrared. The high reflectance feature of surface Trichodesmium blooms was used in conjunction with sea truth and data from the advanced very high resolution radiometer (AVHRR) to map a 300,000-km² Trichodesmium bloom off the Somali Coast in May 1995. The nitrogen fixed by this bloom was estimated to be 9.4 × 10⁸ gN d⁻¹. These results demonstrate the potential of using remote-sensing techniques in the estimation of nitrogen fixation and the contribution of nitrogen fixation to global biogeochemical processes

The α–β phase transition in volcanic cristobalite

Cristobalite is a common mineral in volcanic ash produced from dome-forming eruptions. Assessment of the respiratory hazard posed by volcanic ash requires understanding the nature of the cristobalite it contains. Volcanic cristobalite contains coupled substitutions of Al3+ and Na+ for Si4+; similar co-substitutions in synthetic cristobalite are known to modify the crystal structure, affecting the stability of the [alpha] and [beta] forms and the observed transition between them. Here, for the first time, the dynamics and energy changes associated with the [alpha]-[beta] phase transition in volcanic cristobalite are investigated using X-ray powder diffraction with simultaneous in situ heating and differential scanning calorimetry. At ambient temperature, volcanic cristobalite exists in the [alpha] form and has a larger cell volume than synthetic [alpha]-cristobalite; as a result, its diffraction pattern sits between ICDD [alpha]- and [beta]-cristobalite library patterns, which could cause ambiguity in phase identification. On heating from ambient temperature, volcanic cristobalite exhibits a lower degree of thermal expansion than synthetic cristobalite, and it also has a lower [alpha]-[beta] transition temperature (~473 K) compared with synthetic cristobalite (upwards of 543 K); these observations are discussed in relation to the presence of Al3+ and Na+ defects. The transition shows a stable and reproducible hysteresis loop with [alpha] and [beta] phases coexisting through the transition, suggesting that discrete crystals in the sample have different transition temperatures

Predictors of early and late mortality following open extent IV thoracoabdominal aortic aneurysm repair in a large contemporary single-center experience

ObjectiveThe primary purpose of this study was to examine outcomes following open repair of extent IV thoracoabdominal aortic aneurysms (TAAAs) at a single university hospital. As a secondary aim, comparison was made to patients who underwent open abdominal aortic aneurysm (AAA) repair with supraceliac clamping but without left renal artery bypass to assess the effect of left renal artery bypass on outcomes.MethodsPatients undergoing open extent IV TAAA repair from 1998 to 2008 were identified (n = 108). Primary outcomes were 30-day and long-term survival. Secondary outcomes were major complication, renal failure, and postoperative change in renal function. A second analysis was performed, comparing patients undergoing extent IV TAAA repair with patients undergoing AAA repair with supraceliac clamping but without left renal artery bypass (n = 50).ResultsEighty-three men (76.9%) and 25 women (23.1%), with a mean age of 72.9 years, underwent open extent IV TAAA repair. Nine patients (8.3%) were ruptured. Mean aneurysm maximal diameter was 6.5 ± 1.3 cm. Supraceliac and left renal ischemic times were 22.9 ± 9.3 and 40.6 ± 16.2 minutes, respectively. Six patients (5.6%) died at 30 days. The only predictor of 30-day mortality was decreased preoperative estimated glomerular filtration rate (eGFR) (P = .044 by multivariate analysis; and P = .011 by univariate analysis). One-year and 5-year survival rates were 87% and 50%, respectively. Patients with a history of cerebrovascular disease (P = .001) and postoperative renal insufficiency (P = .034) had increased long-term mortality by log-rank test. Twenty-five (25.3%) patients sustained a postoperative decrease in renal function, while 19 (19.2%) patients had an improvement in renal function. There was no difference in 30-day mortality (5.6% vs 6.0%; P = 1.000), 5-year survival (50% vs 48%; P = .886), major complications (37.0% vs 38.0%; P = 1.000), renal failure (6.1% vs 0%; P = .215), or postoperative change in renal function, in patients undergoing extent IV TAAA repair vs AAA repair with supraceliac clamping but without left renal artery bypass.ConclusionsOpen extent IV TAAA repair can be performed with low morbidity and mortality rates. The performance of left renal artery bypass does not appear to contribute to the morbidity and mortality of extent IV TAAA repair. While decreased preoperative eGFR appears to increase the risk of 30-day mortality, a history of cerebrovascular disease and postoperative renal insufficiency appear to increase the risk of long-term mortality. Finally, open extent IV TAAA repair not uncommonly improves renal function

Bio-optical properties of the marine diazotrophic cyanobacteria Trichodesmium spp. I. Absorption and photosynthetic action spectra

The optical absorption, fluorescence excitation and emission, and photosynthetic action spectra were measured in vivo on intact colonies of Trichodesmium from the Caribbean Sea. The optical cross-sections were dominated by ultraviolet-A (UVA) absorption, which was a consequence of massive accumulations of mycosporinelike amino acids. The visible region of the spectrum was decomposed into several bands, among which chlorophyll a (Chl a), carotenoids, and individual phycobilipigments could be discerned. There was a clear diel periodicity in the ratio of the optical absorption cross-sections of phycourobilin (PUB) to phycoerythrobilin (PEB), increasing from around 1.7 at night to 2.1 at midmorning. The diel cycle in PUB/PEB is consistent with a reversible interconversion of the two pigments. The ratio of PUB/PEB was inversely correlated with the transfer of excitation energy to photosystem II (PSII). Light absorbed by PUB was not transferred to PSII with a high efficiency, but rather, a significant fraction was reemitted at 565 nm as fluorescence. These observations suggest that the PUBs and PEBs in Trichodesmium act as a dynamic biophysical energy valve that modify the rate of excitation energy delivered to PSII in response to changes in ambient light regime. The low-temperature (77 K) fluorescence emission spectra reveal an extremely weak 685-nm emission signal in relation to that at 730 nm. Based on a simple model, these data suggest that the ratio of PSI/PSII reaction centers in Trichodesmium is about 24:1. Such an extraordinary bias against PSII may help minimize damage to nitrogenase from O₂ production in PSII, but it also reduces the photosynthesis-enhanced growth and makes Trichodesmium virtually undetectable by chlorophyll fluorescence. The unique bio-optical properties of Trichodesmium can be used to develop algorithms to study its temporal and spatial distributions from remotely sensed information