Conditional random matrix ensembles and the stability of dynamical systems

There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either specific to a particular model (leading to results that were not general), or chosen for mathematical convenience, yielding results unlikely to be meaningful for any interesting realistic system. May's work, and its subsequent elaborations, relied upon results from random matrix theory, particularly the circular law and its extensions, which only apply when the strengths of interactions between entities in the system are assumed to be independent and identically distributed (i.i.d.). Other studies have optimistically generalised from the analysis of very specific systems, in a way that does not hold up to closer scrutiny. We show here that this debate can be put to rest, once these two contrasting views have been reconciled --- which is possible in the statistical framework developed here. Here we use a range of illustrative examples of dynamical systems to demonstrate that (i) stability probability cannot be summarily deduced from any single property of the system (e.g. its diversity), and (ii) our assessment of stability depends on adequately capturing the details of the systems analysed. Failing to condition on the structure of dynamical systems will skew our analysis and can, even for very small systems, result in an unnecessarily pessimistic diagnosis of their stability

Bilad al-Qadim revisited: recent archaeological research at the Al-Khamis Mosque, Ain Abu Zaydan and Abu Anbra, Bahrain

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.In comparison to our understanding of pre-Islamic occupation and land use on Bahrain, that of the Islamic period has remained less well known. In connection with the building of a visitor centre at the Al-Khamis Mosque and the planning of an associated heritage trail, renewed archaeological research has taken place in Bilad al-Qadim, an archaeologically important area of Islamic settlement in the north-east of the main island of Awal. This has involved excavations in the Abu Anbra cemetery, at Ain Abu Zaydan and at the Al-Khamis Mosque. The results of these excavations are reported here and these contribute to our understanding of Islamic settlement on Bahrain by supporting the interpretation that Bilad al-Qadim was the main centre of Islamic settlement in the eleventh–thirteen century AD

Laser drilling of microholes in single crystal silicon using continuous wave (CW) 1070 nm fiber lasers with millisecond pulse widths

The laser microdrilling of via holes in Si semiconductor wafers was studied using 1 ms pulses from an Yb fibre laser with 1070 nm wavelength. Optical microscopy and cross‑sectional analysis were used to quantify hole dimensions, the distribution of recast material and any microcracking for both (100) and (111) single crystal surface semiconductor wafer orientations. The flexibility of this laser wavelength and simple pulsing scheme were demonstrated for a range of semiconductor substrates of narrow and wide bandgap including InSb, GaSb, InAs, GaAs, InP and sapphire. Detailed observations for Si showed that, between the threshold energies for surface melting and the irradiance for drilling a “thru” hole from the front surface to rear surface, there was a range of irradiances for which microcracking occurred near the hole circumference. The directionality and lengths of these microcracks were studied for the (100) and (111) orientations and possible mechanisms for formation were discussed, including the Griffith criterion for microcracks and the failure mechanism of fatigue usually applied to welding of metals. Above the irradiance for formation of a thru hole, few cracks were observed. Future work will compare similar observations and measurements in other narrow- and wide-bandgap semiconductor wafer substrates

Extension of Yeast Chronological Lifespan by Methylamine

Background: Chronological aging of yeast cells is commonly used as a model for aging of human post-mitotic cells. The yeast Saccharomyces cerevisiae grown on glucose in the presence of ammonium sulphate is mainly used in yeast aging research. We have analyzed chronological aging of the yeast Hansenula polymorpha grown at conditions that require primary peroxisome metabolism for growth. Methodology/Principal Findings: The chronological lifespan of H. polymorpha is strongly enhanced when cells are grown on methanol or ethanol, metabolized by peroxisome enzymes, relative to growth on glucose that does not require peroxisomes. The short lifespan of H. polymorpha on glucose is mainly due to medium acidification, whereas most likely ROS do not play an important role. Growth of cells on methanol/methylamine instead of methanol/ammonium sulphate resulted in further lifespan enhancement. This was unrelated to medium acidification. We show that oxidation of methylamine by peroxisomal amine oxidase at carbon starvation conditions is responsible for lifespan extension. The methylamine oxidation product formaldehyde is further oxidized resulting in NADH generation, which contributes to increased ATP generation and reduction of ROS levels in the stationary phase. Conclusion/Significance: We conclude that primary peroxisome metabolism enhanced chronological lifespan of H. polymorpha. Moreover, the possibility to generate NADH at carbon starvation conditions by an organic nitrogen source supports further extension of the lifespan of the cell. Consequently, the interpretation of CLS analyses in yeast should include possible effects on the energy status of the cell.

Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation, and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.Comment: Submitted to 'Systems Medicine' as a book chapte

Resection of the liver for colorectal carcinoma metastases - A multi-institutional study of long-term survivors

In this review of a collected series of patients undergoing hepatic resection for colorectal metastases, 100 patients were found to have survived greater than five years from the time of resection. Of these 100 long-term survivors, 71 remain disease-free through the last follow-up, 19 recurred prior to five years, and ten recurred after five years. Patient characteristics that may have contributed to survival were examined. Procedures performed included five trisegmentectomies, 32 lobectomies, 16 left lateral segmentectomies, and 45 wedge resections. The margin of resection was recorded in 27 patients, one of whom had a positive margin, nine of whom had a less than or equal to 1-cm margin, and 17 of whom had a greater than 1-cm margin. Eighty-one patients had a solitary metastasis to the liver, 11 patients had two metastases, one patient had three metastases, and four patients had four metastases. Thirty patients had Stage C primary carcinoma, 40 had Stage B primary carcinoma, and one had Stage A primarycarcinoma. The disease-free interval from the time of colon resection to the time of liver resection was less than one year in 65 patients, and greater than one year in 34 patients. Three patients had bilobar metastases. Four of the patients had extrahepatic disease resected simultaneously with the liver resection. Though several contraindications to hepatic resection have been proposed in the past, five-year survival has been found in patients with extrahepatic disease resected simultaneously, patients with bilobar metastases, patients with multiple metastases, and patients with positive margins. Five-year disease-free survivors are also present in each of these subsets. It is concluded that five-year survival is possible in the presence of reported contraindications to resection, and therefore that the decision to resect the liver must be individualized. © 1988 American Society of Colon and Rectal Surgeons

Laser drilling of microholes in single crystal silicon using continuous wave (CW) 1070 nm fiber lasers with millisecond pulse widths

The laser microdrilling of via holes in Si semiconductor wafers was studied using 1 ms pulses from an Yb fibre laser with 1070 nm wavelength. Optical microscopy and cross‑sectional analysis were used to quantify hole dimensions, the distribution of recast material and any microcracking for both (100) and (111) single crystal surface semiconductor wafer orientations. The flexibility of this laser wavelength and simple pulsing scheme were demonstrated for a range of semiconductor substrates of narrow and wide bandgap including InSb, GaSb, InAs, GaAs, InP and sapphire. Detailed observations for Si showed that, between the threshold energies for surface melting and the irradiance for drilling a “thru” hole from the front surface to rear surface, there was a range of irradiances for which microcracking occurred near the hole circumference. The directionality and lengths of these microcracks were studied for the (100) and (111) orientations and possible mechanisms for formation were discussed, including the Griffith criterion for microcracks and the failure mechanism of fatigue usually applied to welding of metals. Above the irradiance for formation of a thru hole, few cracks were observed. Future work will compare similar observations and measurements in other narrow- and wide-bandgap semiconductor wafer substrates

Investigating the effect of sintering rate and solvent type on the liquid transport kinetics of α-alumina powder compacts

The ceramic materials' properties and the penetrating liquid both influence liquid transport into ceramic catalytic materials. Terahertz pulsed imaging (TPI) in combination with a flow cell was used to investigate the transport process of polar and less polar solvents into a range of α-alumina powder compacts. The TPI results show that the alumina samples with the largest heating rate (200 °C h−1) have the fastest water transport. The TPI results also reveal that 1-octanol takes much longer to transport through the alumina samples than water, as the viscosity of 1-octanol is much larger than that of water. Since 1-octanol is semi-transparent to terahertz radiation, it was possible to study the liquid transport process and the structural changes behind the liquid front, such as the change in the refractive index of the compact and the fill fraction of 1-octanol in the compact as a function of time

Conductance Ratios and Cellular Identity

Recent experimental evidence suggests that coordinated expression of ion channels plays a role in constraining neuronal electrical activity. In particular, each neuronal cell type of the crustacean stomatogastric ganglion exhibits a unique set of positive linear correlations between ionic membrane conductances. These data suggest a causal relationship between expressed conductance correlations and features of cellular identity, namely electrical activity type. To test this idea, we used an existing database of conductance-based model neurons. We partitioned this database based on various measures of intrinsic activity, to approximate distinctions between biological cell types. We then tested individual conductance pairs for linear dependence to identify correlations. Contrary to experimental evidence, in which all conductance correlations are positive, 32% of correlations seen in this database were negative relationships. In addition, 80% of correlations seen here involved at least one calcium conductance, which have been difficult to measure experimentally. Similar to experimental results, each activity type investigated had a unique combination of correlated conductances. Finally, we found that populations of models that conform to a specific conductance correlation have a higher likelihood of exhibiting a particular feature of electrical activity. We conclude that regulating conductance ratios can support proper electrical activity of a wide range of cell types, particularly when the identity of the cell is well-defined by one or two features of its activity. Furthermore, we predict that previously unseen negative correlations and correlations involving calcium conductances are biologically plausible