Optimization under uncertainty and risk: Quadratic and copositive approaches

Robust optimization and stochastic optimization are the two main paradigms for dealing with the uncertainty inherent in almost all real-world optimization problems. The core principle of robust optimization is the introduction of parameterized families of constraints. Sometimes, these complicated semi-infinite constraints can be reduced to finitely many convex constraints, so that the resulting optimization problem can be solved using standard procedures. Hence flexibility of robust optimization is limited by certain convexity requirements on various objects. However, a recent strain of literature has sought to expand applicability of robust optimization by lifting variables to a properly chosen matrix space. Doing so allows to handle situations where convexity requirements are not met immediately, but rather intermediately. In the domain of (possibly nonconvex) quadratic optimization, the principles of copositive optimization act as a bridge leading to recovery of the desired convex structures. Copositive optimization has established itself as a powerful paradigm for tackling a wide range of quadratically constrained quadratic optimization problems, reformulating them into linear convex-conic optimization problems involving only linear constraints and objective, plus constraints forcing membership to some matrix cones, which can be thought of as generalizations of the positive-semidefinite matrix cone. These reformulations enable application of powerful optimization techniques, most notably convex duality, to problems which, in their original form, are highly nonconvex. In this text we want to offer readers an introduction and tutorial on these principles of copositive optimization, and to provide a review and outlook of the literature that applies these to optimization problems involving uncertainty

Did Bacillus megaterium pick up plasmid virulence genes?

Includes bibliographical references.Plasmids are known to carry genes that allow bacteria to survive in different environments. Virulence genes that cause bacteria to be pathogenic are also found on plasmids. Bacillus megaterium is a non-pathogenic, spore-forming bacteria that is found in soil, but recently a strain of B. megaterium was reported to cause a mild case of diarrhea in an infant. This appears to be the first case of infection caused by B. megaterium (CHI). Bacillus cereus is a related species and a known gastroenteric pathogen. Research has shown that the pathogenicity in some strains of B. cereus is caused by either an operon containing four genes, hblA/B/C/D, or by a single gene, bceT. The pathogenic strain of B. megaterium, (CHI), was tested by PCR and hybridization, to see if it picked up either of these two factors that cause pathogenicity in B. cereus by plasmid exchange. PCR products were obtained in CHI for the genes hblA and bceT using specific primers suggesting that such genes are present in the B. megaterium (CHI) strain. However, a hybridization experiment using bceT product as a probe for CHI failed to show a signal.B.S. (Bachelor of Science

Accuracy Analysis of the Measurement of Centre of Gravity and Moment of Inertia with a Swing

Floating devices under wave and current loads are typically designed based on numerical methods followed by a validation with experimental investigations. This allows an independent check due to the comparison of two different modelling approaches based on different assumptions. At an early stage of the project, numerical simulations are based on theoretical (ideal) values of the centre of gravity (CG) and moment of inertia (MI). The building process of a scaled model results very often in a requested simplification of certain parts, which can influence the CG and also the MI of the scaled model. Knowing those discrepancies allows us to improve the comparability of both approaches but the measurement of those values is connected with either a higher uncertainty or a high level of effort. A significant improvement of such measurements can be reached by the deployment of a specific experimental set-up. This paper presents the classification of the newly designed swing with a high accuracy inertial inclinometer, which was verified by the marker-based motion capturing system. The achieved experiences are useful for the future use of the set-up as well as similar investigations. The comparison with the theoretical values for the swing as well as an example model showed very good agreements and a high accuracy of few millimetres for the CG and an error smaller 1% for MI

Isoenzyme der Creatinkinase in der Perinatalperiode

Peer Reviewe

The dispersion of spherical droplets in source–sink flows and their relevance to the COVID-19 pandemic

In this paper, we investigate the dynamics of spherical droplets in the presence of a source-sink pair flow field. The dynamics of the droplets is governed by the Maxey-Riley equation with Basset-Boussinesq history term neglected. We find that, in the absence of gravity, there are two distinct behaviours for the droplets: small droplets cannot go further than a specific distance, which we determine analytically, from the source before getting pulled into the sink. Larger droplets can travel further from the source before getting pulled into the sink by virtue of their larger inertia, and their maximum travelled distance is determined analytically. We investigate the effects of gravity, and we find that there are three distinct droplet behaviours categorised by their relative sizes: small, intermediate-sized, and large. Counterintuitively, we find that the droplets with minimum horizontal range are neither small nor large, but of intermediate size. Furthermore, we show that in conditions of regular human respiration, these intermediate-sized droplets range in size from a few $\mu$m to a few hundred $\mu$m. The result that such droplets have a very short range could have important implications for the interpretation of existing data on droplet dispersion.Comment: 14 pages, 7 figure

Capturing the Motion of the Free Surface of a Fluid Stored within a Floating Structure

Large floating structures, such as liquefied natural gas (LNG) ships, are subject to both internal and external fluid forces. The internal fluid forces may also be detrimental to a vessel’s stability and cause excessive loading regimes when sloshing occurs. Whilst it is relatively easy to measure the motion of external free surface with conventional measurement techniques, the sloshing of the internal free surface is more difficult to capture. The location of the internal free surface is normally extrapolated from measuring the pressure acting on the internal walls of the vessel. In order to understand better the loading mechanisms of sloshing internal fluids, a method of capturing the transient inner free surface motion with negligible affect on the response of the fluid or structure is required. In this paper two methods will be demonstrated for this purpose. The first approach uses resistive wave gauges made of copper tape to quantify the water run-up height on the walls of the structure. The second approach extends the conventional use of optical motion tracking to report the position of randomly distributed free floating markers on the internal water surface. The methods simultaneously report the position of the internal free surface with good agreement under static conditions, with absolute variation in the measured water level of around 4 mm. This new combined approach provides a map of the free surface elevation under transient conditions. The experimental error is shown to be acceptable (low mm-range), proving that these experimental techniques are robust free surface tracking methods in a range of situations

Round Robin Testing: Exploring Experimental Uncertainties through a Multifacility Comparison of a Hinged Raft Wave Energy Converter

The EU H2020 MaRINET2 project has a goal to improve the quality, robustness and accuracy of physical modelling and associated testing practices for the offshore renewable energy sector. To support this aim, a round robin scale physical modelling test programme was conducted to deploy a common wave energy converter at four wave basins operated by MaRINET2 partners. Test campaigns were conducted at each facility to a common specification and test matrix, providing the unique opportunity for intercomparison between facilities and working practices. A nonproprietary hinged raft, with a nominal scale of 1:25, was tested under a set of 12 irregular sea states. This allowed for an assessment of power output, hinge angles, mooring loads, and six-degree-of-freedom motions. The key outcome to be concluded from the results is that the facilities performed consistently, with the majority of variation linked to differences in sea state calibration. A variation of 5–10% in mean power was typical and was consistent with the variability observed in the measured significant wave heights. The tank depth (which varied from 2–5 m) showed remarkably little influence on the results, although it is noted that these tests used an aerial mooring system with the geometry unaffected by the tank depth. Similar good agreement was seen in the heave, surge, pitch and hinge angle responses. In order to maintain and improve the consistency across laboratories, we make recommendations on characterising and calibrating the tank environment and stress the importance of the device–facility physical interface (the aerial mooring in this case).</jats:p