Abstracting Continuous Nonpolynomial Dynamical Systems

The reachability problem, whether some unsafe state can be reached, is known to be undecidable for nonlinear dynamical systems. However, finite-state abstractions have successfully been used for safety verification. This paper presents a method for automatically abstracting nonpolynomial systems that do not have analytical or closed form solutions. The abstraction is constructed by splitting up the state-space using nonpolynomial Lyapunov functions. These functions place guarantees on the behaviour of the system without requiring the explicit calculation of trajectories. MetiTarski, an automated theorem prover for special functions (sin, cos, sqrt, exp) is used to identify possible transitions between the abstract states. The resulting finite-state system is perfectly suited for verification by a model checker

Automated Real Proving in PVS via MetiTarski

This paper reports the development of a proof strategy that integrates the MetiTarski theorem prover as a trusted external decision procedure into the PVS theorem prover. The strategy automatically discharges PVS sequents containing real-valued formulas, including transcendental and special functions, by translating the sequents into first order formulas and submitting them to MetiTarski. The new strategy is considerably faster and more powerful than other strategies for nonlinear arithmetic available to PVS

Towards the automated modelling and formal verification of analog designs

The verification of analog circuits remains a very time consuming and expensive part of the design process. Complete simulation of the state space is not possible; a line is drawn by the designer when it is deemed that enough sets of inputs and outputs have been covered and therefore the circuit is "verified". Unfortunately, bugs could still exist and for safety critical applications this is not acceptable. As well, a bug in the design could lead to costly recalls and a loss of revenue. Formal methods, which use mathematical logic to prove correctness of a design have been developed. However, available techniques for the formal verification of analog circuits are plagued by inaccuracies and a high level of user effort and interaction. We propose in this thesis a complete methodology for the modelling and formal verification of analog circuits. Bond graphs, which are based on the flow of power, are used to automatically extract the circuit's system of Ordinary Differential Equations. Subsequently, two formal verification methods, one based on automated theorem proving with MetiTarski, the other on predicate abstraction based model checking with HybridSal, are then used to verify functional properties on the extracted models. The methodology proposed is mechanical in nature and can be made completely automated. We apply this modelling and verification methodology on a set of analog designs that exhibit complex non-linear behaviour

Transient extreme ultraviolet measurement of element-specific charge transfer dynamics in multiple-material junctions

The absorption of solid state materials in complex photonic and optoelectronic devices overlap in the visible spectrum. Due to the overlap of spectral features, ultrafast measurements of charge carrier dynamics and transport is obscured. Here, the element specificity of transient extreme ultraviolet (XUV) spectroscopy is advanced as a probe for studying photoexcited charge transport in multiple-material junctions. The core-hole excited by the XUV transitions also imparts structural information on to the probed electronic transition. Transient XUV can therefore measure electron and averaged phonon dynamics for each elemental species in a junction. Application to polaron measurement in α-Fe_2O_3, valley-specific scattering in Si, and charge transfer in a nanoscale Ni-TiO_2-Si junction will be discussed

The Birth of PICL: New Laboratory Experiments for Understanding Ocean Worlds

A laboratory set up was built analogous to that of the environment of the Galilean system. Previous work has focused on vapor deposition and shied away from bulk samples which more closely resemble the surface of Europa. The focus of this research has been the relationship between laboratory data to observational spectra collected. Data from various telescopes has given an indication of the species which exist on the surface of Europa. Linear spectral modeling has not been effective in identifying these species due to a lack of viable candidates. Chapter II focuses on the instrumentation and sample preparation for the laboratory set up. In Chapter III data is presented on the irradiation of sodium chloride at Europa like conditions and the features that arise with cryogenic irradiation. This data is compared to observational data from HST and provides strong evidence for the presences of sodium chloride (NaCl) on Europa's leading hemisphere. Chapter IV presents FTIR and UV/VIS data for the irradiation of sulfate salts suspected to be present on Europa. This presents one of the first instances of cyrogenic electron irradiation of sulfates compared to new data from JWST. Mechanisms for the trapping of carbon dioxide at both Europa and Ganymede have also been investigated. These experiments are paramount for understanding the composition of Europa’s ocean and can be utilized by the Europa Clipper team. Future experiments involving laboratory spectroscopy of carbon dioxide trapping are also highlighted. The use of cyrogenic gamma irradiation experiments and their feasibility are explored

