Off-axis transmission holographic system for recording aquatic particles

We describe a holographic system for recording particles suspended in water. The hologram plate is located in air, separated from the test tank by an air/glass/water boundary. The holographic emulsion is therefore unaffected by adverse aquatic conditions within the tank (i.e. surface contamination, non-uniform swelling). The design geometry is intended to minimise the aberrations that arise from recording subjects located in water and replaying their hologram image in air. Third order aberrations, most crucially spherical aberration and astigmatism, are suppressed to give an experimental resolution of 7 lp/mm using USAF 1951 target in water 600mm from the boundary. Particles (plankton species) in the sub-millimeter to several millimeters size range are observed at planar sections within the recording volume by visual inspection of the hologram replayed in real image mode

Holographic mensuration of suspended particles in aquatic systems

The distribution and dynamics of aggregates in the aquatic environment play an important role in the modelling of biogeochemical processes. Previous work on aggregates in the ocean (e.g. sedimentary 'marine snow' particles), which vary in size from tens of microns to several millimetres, has used electronic counting or conventional photography coupled with image analysis. Here we describe a non-destructive in situ approach by use of holographic mensuration, hologrammetry, that affords greater scope and higher accuracy for the enumeration, sizing, and spatial distribution determination of aggregate particles. By means of two complimentary techniques, in-line and offaxis transmission holography, we present the initial experiments conducted in our laboratory and discuss the preliminaiy results from real image analysis

In situ off-axis holography of marine plankton

We present an off-axis transmission holographic technique for recording marine plankton in situ within a test tank of 36,000 ml with a pulsed laser in a 40 ns interval. The holographic plate is located in air and is therefore unaffected by aquatic conditions that may cause emulsion degradation (e.g. non-uniform swelling and surface contamination). The reference beam traverses a path in air only, and thus remains unaffected by dense concentrations of plankton. Third order aberrations, notably spherical aberration and astigmatism, are suppressed to yield an experimental resolution of 7 lp/mm (70 micrometres) with a USAF 1951 target located 600 mm in water from the observation window. Plankton particle counts examined by real image reconstruction show a strong correlation with duplicate samples examined under a microscope

Validation of the frequency modulation technique applied to the pulsating Sct- Dor eclipsing binary star KIC 8569819

KIC 8569819 is an eclipsing binary star with an early F primary and G secondary in a 20.85-d eccentric orbit. The primary is a δ Sct–γ Dor star pulsating in both p modes and g modes. Using four years of Kepler Mission photometric data, we independently model the light curve using the traditional technique with the modelling code PHOEBE, and we study the orbital characteristics using the new frequency modulation technique. We show that both methods provide the equivalent orbital period, eccentricity and argument of periastron, thus illustrating and validating the FM technique. In the amplitude spectrum of the p-mode pulsations, we also discovered an FM signal compatible with a third body in the system, a low-mass M dwarf in an 861-d orbit around the primary pair. However, the eclipses show no timing variations, indicating that the FM signal is a consequence of the intrinsic change in pulsation frequency, thus providing a cautionary tale. Our analysis shows the potential of the FM technique using Kepler data, and we discuss the prospects to detect planets and brown dwarfs in Kepler data for A and F stars even in the absence of transits and with no spectroscopic radial velocity curves. This opens the possibility of finding planets orbiting hotter stars that cannot be found by traditional techniques

A data extraction system for underwater particle holography

Pulsed laser holography is an extremely powerful technique for the study of particle fields as it allows instantaneous, noninvasive high-resolution recording of substantial volumes. By replaying the real image one can obtain the size, shape, position and - if multiple exposures are made - velocity of every object in the recorded field. Manual analysis of large volumes containing thousands of particles is, however, an enormous and time-consuming task, with operator fatigue an unpredictable source of errors. Clearly the value of holographic measurements also depends crucially on the quality of the reconstructed image: not only will poor resolution degrade size and shape measurements, but aberrations such as coma and astigmatism can change the perceived centroid of a particle, affecting position and velocity measurements. For large-scale applications of particle field holography, specifically the in situ recording of marine plankton with 'HoloCam,' we have developed an automated data extraction system that can be readily switched between the in-line and off-axis geometries and provides optimised reconstruction from holograms recorded underwater. As a videocamera is automatically stepped through the 200 by 200 by 1000mm sample volume, image processing and object tracking routines locate and extract particle images for further classification by a separate software module

