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This report seeks to explore some of the reasons Sweden developed an independent school sector dominated by for-profit schools by drawing on prior scholarship and reports as well interview material from Swedish school entrepreneurs, researchers, and prior public representatives that helped create and implement the Swedish voucher program. This report is based on a descriptive qualitatively-oriented, research approach drawing on archival material, public data, and information gathered from interviews with key informants. The implementation of the Swedish voucher program appears to have been propelled by an appetite for change, and quest for greater diversity among educational providers, that had taken root in political parties on both the left and right. Today, however, the situation looks rather different as debates regarding inequality, segregation, grade inflation, and the notion of "vinster i välfärden" (profits in welfare services) have shifted the perception and opinions regarding school vouchers, and for-profit voucher schools in particular. We do not want to speculate what is going to happen, but it seems feasible to assume that future for-profit school entrepreneurs will have to operate, and be willing to accept, a very different public and political climate when it comes to the role of for-profit providers in the Swedish school sector. If the U.S. desires to increase the number of for-profit school entrepreneurs it will require substantial revisions of many formal as well as informal institutions. The current formal institutions in most U.S. voucher systems, which typically limits who can participate combined with lower per-pupil voucher payments, would need to be altered in order make this calculus attainable and attractive enough to spur action. The following are appended: (1) Methodology; and (2) About the authors.

Mitigating the energy requirements of artificial intelligence requires novel physical substrates for computation. Phononic metamaterials have a vanishingly low power dissipation and hence are a prime candidate for green, always-on computers. However, their use in machine learning applications has not been explored due to the complexity of their design process: Current phononic metamaterials are restricted to simple geometries (e.g. periodic, tapered), and hence do not possess sufficient expressivity to encode machine learning tasks. We design and fabricate a non-periodic phononic metamaterial, directly from data samples, that can distinguish between pairs of spoken words in the presence of a simple readout nonlinearity; hence demonstrating that phononic metamaterials are a viable avenue towards zero-power smart devices., Comment: 13 pages, 11 figures

We describe a method for removing the numerical errors in the modeling of linear evolution equations that are caused by approximating the time derivative by a finite difference operator. The method is based on integral transforms realized as certain Fourier integral operators, called time dispersion transforms, and we prove that, under an assumption about the frequency content, it yields a solution with correct evolution throughout the entire lifespan. We demonstrate the method on a model equation as well as on the simulation of elastic and viscoelastic wave propagation., Comment: 41 pages, 8 figures

Since the beginnings of tomography, the requirement that the sample does not change during the acquisition of one tomographic rotation is unchanged. We derived and successfully implemented a tomographic reconstruction method which relaxes this decades-old requirement of static samples. In the presented method, dynamic tomographic data sets are decomposed in the temporal domain using basis functions and deploying an L1 regularization technique where the penalty factor is taken for spatial and temporal derivatives. We implemented the iterative algorithm for solving the regularization problem on modern GPU systems to demonstrate its practical use.

A major focus of research in the seismic industry of the past two decades has been the acquisition and subsequent separation of seismic data using multiple sources fired simultaneously. The recently introduced method of {\it signal apparition} provides a new take on the problem by replacing the random time-shifts usually employed to encode the different sources by fully deterministic periodic time-shifts. In this paper we give a mathematical proof showing that the signal apparition method results in optimally large regions in the frequency-wavenumber space where exact separation of sources is achieved. These regions are diamond-shaped and we prove that using any other method of source encoding results in strictly smaller regions of exact separation. The results are valid for arbitrary number of sources. Numerical examples for different number of sources (three resp.~four sources) demonstrate the exact recovery of these diamond-shaped regions. The theoretical proofs' implementation in the field is illustrated by the results of a conducted field test., Comment: 16 pages, 5 figures. Expanded Section 3 with an additional numerical experiment and the results of a field test. Added references

We present a new method for complex frequency estimation in several variables, extending the classical (1d) ESPRIT-algorithm. We also consider how to work with data sampled on non-standard domains (i.e going beyond multi-rectangles).

This paper considers the problem of recovering either a low rank matrix or a sparse vector from observations of linear combinations of the vector or matrix elements. Recent methods replace the non-convex regularization with $\ell_1$ or nuclear norm relaxations. It is well known that this approach can be guaranteed to recover a near optimal solutions if a so called restricted isometry property (RIP) holds. On the other hand it is also known to perform soft thresholding which results in a shrinking bias which can degrade the solution. In this paper we study an alternative non-convex regularization term. This formulation does not penalize elements that are larger than a certain threshold making it much less prone to small solutions. Our main theoretical results show that if a RIP holds then the stationary points are often well separated, in the sense that their differences must be of high cardinality/rank. Thus, with a suitable initial solution the approach is unlikely to fall into a bad local minima. Our numerical tests show that the approach is likely to converge to a better solution than standard $\ell_1$/nuclear-norm relaxation even when starting from trivial initializations. In many cases our results can also be used to verify global optimality of our method.