Integrating Abstraction Techniques for Formal Verification of Analog Designs

The verification of analog designs is a challenging and exhaustive task that requires deep understanding of physical behaviours. In this paper, we propose a qualitative based predicate abstraction method for the verification of a class of non-linear analog circuits. In the proposed method, system equations are automatically extracted from a circuit diagram by means of a bond graph. Verification is applied based on combining techniques from constraint solving and computer algebra along with symbolic model checking. Our methodology has the advantage of avoiding exhaustive simulation normally encountered in the verification of analog designs. To this end, we have used Dymola, Hsolver, SMV and Mathematica to implement the verification flow. We illustrate the methodology on several analog examples including Colpitts and tunnel diode oscillators

Transient extreme ultraviolet measurement of element-specific charge transfer dynamics in multiple-material junctions

The absorption of solid state materials in complex photonic and optoelectronic devices overlap in the visible spectrum. Due to the overlap of spectral features, ultrafast measurements of charge carrier dynamics and transport is obscured. Here, the element specificity of transient extreme ultraviolet (XUV) spectroscopy is advanced as a probe for studying photoexcited charge transport in multiple-material junctions. The core-hole excited by the XUV transitions also imparts structural information on to the probed electronic transition. Transient XUV can therefore measure electron and averaged phonon dynamics for each elemental species in a junction. Application to polaron measurement in α-Fe_2O_3, valley-specific scattering in Si, and charge transfer in a nanoscale Ni-TiO_2-Si junction will be discussed

Influence of turbulent advection on a phytoplankton ecosystem with nonuniform carrying capacity

In this work we study a plankton ecosystem model in a turbulent flow. The plankton model we consider contains logistic growth with a spatially varying background carrying capacity and the flow dynamics are generated using the two-dimensional (2D) Navier-Stokes equations. We characterize the system in terms of a dimensionless parameter, γ TB / TF, which is the ratio of the ecosystem biological time scales TB and the flow time scales TF. We integrate this system numerically for different values of γ until the mean plankton reaches a statistically stationary state and examine how the steady-state mean and variance of plankton depends on γ. Overall we find that advection in the presence of a nonuniform background carrying capacity can lead to very different plankton distributions depending on the time scale ratio γ. For small γ the plankton distribution is very similar to the background carrying capacity field and has a mean concentration close to the mean carrying capacity. As γ increases the plankton concentration is more influenced by the advection processes. In the largest γ cases there is a homogenization of the plankton concentration and the mean plankton concentration approaches the harmonic mean, 1/K -1. We derive asymptotic approximations for the cases of small and large γ. We also look at the dependence of the power spectra exponent, β, on γ where the power spectrum of plankton is k-β. We find that the power spectra exponent closely obeys β=1+2/γ as predicted by earlier studies using simple models of chaotic advection

Integrating Abstraction Techniques for Formal Verification of Analog Designs

The verification of analog designs is a challenging and exhaustive task that requires deep understanding of physical behaviours. In this paper, we propose a qualitative based predicate abstraction method for the verification of a class of non-linear analog circuits. In the proposed method, system equations are automatically extracted from a circuit diagram by means of a bond graph. Verification is applied based on combining techniques from constraint solving and computer algebra along with symbolic model checking. Our methodology has the advantage of avoiding exhaustive simulation normally encountered in the verification of analog designs. To this end, we have used Dymola, Hsolver, SMV and Mathematica to implement the verification flow. We illustrate the methodology on several analog examples including Colpitts and tunnel diode oscillators

The effectiveness of chemotherapy for treatment of high grade astrocytoma in children: Results of a randomized trial

Fifty-eight patients with high-grade astrocytoma were treated by members of the Childrens Cancer Study Group in a prospective randomized trial designed to study the effectiveness of chemotherapy as an adjuvant to standard surgical treatment and radiotherapy. Following surgical therapy, patients were assigned randomly to radiotherapy with or without chemotherapy consisting of chloroethyl-cyclohexyl nitrosourea, vincristine, and prednisone. Treatment with chemotherapy prolonged survival and event-free survival. Five-year event-free survival was 46% for patients in the radiotherapy and chemotherapy group, and 18% for patients in the radiotherapy-alone group. Five-year survival was similarly improved. The differences in outcome due to treatment were statistically significant after correcting for imbalances in important prognostic factors (event-free survival, p = 0.026; survival, p = 0.067). The presence of mitoses or necrosis in the tumor specimen was associated with poorer outcome. Patients whose initial surgery was limited to biopsy, and patients with basal ganglia lesions, also had significantly worse outcome. Chemotherapy administered at the time of recurrence in a small number of patients did not produce any long-term survivors. This study is to our knowledge the only randomized trial to investigate effectiveness of chemotherapy in the treatment of high-grade astrocytoma in children.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45395/1/11060_2004_Article_BF00165101.pd