A Hierarchy of Scheduler Classes for Stochastic Automata

Stochastic automata are a formal compositional model for concurrent stochastic timed systems, with general distributions and non-deterministic choices. Measures of interest are defined over schedulers that resolve the nondeterminism. In this paper we investigate the power of various theoretically and practically motivated classes of schedulers, considering the classic complete-information view and a restriction to non-prophetic schedulers. We prove a hierarchy of scheduler classes w.r.t. unbounded probabilistic reachability. We find that, unlike Markovian formalisms, stochastic automata distinguish most classes even in this basic setting. Verification and strategy synthesis methods thus face a tradeoff between powerful and efficient classes. Using lightweight scheduler sampling, we explore this tradeoff and demonstrate the concept of a useful approximative verification technique for stochastic automata

Near-optimal asymmetric binary matrix partitions

We study the asymmetric binary matrix partition problem that was recently introduced by Alon et al. (WINE 2013) to model the impact of asymmetric information on the revenue of the seller in take-it-or-leave-it sales. Instances of the problem consist of an $n \times m$ binary matrix $A$ and a probability distribution over its columns. A partition scheme $B=(B_1,...,B_n)$ consists of a partition $B_i$ for each row $i$ of $A$. The partition $B_i$ acts as a smoothing operator on row $i$ that distributes the expected value of each partition subset proportionally to all its entries. Given a scheme $B$ that induces a smooth matrix $A^B$, the partition value is the expected maximum column entry of $A^B$. The objective is to find a partition scheme such that the resulting partition value is maximized. We present a $9/10$-approximation algorithm for the case where the probability distribution is uniform and a $(1-1/e)$-approximation algorithm for non-uniform distributions, significantly improving results of Alon et al. Although our first algorithm is combinatorial (and very simple), the analysis is based on linear programming and duality arguments. In our second result we exploit a nice relation of the problem to submodular welfare maximization.Comment: 17 page

The fundamental problem of command : plan and compliance in a partially centralised economy

When a principal gives an order to an agent and advances resources for its implementation, the temptations for the agent to shirk or steal from the principal rather than comply constitute the fundamental problem of command. Historically, partially centralised command economies enforced compliance in various ways, assisted by nesting the fundamental problem of exchange within that of command. The Soviet economy provides some relevant data. The Soviet command system combined several enforcement mechanisms in an equilibrium that shifted as agents learned and each mechanism's comparative costs and benefits changed. When the conditions for an equilibrium disappeared, the system collapsed.Comparative Economic Studies (2005) 47, 296–314. doi:10.1057/palgrave.ces.810011

Predicting cortical bone adaptation to axial loading in the mouse tibia

The development of predictive mathematical models can contribute to a deeper understanding of the specific stages of bone mechanobiology and the process by which bone adapts to mechanical forces. The objective of this work was to predict, with spatial accuracy, cortical bone adaptation to mechanical load, in order to better understand the mechanical cues that might be driving adaptation. The axial tibial loading model was used to trigger cortical bone adaptation in C57BL/6 mice and provide relevant biological and biomechanical information. A method for mapping cortical thickness in the mouse tibia diaphysis was developed, allowing for a thorough spatial description of where bone adaptation occurs. Poroelastic finite-element (FE) models were used to determine the structural response of the tibia upon axial loading and interstitial fluid velocity as the mechanical stimulus. FE models were coupled with mechanobiological governing equations, which accounted for non-static loads and assumed that bone responds instantly to local mechanical cues in an on–off manner. The presented formulation was able to simulate the areas of adaptation and accurately reproduce the distributions of cortical thickening observed in the experimental data with a statistically significant positive correlation (Kendall's τ rank coefficient τ = 0.51, p < 0.001). This work demonstrates that computational models can spatially predict cortical bone mechanoadaptation to a time variant stimulus. Such models could be used in the design of more efficient loading protocols and drug therapies that target the relevant physiological mechanisms

More Than 1700 Years of Word Equations

Geometry and Diophantine equations have been ever-present in mathematics. Diophantus of Alexandria was born in the 3rd century (as far as we know), but a systematic mathematical study of word equations began only in the 20th century. So, the title of the present article does not seem to be justified at all. However, a linear Diophantine equation can be viewed as a special case of a system of word equations over a unary alphabet, and, more importantly, a word equation can be viewed as a special case of a Diophantine equation. Hence, the problem WordEquations: "Is a given word equation solvable?" is intimately related to Hilbert's 10th problem on the solvability of Diophantine equations. This became clear to the Russian school of mathematics at the latest in the mid 1960s, after which a systematic study of that relation began. Here, we review some recent developments which led to an amazingly simple decision procedure for WordEquations, and to the description of the set of all solutions as an EDT0L language.Comment: The paper will appear as an invited address in the LNCS proceedings of CAI 2015, Stuttgart, Germany, September 1 - 4, 201