Estimation of drift and diffusion functions from time series data: A maximum likelihood framework

Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic dynamics in time. Recently techniques for the estimation of the corresponding stochastic differential equations from measured data have been introduced. This contribution develops a framework for the estimation of the functions and their respective (Bayesian posterior) confidence regions based on likelihood estimators. In succession approximations are introduced that significantly improve the efficiency of the estimation procedure. While being consistent with standard approaches to the problem this contribution solves important problems concerning the applicability and the accuracy of estimated parameters.Comment: 18 pages, 2 figure

Physical parameters, modeling, and methodological details in using IR laser pulses to warm frozen or vitrified cells ultra-rapidly

We report additional details of the thermal modeling, selection of the laser, and construction of the Cryo Jig used for our ultra-rapid warming studies of mouse oocytes (Jin et al., 2014). A Nd:YAG laser operating at 1064 nm was selected to deliver short 1ms pulses of sufficient power to produce a warming rate of 1×10(7)°C/min from -190°C to 0°C. A special Cryo Jig was designed and built to rapidly remove the sample from LN2 and expose it to the laser pulse. India ink carbon black particles were required to increase the laser energy absorption of the sample. The thermal model reported here is more general than that previously reported. The modeling reveals that the maximum warming rate achievable via external warming across the cell membrane is proportional to (1/R(2)) where R is the cell radius

Report of the sensor readout electronics panel

The findings of the Sensor Readout Electronics Panel are summarized in regard to technology assessment and recommended development plans. In addition to two specific readout issues, cryogenic readouts and sub-electron noise, the panel considered three advanced technology areas that impact the ability to achieve large format sensor arrays. These are mega-pixel focal plane packaging issues, focal plane to data processing module interfaces, and event driven readout architectures. Development in each of these five areas was judged to have significant impact in enabling the sensor performance desired for the Astrotech 21 mission set. Other readout issues, such as focal plane signal processing or other high volume data acquisition applications important for Eos-type mapping, were determined not to be relevant for astrophysics science goals

Groundwater seepage landscapes from distant and local sources in experiments and on Mars

© 2014 Author(s). Valleys with theater-shaped heads can form due to the seepage of groundwater and as a result of knickpoint (waterfall) erosion generated by overland flow. This ambiguity in the mechanism of formation hampers the interpretation of such valleys on Mars, particularly since there is limited knowledge of material properties. Moreover, the hydrological implications of a groundwater or surface water origin are important for our understanding of the evolution of surface features on Mars, and a quantification of valley morphologies at the landscape scale may provide diagnostic insights on the formative hydrological conditions. However, flow patterns and the resulting landscapes produced by different sources of groundwater are poorly understood. We aim to improve the understanding of the formation of entire valley landscapes through seepage processes from different groundwater sources that will provide a framework of landscape metrics for the interpretation of such systems. We study groundwater seepage from a distant source of groundwater and from infiltration of local precipitation in a series of sandbox experiments and combine our results with previous experiments and observations of the Martian surface. Key results are that groundwater flow piracy acts on valleys fed by a distant groundwater source and results in a sparsely dissected landscape of many small and a few large valleys. In contrast, valleys fed by a local groundwater source, i.e., nearby infiltration, result in a densely dissected landscape. In addition, valleys fed by a distant groundwater source grow towards that source, while valleys with a local source grow in a broad range of directions and have a strong tendency to bifurcate, particularly on flatter surfaces. We consider these results with respect to two Martian cases: Louros Valles shows properties of seepage by a local source of groundwater and Nirgal Vallis shows evidence of a distant source, which we interpret as groundwater flow from Tharsis

Critical dependence of morphodynamic models of fluvial and tidal systems on empirical downslope sediment transport

The morphological development of fluvial and tidal systems is forecast more and more frequently by models in scientific and engineering studies for decision making regarding climate change mitigation, flood control, navigation and engineering works. However, many existing morphodynamic models predict unrealistically high channel incision, which is often dampened by increased gravity-driven sediment transport on side-slopes by up to two orders of magnitude too high. Here we show that such arbitrary calibrations dramatically bias sediment dynamics, channel patterns, and rate of morphological change. For five different models bracketing a range of scales and environments, we found that it is impossible to calibrate a model on both sediment transport magnitude and morphology. Consequently, present calibration practice may cause an order magnitude error in either morphology or morphological change. We show how model design can be optimized for different applications. We discuss the major implications for model interpretation and a critical knowledge gap