In this paper, robust detection, tracking and geometry estimation methods are developed and combined into a system for estimating time-difference estimates, microphone localization and sound source movement. No assumptions on the 3D locations of the microphones and sound sources are made. The system is capable of tracking continuously moving sound sources in an reverberant environment. The multi-path components are explicitly tracked and used in the geometry estimation parts. The system is based on matching between pairs of channels using GCC-PHAT. Instead of taking a single maximum at each time instant from each such pair, we select the four strongest local maxima. This produce a set of hypothesis to work with in the subsequent steps, where consistency constraints between the channels and time-continuity constraints are exploited. In the paper it demonstrated how such detections can be used to estimate microphone positions, sound source movement and room geometry. The methods are tested and verified using real data from several reverberant environments. The evaluation demonstrated accuracy in the order of few millimeters.

We revisit the classical dual ascent algorithm for minimization of convex functionals in the presence of linear constraints, and give convergence results which apply even for non-convex functionals. We describe limit points in terms of the convex envelope. We also introduce a new augmented version, which is shown to have superior convergence properties, and provide new results even for convex but non-differentiable objective functionals (as well as non-convex). The results are applied to low rank approximation of a given matrix, subject to linear constraints. In particular, letting the linear constraints enforce Hankel structure of the respective matrices, the algorithms can be applied to complex frequency estimation. We provide numerical tests in this setting.

A convex envelope for the problem of finding the best approximation to a given matrix with a prescribed rank is constructed. This convex envelope allows the usage of traditional optimization techniques when additional constraints are added to the finite rank approximation problem. Expression for the dependence of the convex envelope on the singular values of the given matrix is derived and global minimization properties are derived. The corresponding proximity operator is also studied.

The hyperbolic Radon transform is a commonly used tool in seismic processing, for instance in seismic velocity analysis, data interpolation and for multiple removal. A direct implementation by summation of traces with different moveouts is computationally expensive for large data sets. In this paper we present a new method for fast computation of the hyperbolic Radon transforms. It is based on using a log-polar sampling with which the main computational parts reduce to computing convolutions. This allows for fast implementations by means of FFT. In addition to the FFT operations, interpolation procedures are required for switching between coordinates in the time-offset; Radon; and log-polar domains. Graphical Processor Units (GPUs) are suitable to use as a computational platform for this purpose, due to the hardware supported interpolation routines as well as optimized routines for FFT. Performance tests show large speed-ups of the proposed algorithm. Hence, it is suitable to use in iterative methods, and we provide examples for data interpolation and multiple removal using this approach., Comment: 21 pages, 10 figures, 2 tables

We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic formulation of the fixed-point algorithm we show that it converges to the minimum of the convex envelope of the original objective function along with its structured matrix constraint. It often happens that this solution agrees with the solution to the original minimization problem, and we provide a simple criterium for when this is true. We also provide more general fixed-point algorithms that can be used to treat the problems of making weighted approximations by sums of exponentials given equally or unequally spaced sampling. We apply the method to the case of missing data, although optimal convergence of the fixed-point algorithm is not guaranteed in this case. However, it turns out that the method often gives perfect reconstruction (up to machine precision) in such cases. We also discuss multidimensional extensions, and illustrate how the proposed algorithms can be used to recover sums of exponentials in several variables, but when samples are available only along a curve.

Multivariate versions of the Kronecker theorem in the continuous multivariate setting has recently been published. These theorems characterize the symbols that give rise to finite rank multidimensional Hankel and Toeplitz type operators defined on general domains. In this paper we study how the additional assumption of positive semidefinite affects the characterization of the corresponding symbols, which we refer to as Carath\'eodory-Fejer type theorems. We show that these theorems become particularly transparent in the continuous setting, by providing elegant if and only if statements connecting the rank with sums of exponential functions. We also discuss how these objects can be discretized, giving rise to an interesting class of structured matrices that inherit these desirable properties from their continuous analogs. We describe how the continuous Kronecker theorem also applies to these structured matrices, given sufficient sampling. We also provide a new proof for the Carath\'eodory-Fejer theorem for block Toeplitz matrices, based on tools from tensor algebra.

The Radon transform and its adjoint, the back-projection operator, can both be expressed as convolutions in log-polar coordinates. Hence, fast algorithms for the application of the operators can be constructed by using FFT, if data is resampled at log-polar coordinates. Radon data is typically measured on an equally spaced grid in polar coordinates, and reconstructions are represented (as images) in Cartesian coordinates. Therefore, in addition to FFT, several steps of interpolation have to be conducted in order to apply the Radon transform and the back-projection operator by means of convolutions. Both the interpolation and the FFT operations can be efficiently implemented on Graphical Processor Units (GPUs). For the interpolation, it is possible to make use of the fact that linear interpolation is hard-wired on GPUs, meaning that it has the same computational cost as direct memory access. Cubic order interpolation schemes can be constructed by combining linear interpolation steps which provides important computation speedup. We provide details about how the Radon transform and the back-projection can be implemented efficiently as convolution operators on GPUs. For large data sizes, speedups of about 10 times are obtained in relation to the computational times of other software packages based on GPU implementations of the Radon transform and the back-projection operator. Moreover, speedups of more than a 1000 times are obtained against the CPU-implementations provided in the MATLAB image processing toolbox.

We consider a functional calculus for compact operators, acting on the singular values rather than the spectrum, which appears frequently in applied mathematics. Necessary and sufficient conditions for this singular value functional calculus to be Lipschitz-continuous with respect to the Hilbert-Schmidt norm are given. We also provide sharp constants., Comment: 8 pages