Fast Reachable Set Approximations via State Decoupling Disturbances

With the recent surge of interest in using robotics and automation for civil purposes, providing safety and performance guarantees has become extremely important. In the past, differential games have been successfully used for the analysis of safety-critical systems. In particular, the Hamilton-Jacobi (HJ) formulation of differential games provides a flexible way to compute the reachable set, which can characterize the set of states which lead to either desirable or undesirable configurations, depending on the application. While HJ reachability is applicable to many small practical systems, the curse of dimensionality prevents the direct application of HJ reachability to many larger systems. To address computation complexity issues, various efficient computation methods in the literature have been developed for approximating or exactly computing the solution to HJ partial differential equations, but only when the system dynamics are of specific forms. In this paper, we propose a flexible method to trade off optimality with computation complexity in HJ reachability analysis. To achieve this, we propose to simplify system dynamics by treating state variables as disturbances. We prove that the resulting approximation is conservative in the desired direction, and demonstrate our method using a four-dimensional plane model.Comment: in Proceedings of the IEE Conference on Decision and Control, 201

Anomalous molecular orbital variation upon adsorption on wide band gap insulator

It is commonly believed that organic molecules are physisorbed on the ideal non-polar surfaces of wide band gap insulators with limited variation of the electronic properties of the adsorbate molecule. On the basis of first principles calculations within density functional theory (DFT) and $GW$ approximation, we show that this is not generally true. We find that the molecular frontier orbitals undergo significant changes when a hydroxy acid (here we chose gluconic acid) is adsorbed on MgSO$_4$$\cdot$H$_2$O(100) surface due to the complex interaction between the molecule and the insulating surface. The predicted trend of the adsorption effect on the energy gap obtained by DFT is reversed when the surface polarization effect is taken into account via the many-body corrections.Comment: 5 pages, 3 figure

Submillimeter-Wave Measurements and Analysis of the Ground and ν2 = 1 States of Water

In order to facilitate further studies of water in the interstellar medium, the envelopes of late-type stars, jets, and shocked regions, the frequencies of 17 newly measured H_2 ^(16)O transitions between 0.841 and 1.575 THz are reported. A complete update of the available water line frequencies and a detailed calculation of unmeasured rotational transitions and transition intensities as a function of temperature are presented for the ground and ν_2 = 1 state levels below 3000 cm^(-1) of excitation energy. The new terahertz transitions were measured with a recently developed laser difference frequency spectrometer. Six of these transitions arise from the ν_2 = 1 state, and the other 11 are in the ground state; all have lower state energies from 700 to 1750 cm^(-1) and should be accessible to Stratospheric Observatory For Infrared Astronomy (SOFIA) through the atmosphere. The transitions near 0.850 THz are accessible from the ground with existing receivers. Observations of the newly measured ν_2 = 1 state transitions, which include the 1_(1, 1)-0_(0, 0) fundamental at 1.2057 THz and five other very low J transitions, should provide valuable insights into role played by the ν2 = 1 state in the cooling dynamics of jets, shocks, masers, and strongly infrared-pumped regions. The line list is presented to assist in the planning of observational campaigns with the Far-Infrared Space Telescope (FIRST) and other proposed space missions with which a full suite of water observations can be carried out

A tunable cavity-locked diode laser source for terahertz photomixing

An all solid-state approach to the precise frequency synthesis and control of widely tunable terahertz radiation by differencing continuous-wave diode lasers at 850 nm is reported in this paper. The difference frequency is synthesized by three fiber-coupled external-cavity laser diodes. Two of the lasers are Pound-Drever-Hall locked to different orders of a Fabry-Perot (FP) cavity, and the third is offset-frequency locked to the second of the cavity-locked lasers using a tunable microwave oscillator. The first cavity-locked laser and the offset-locked laser produce the difference frequency, whose value is accurately determined by the sum of an integer multiple of the free spectral range of the FP cavity and the offset frequency. The dual-frequency 850-nm output of the three laser system is amplified to 500 mW through two-frequency injection seeding of a single semiconductor tapered optical amplifier. As proof of precision frequency synthesis and control of tunability, the difference frequency is converted into a terahertz wave by optical-heterodyne photomixing in low-temperature-grown GaAs and used for the spectroscopy of simple molecules. The 3-dB spectral power bandwidth of the terahertz radiation is routinely observed to be ≾1 MHz. A simple, but highly accurate, method of obtaining an absolute frequency calibration is proposed and an absolute calibration of 10^(-7) demonstrated using the known frequencies of carbon monoxide lines between 0.23-1.27 THz

A High Power Frequency-Stabilized Tunable Two-Frequency Diode Laser System for the Generation of Coherent THz-Waves by Photomixing

A tunable two-frequency high-power diode laser system at 850 nm for terahertz (Thz)-wave generation by photomixing in low-temperature-grown GaAs photo-conductors has been developed. The difference frequency is obtained through a three laser system, where two lasers are locked to different orders of a Fabry-Perot cavity and a third is offset-locked to the first, The difference-frequency signal is generated by the offset laser and the other cavity-locked laser. The spectral purity of the beat note is better than 1 MHz. The maximum output power of -500 mW was obtained by using the master oscillator power amplifier (MOPA) technique, simultaneous injection of two seed frequencies with a single semiconductor optical amplifier. Here we report the generation of THz waves and spectroscopy of acetonitrile as proof of concept

Diffusion runs low on persistence fast

Interpreting an image as a function on a compact sub- set of the Euclidean plane, we get its scale-space by diffu- sion, spreading the image over the entire plane. This gener- ates a 1-parameter family of functions alternatively defined as convolutions with a progressively wider Gaussian ker- nel. We prove that the corresponding 1-parameter family of persistence diagrams have norms that go rapidly to zero as time goes to infinity. This result rationalizes experimental observations about scale-space. We hope this will lead to targeted improvements of related computer vision methods