Transient chaos and resonant phase mixing in violent relaxation

This paper explores how orbits in a galactic potential can be impacted by large amplitude time-dependences of the form that one might associate with galaxy or halo formation or strong encounters between pairs of galaxies. A period of time-dependence with a strong, possibly damped, oscillatory component can give rise to large amounts of transient chaos, and it is argued that chaotic phase mixing associated with this transient chaos could play a major role in accounting for the speed and efficiency of violent relaxation. Analysis of simple toy models involving time-dependent perturbations of an integrable Plummer potential indicates that this chaos results from a broad, possibly generic, resonance between the frequencies of the orbits and harmonics thereof and the frequencies of the time-dependent perturbation. Numerical computations of orbits in potentials exhibiting damped oscillations suggest that, within a period of 10 dynamical times t_D or so, one could achieve simultaneously both `near-complete' chaotic phase mixing and a nearly time-independent, integrable end state.Comment: 11 pages and 12 figures: an extended version of the original manuscript, containing a modified title, one new figure, and approximately one page of additional text, to appear in Monthly Notices of the Royal Astronomical Societ

State-Space Quantization Design for the Suboptimal Control of Constrained Systems Using Neuromorphic Controllers

During the last few years there has been considerable interest in the use of trainable controllers based upon the use of neuron-like elements, with the expectation being that these controllers can be trained, with relatively little effort, to achieve good performance. However, good performance hinges on the ability of the neural net to generate a "good" control law even when the input does not belong to the training set, and it has been shown that neural-nets do not necessarily generalize well. It has been proposed that this problem can be solved by essentially quantizing the state-space and then using a neural-net to implement a table look-up procedure. However, there is little information on the effect of this quantization upon the controllability properties of the system. In this paper we address this problem by extending the theory of control of constrained systems to the case where the controls and measured states are restricted to finite or countably infinite sets. These results provide the theoretical framework for recently suggested neuromorphic controllers but they are also valuable for analyzing the controllability properties of computer-based control systems

Norm Based Optimally Robust Control of Constrained Discrete Time Linear Systems

Most realistic control problems involve both some type of time-domain constraints and model uncertainty. However, the majority of controller design procedures currently available focus only on one aspect of the problem, with only a handful of method capable of simultaneously addressing, albeit in a limited fashion, both issues. In this paper we propose a simple design procedure that takes explicitly into account both time domain constraints and model uncertainty. Specifically, we use a operator norm approach to define a simple robustness measure for constrained systems. The available degrees of freedom are then used to optimize this measure subject to additional performance specifications. We believe that the results presented here provide a useful new approach for designing controllers capable of yielding good performance under substantial uncertainty while meeting design constraints

Screening and prevention of ovarian cancer.

Ovarian cancer remains the most lethal gynaecological malignancy with 314 000 cases and 207 000 deaths annually worldwide. Ovarian cancer cases and deaths are predicted to increase in Australia by 42% and 55% respectively by 2040. Earlier detection and significant downstaging of ovarian cancer have been demonstrated with multimodal screening in the largest randomised controlled trial of ovarian cancer screening in women at average population risk. However, none of the randomised trials have demonstrated a mortality benefit. Therefore, ovarian cancer screening is not currently recommended in women at average population risk. More frequent surveillance for ovarian cancer every three to four months in women at high risk has shown good performance characteristics and significant downstaging, but there is no available information on a survival benefit. Population testing offers an emerging novel strategy to identify women at high risk who can benefit from ovarian cancer prevention. Novel multicancer early detection biomarker, longitudinal multiple marker strategies, and new biomarkers are being investigated and evaluated for ovarian cancer screening. Risk-reducing salpingo-oophorectomy (RRSO) decreases ovarian cancer incidence and mortality and is recommended for women at over a 4-5% lifetime risk of ovarian cancer. Pre-menopausal women without contraindications to hormone replacement therapy (HRT) undergoing RRSO should be offered HRT until 51 years of age to minimise the detrimental consequences of premature menopause. Currently risk-reducing early salpingectomy and delayed oophorectomy (RRESDO) should only be offered to women at increased risk of ovarian cancer within the context of a research trial. Pre-menopausal early salpingectomy is associated with fewer menopausal symptoms and better sexual function than bilateral salpingo-oophorectomy. A Sectioning and Extensively Examining the Fimbria (SEE-FIM) protocol should be used for histopathological assessment in women at high risk of ovarian cancer who are undergoing surgical prevention. Opportunistic salpingectomy may be offered at routine gynaecological surgery to all women who have completed their family. Long term prospective opportunistic salpingectomy studies are needed to determine the effect size of ovarian cancer risk reduction and the impact on menopause

Gravimetric geoid refinement using high resolution gravity and terrain data

In regions where additional, spatially dense gravity and terrain information are available to augment existing data, a gravimetric determination of the geoid can be improved by incorporating these new data. In this study, 4,016 additional gravity observations, measured on a near-regular 2km by 3km grid in Western Australia have been used to compute a gravimetric geoid model using fast Fourier transform (FFT) techniques. A digital terrain model is also used during the geoid computations, which is derived from gravity station elevations and spot heights in the area. Using 21 spirit-levelled Australian Height Datum (AHD) heights in conjunction with Global Positioning System (GPS) ellipsoidal heights as control data, the standard deviation of the new gravimetric geoid is ±0.0824m. This represents a 31% improvement over the existing AUSGEOID93 gravimetric geoid and a 48% improvement over the OSU91A global geopotential model. Of these improvements, approximately 10% is due to the additional gravity data and approximately 1% is due to the terrain effects; the remainder is due to the dense gridding of the data prior to the FFT computations

Blow-up of the hyperbolic Burgers equation

The memory effects on microscopic kinetic systems have been sometimes modelled by means of the introduction of second order time derivatives in the macroscopic hydrodynamic equations. One prototypical example is the hyperbolic modification of the Burgers equation, that has been introduced to clarify the interplay of hyperbolicity and nonlinear hydrodynamic evolution. Previous studies suggested the finite time blow-up of this equation, and here we present a rigorous proof of this fact

Optimization of Tetrapolar Impedance Electrodes in Microfluidic Devices for Point of Care Diagnostics using Finite Element Modeling

Electrophoresis is widely applied in the field of biochemistry and molecular biology. Tetrapolar electrical impedance sensing (TEIS) has been shown capable of replacing the conventional detection technology in order to develop a point of care electrophoretic analyzer. Besides the advantages of reduced influence of electrode polarization, TEIS is affected by sensitivity distribution depending on the electrode design. A well reported practice outside of electrophoresis, systematic investigation of the effects of sensitivity distribution on the TEIS in microfluidic devices has not been conducted. Here we utilize finite element modeling, backed by experimental results, to optimize the sensor design within an electrophoretic separation device. Numerous sensor designs were validated regarding detectability, sensitivity and spatial resolution. The results show, that minimizing the distance between the central/pick-up electrodes increases sensitivity and spatial resolution whereas the distance between the central electrodes and the outer electrode do not influence sensitivity and spatial resolution