Balancing and model reduction for discrete-time nonlinear systems based on Hankel singular value analysis

This paper is concerned with balanced realization and model reduction for discrete-time nonlinear systems. Singular perturbation type balanced truncation method is proposed. In this procedure, the Hankel singular values and the related controllability and observability properties are preserved, which is a natural generalization of both the linear discrete-time case and the nonlinear continuous-time case.

High magnitude and rapid incision from river capture: Rhine River, Switzerland

Landscape evolution is controlled by the development and organization of drainage basins. As a landscape evolves, drainage reorganization events can occur via river capture or piracy, whereby one river basin grows at the expense of another. The river downstream of a capture location will generate a transient topographic response as the added water discharge increases sediment transport and erosion efficiency. This erosional response will propagate upstream through both the captured and original river basins. Here we focus on quantifying the impact of drainage reorganization along the Rhine/Aare River system (~45,000 km 2 ) during the late Pliocene/early Pleistocene, where gravel remnants indicate total incision of ~650 m during the last ~4.2 Myr in the region of the recent Aare‐Rhine confluence. We develop a numerical model of drainage capture to quantify the range of possible magnitudes of erosion and the transient river response resulting from the reorganization of the Rhine River. The model accounts for both fluvial incision and sediment transport. Our model estimates 400–800 m of river elevation change (lowering profiles) during the last ~4 Myr due to river capture events, providing an important component to the recent exhumation budget of the Swiss Alpine Foreland. The model indicates a rapid response to capture events (re‐equilibration timescale of ~1 Myr). The predicted incision magnitudes are consistent with incision measured from the elevation of Pliocene and early Pleistocene river gravels, suggesting that across northern Switzerland, a significant amount of incision can be explained by drainage reorganization. Key Points Drainage capture has caused significant erosion along the Rhine River The transient erosional wave propagates quickly through the landscape The incision is a significant fraction of Plio‐Pleistocene erosion in the regionPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/99064/1/jgrf20056.pd

Transverse thermal depinning and nonlinear sliding friction of an adsorbed monolayer

We study the response of an adsorbed monolayer under a driving force as a model of sliding friction phenomena between two crystalline surfaces with a boundary lubrication layer. Using Langevin-dynamics simulation, we determine the nonlinear response in the direction transverse to a high symmetry direction along which the layer is already sliding. We find that below a finite transition temperature, there exist a critical depinning force and hysteresis effects in the transverse response in the dynamical state when the adlayer is sliding smoothly along the longitudinal direction.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let

Cognitive facilitation following intentional odor exposure

This paper reviews evidence that, in addition to incidental olfactory pollutants, intentional odor delivery can impact cognitive operations both positively and negatively. Evidence for cognitive facilitation/interference is reviewed alongside four potential explanations for odor-induced effects. It is concluded that the pharmacological properties of odors can induce changes in cognition. However, these effects can be accentuated/attenuated by the shift in mood following odor exposure, expectancy of cognitive effects, and cues to behavior via the contextual association with the odor. It is proposed that greater consideration is required in the intentional utilization of odors within both industrial and private locations, since differential effects are observed for odors with positive hedonic qualities

Del Pezzo surfaces with 1/3(1,1) points

We classify del Pezzo surfaces with 1/3(1,1) points in 29 qG-deformation families grouped into six unprojection cascades (this overlaps with work of Fujita and Yasutake), we tabulate their biregular invariants, we give good model constructions for surfaces in all families as degeneracy loci in rep quotient varieties and we prove that precisely 26 families admit qG-degenerations to toric surfaces. This work is part of a program to study mirror symmetry for orbifold del Pezzo surfaces.Comment: 42 pages. v2: model construction added of last remaining surface, minor corrections, minor changes to presentation, references adde

What is the evidence for giving chemoprophylaxis to children or students attending the same preschool, school or college as a case of meningococcal disease?

We performed a systematic literature review to assess the effectiveness of chemoprophylaxis for contacts of sporadic cases of invasive meningococcal disease (IMD) in educational settings. No studies directly compared IMD risk in contacts with/without chemoprophylaxis. However, compared to the background incidence, an elevated IMD risk was identified in settings without a general recommendation for chemoprophylaxis in pre-schools [pooled risk difference (RD) 58·2/10⁵, 95% confidence interval (CI) 27·3-89·0] and primary schools (pooled RD 4·9/10⁵, 95% CI 2·9-6·9) in the ~30 days after contact with a sporadic IMD case, but not in other educational settings. Thus, limited but consistent evidence suggests the risk of IMD in pre-school contacts of sporadic IMD cases is significantly increased above the background risk, but lower than in household contacts (pooled RD for household contacts with no chemoprophylaxis vs. background incidence: 480·1/10⁵, 95% CI 321·5-639·9). We recommend chemoprophylaxis for pre-school contacts depending on an assessment of duration and closeness of contact

Anisotropic Local Stress and Particle Hopping in a Deeply Supercooled Liquid

The origin of the microscopic motions that lead to stress relaxation in deeply supercooled liquid remains unclear. We show that in such a liquid the stress relaxation is locally anisotropic which can serve as the driving force for the hopping of the system on its free energy surface. However, not all hopping are equally effective in relaxing the local stress, suggesting that diffusion can decouple from viscosity even at local level. On the other hand, orientational relaxation is found to be always coupled to stress relaxation.Comment: 4 pages, 3 figure

Boundary lubrication properties of materials with expansive freezing

We have performed molecular dynamics simulations of solid-solid contacts lubricated by a model fluid displaying many of the properties of water, particularly its expansive freezing. Near the region where expansive freezing occurs, the lubricating film remains fluid, and the friction force decreases linearly as the shear velocity is reduced. No sign of stick-slip motion is observed even at the lowest velocities. We give a simple interpretation of these results, and suggest that in general good boundary lubrication properties will be found in the family of materials with expansive freezing.Comment: Version to appear in Phys. Rev. Let

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