Automatic linearity detection

Given a function, or more generally an operator, the question "Is it linear?" seems simple to answer. In many applications of scientific computing it might be worth determining the answer to this question in an automated way; some functionality, such as operator exponentiation, is only defined for linear operators, and in other problems, time saving is available if it is known that the problem being solved is linear. Linearity detection is closely connected to sparsity detection of Hessians, so for large-scale applications, memory savings can be made if linearity information is known. However, implementing such an automated detection is not as straightforward as one might expect. This paper describes how automatic linearity detection can be implemented in combination with automatic differentiation, both for standard scientific computing software, and within the Chebfun software system. The key ingredients for the method are the observation that linear operators have constant derivatives, and the propagation of two logical vectors, $\ell$ and $c$, as computations are carried out. The values of $\ell$ and $c$ are determined by whether output variables have constant derivatives and constant values with respect to each input variable. The propagation of their values through an evaluation trace of an operator yields the desired information about the linearity of that operator

The high-frequency backscattering angular response of gassy sediments: Model/data comparison from the Eel River Margin, California

A model for the high-frequency backscatter angular response of gassy sediments is proposed. For the interface backscatter contribution we adopted the model developed by Jackson et al. @J. Acoust. Soc. Am. 79, 1410–1422 ~1986!#, but added modifications to accommodate gas bubbles. The model parameters that are affected by gas content are the density ratio, the sound speed ratio, and the loss parameter. For the volume backscatter contribution we developed a model based on the presence and distribution of gas in the sediment. We treat the bubbles as individual discrete scatterers that sum to the total bubble contribution. This total bubble contribution is then added to the volume contribution of other scatters. The presence of gas affects both the interface and the volume contribution of the backscatter angular response in a complex way that is dependent on both grain size and water depth. The backscatter response of fine-grained gassy sediments is dominated by the volume contribution while that of coarser-grained gassy sediments is affected by both volume and interface contributions. In deep water the interface backscatter is only slightly affected by the presence of gas while the volume scattering is strongly affected. In shallow water the interface backscatter is severely reduced in the presence of gas while the volume backscatter is only slightly increased. Multibeam data acquired offshore northern California at 95 kHz provides raw measurements for the backscatter as a function of grazing angle. These raw backscatter measurements are then reduced to scattering strength for comparison with the results of the proposed model. The analysis of core samples at various locations provides local measurements of physical properties and gas content in the sediments that, when compared to the model, show general agreement

Blood volume changes

Analysis of radionuclide volume determinations made for the crewmembers of selected Gemini and Apollo missions showed that orbital spaceflight has an effect on red cell mass. Because the methods and the protocol developed for earlier flights were used for the crews of the three Skylab missions, direct comparisons are possible. After each Skylab mission, decreases were found in crewmembers' red cell masses. The mean red cell mass decrease of 11 percent or 232 milliliters was approximately equal to the 10 percent mean red cell mass decrease of the Apollo 14 to 17 crewmembers. The red cell mass drop was greatest and the postrecovery reticulocyte response least for crewmembers of the 28-day Skylab 2 mission. Analyses of data from the red cell mass determinations indicate that the red cell mass drops occurred in the first 30 days of flight and that a gradual recovery of the red cell mass deficits began approximately 60 days after launch. The beginning of red cell mass regeneration during the Skylab 4 flight may explain the higher postmission reticulocyte counts

In Situ Treatment of a Scanning Gate Microscopy Tip

In scanning gate microscopy, where the tip of a scanning force microscope is used as a movable gate to study electronic transport in nanostructures, the shape and magnitude of the tip-induced potential are important for the resolution and interpretation of the measurements. Contaminations picked up during topography scans may significantly alter this potential. We present an in situ high-field treatment of the tip that improves the tip-induced potential. A quantum dot was used to measure the tip-induced potential.Comment: 3 pages, 1 figure, minor changes to fit published versio

The chebop system for automatic solution of differential equations

In MATLAB, it would be good to be able to solve a linear differential equation by typing u = L\f, where f, u, and L are representations of the right-hand side, the solution, and the differential operator with boundary conditions. Similarly it would be good to be able to exponentiate an operator with expm(L) or determine eigenvalues and eigenfunctions with eigs(L). A system is described in which such calculations are indeed possible, based on the previously developed chebfun system in object-oriented MATLAB. The algorithms involved amount to spectral collocation methods on Chebyshev grids of automatically determined resolution

Time-Resolved Detection of Individual Electrons in a Quantum Dot

We present measurements on a quantum dot and a nearby, capacitively coupled, quantum point contact used as a charge detector. With the dot being weakly coupled to only a single reservoir, the transfer of individual electrons onto and off the dot can be observed in real time in the current signal from the quantum point contact. From these time-dependent traces, the quantum mechanical coupling between dot and reservoir can be extracted quantitatively. A similar analysis allows the determination of the occupation probability of the dot states.Comment: 3 pages, 3 figure

Finite bias charge detection in a quantum dot

We present finite bias measurements on a quantum dot coupled capacitively to a quantum point contact used as a charge detector. The transconductance signal measured in the quantum point contact at finite dot bias shows structure which allows us to determine the time-averaged charge on the dot in the non-blockaded regime and to estimate the coupling of the dot to the leads.Comment: 6 pages, 4 figure