Trehalose Is A Chemical Attractant In The Establishment Of Coral Symbiosis

Coral reefs have evolved with a crucial symbiosis between photosynthetic dinoflagellates (genus Symbiodinium) and their cnidarian hosts (Scleractinians). Most coral larvae take up Symbiodinium from their environment; however, the earliest steps in this process have been elusive. Here we demonstrate that the disaccharide trehalose may be an important signal from the symbiont to potential larval hosts. Symbiodinium freshly isolated from Fungia scutaria corals constantly released trehalose (but not sucrose, maltose or glucose) into seawater, and released glycerol only in the presence of coral tissue. Spawning Fungia adults increased symbiont number in their immediate area by excreting pellets of Symbiodinium, and when these naturally discharged Symbiodinium were cultured, they also released trehalose. In Y-maze experiments, coral larvae demonstrated chemoattractant and feeding behaviors only towards a chamber with trehalose or glycerol. Concomitantly, coral larvae and adult tissue, but not symbionts, had significant trehalase enzymatic activities, suggesting the capacity to utilize trehalose. Trehalase activity was developmentally regulated in F. scutaria larvae, rising as the time for symbiont uptake occurs. Consistent with the enzymatic assays, gene finding demonstrated the presence of a trehalase enzyme in the genome of a related coral, Acropora digitifera, and a likely trehalase in the transcriptome of F. scutaria. Taken together, these data suggest that adult F. scutaria seed the reef with Symbiodinium during spawning and the exuded Symbiodinium release trehalose into the environment, which acts as a chemoattractant for F. scutaria larvae and as an initiator of feeding behavior- the first stages toward establishing the coral-Symbiodinium relationship. Because trehalose is a fixed carbon compound, this cue would accurately demonstrate to the cnidarian larvae the photosynthetic ability of the potential symbiont in the ambient environment. To our knowledge, this is the first report of a chemical cue attracting the motile coral larvae to the symbiont

Improved estimation of Fokker-Planck equations through optimisation

An improved method for the description of hierarchical complex systems by means of a Fokker-Planck equation is presented. In particular the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm for constraint problems (L-BFGS-B) is used to minimize the distance between the numerical solutions of the Fokker-Planck equation and the empirical probability density functions and thus to estimate properly the drift and diffusion term of the Fokker-Planck equation. The optimisation routine is applied to a time series of velocity measurements obtained from a turbulent helium gas jet in order to demonstrate the benefits and to quantify the improvements of this new optimisation routine

Scour holes and ripples occur below the hydraulic smooth to rough transition of movable beds

© 2017 The Authors. Scour holes often form in shallow flows over sand on the beach and in morphodynamic scale experiments of river reaches, deltas and estuarine landscapes. The scour holes are on average 2cm deep and 5cm long, regardless of the flow depth and appear to occur under similar conditions as current ripples: at low boundary Reynolds numbers, in fine sand and under relatively low sediment mobility. In landscape experiments, where the flow is only about 1cm deep, such scours may be unrealistically large and have unnatural effects on channel formation, bar pattern and stratigraphy. This study tests the hypotheses that both scours and ripples occur in the same conditions and that the roughness added by sediment saltation explains the difference between the ripple–dune transition and the clear-water hydraulic smooth to rough transition. About 500 experiments are presented with a range of sediment types, sediment mobility and obstructions to provoke scour holes, or removal thereof to assess scour hole persistence. Most experiments confirm that ripples and scour holes both form in the ripple stability field in two different bedform stability diagrams. The experiments also show that scours can be provoked by perturbations even below generalized sediment motion. Moreover, the hydraulic smooth to rough transition modified with saltation roughness depending on sediment mobility was similar in magnitude and in slope to ripple–dune transitions. Given uncertainties in saltation relations, the smooth to rough transitions modified for movable beds are empirically equivalent to the ripple–dune transitions. These results are in agreement with the hypothesis that scours form by turbulence caused by localized flow separation under low boundary Reynolds numbers, and do not form under generalized flow separation over coarser particles and intense sediment saltation. Furthermore, this suggests that ripples are a superposition of two independent forms: periodic bedforms occurring in smooth and rough conditions plus aperiodic scours occurring only in hydraulic smooth conditions

Morphological effects of vegetation on the tidal-fluvial transition in Holocene estuaries

Vegetation enhances bank stability and sedimentation to such an extent that it can modify river patterns, but how these processes manifest themselves in full-scale estuarine settings is poorly understood. On the one hand, tidal flats accrete faster in the presence of vegetation, reducing the flood storage and ebb dominance over time. On the other hand flow-focusing effects of a tidal floodplain elevated by mud and vegetation could lead to channel concentration and incision. Here we study isolated and combined effects of mud and tidal marsh vegetation on estuary dimensions. A 2-D hydromorphodynamic estuary model was developed, which was coupled to a vegetation model and used to simulate 100 years of morphological development. Vegetation settlement, growth and mortality were determined by the hydromorphodynamics. Eco-engineering effects of vegetation on the physical system are here limited to hydraulic resistance, which affects erosion and sedimentation pattern through the flow field. We investigated how vegetation, combined with mud, affects the average elevation of tidal flats and controls the system-scale planform. Modelling with vegetation only results in a pattern with the largest vegetation extent in the mixed-energy zone of the estuary, which is generally shallower. Here vegetation can cover more than 50 % of the estuary width while it remains below 10 %–20 % in the outer, tide-dominated zone. This modelled distribution of vegetation along the estuary shows general agreement with trends in natural estuaries observed by aerial image analysis. Without mud, the modelled vegetation has a limited effect on morphology, again peaking in the mixed-energy zone. Numerical modelling with mud only shows that the presence of mud leads to stabilisation and accretion of the intertidal area and a slight infill of the mixed-energy zone. Combined modelling of mud and vegetation leads to mutual enhancement with mud causing new colonisation areas and vegetation stabilising the mud. This occurs in particular in a zone previously described as the bedload convergence zone. While vegetation focusses the flow into the channels such that mud sedimentation in intertidal side channels is prevented on a timescale of decades, the filling of intertidal area and the resulting reduction in tidal prism may cause the infilling of estuaries over centuries