Outsourcing with Heterogeneous Firms

A general framework for the study of outsourcing is introduced that incorporates dynamics and heterogeneity among both upstream and downstream producers to mimic an exit approach (Hirschman, 1970) to building vertical relations. The environment is one of search friction and incomplete contracts, where final-good producers require a specialized input and, upon matching with a supplier, can only contract the quantity of input. The results imply an assorted matching between producers and suppliers, so that more productive producers pair with more productive suppliers in the long run. It is shown that most efficient producers have some propensity to outsource, but only when there is a thick enough density of highly productive suppliers. Average employment in this model might increase or decrease with outsourcing, which is an observed pattern in the data. Some other diversities in plant-level behavior are also present in the results.Outsourcing; Productivity; Heterogeneity; Search Friction; Incomplete Contracts; Exit Strategy

Bessel Filter Analysis

In this technical report, we prove two fundamental theorems for an edge detection algorithm based on a Bessel filter. These theorems are bases of a scale invariant feature extraction method in which extracted features are independent of scale

Discontinuity Preserving Noise Removal Method based on Anisotropic Diffusion for Band Pass Signals

nonlinear discontinuity-preserving method for noise removal for band pass signals such as signals modulated with Binary Phase-Shift Keying (BPSK) modulation is proposed in this paper. This method is inspired by the anisotropic diffusion algorithm to remove noise and preserve discontinuities in band pass signals modulated with a single frequency. It is demonstrated here that nonlinear noise removal method for a real valued band pass signal requires a solution for a nonlinear partial differential equation which is of fourth order in space and second order in time. The results presented in this work show better performance in nonlinear noise removal for real valued band pass signals in comparison with the previous work in the literature

Single-mode and single-polarization photonics with anchored-membrane waveguides

An integrated photonic platform with anchored-membrane structures, the T-Guide, is proposed and numerically investigated. These compact air-clad structures have high index contrast and are much more stable than prior membrane-type structures. Their semi-infinite geometry enables single-mode and single-polarization (SMSP) operation over unprecedented bandwidths. Modal simulations quantify this behavior, showing that an SMSP window of 2.75 octaves (1.2 - 8.1 {\mu}m) is feasible for silicon T-Guides, spanning almost the entire transparency range of silicon. Dispersion engineering for T-Guides yields broad regions of anomalous group velocity dispersion, rendering them a promising platform for nonlinear applications, such as wideband frequency conversion

A nonlinear variational method for signal segmentation and reconstruction using level set algorithm

A nonlinear functional is considered in this letter for segmentation and noise removal of piecewise continuous signals containing binary information contaminated with Gaussian noise. A discontinuity is defined as points in time scale that separates two signal segments with different amplitude spectra. Segmentation and noise removal of a piecewise continuous signal are obtained by deriving equations minimising the nonlinear functional. An algorithm based on the level set method is employed to implement the solutions minimising the functional. The proposed method is robust in noisy signals and can avoid local minima

Geometrical-based algorithm for variational segmentation and smoothing of vector-valued images

An optimisation method based on a nonlinear functional is considered for segmentation and smoothing of vector-valued images. An edge-based approach is proposed to initially segment the image using geometrical properties such as metric tensor of the linearly smoothed image. The nonlinear functional is then minimised for each segmented region to yield the smoothed image. The functional is characterised with a unique solution in contrast with the Mumford–Shah functional for vector-valued images. An operator for edge detection is introduced as a result of this unique solution. This operator is analytically calculated and its detection performance and localisation are then compared with those of the DroGoperator. The implementations are applied on colour images as examples of vector-valued images, and the results demonstrate robust performance in noisy environments

Scale Space Smoothing, Image Feature Extraction and Bessel Filters

The Green function of Mumford-Shah functional in the absence of discontinuities is known to be a modified Bessel function of the second kind and zero degree. Such a Bessel function is regularized here and used as a filter for feature extraction. It is demonstrated in this paper that a Bessel filter does not follow the scale space smoothing property of bounded linear filters such as Gaussian filters. The features extracted by the Bessel filter are therefore scale invariant. Edges, blobs, and junctions are features considered here to show that the extracted features remain unchanged by varying the scale of a Bessel filter. The scale invariance property of Bessel filters for edges is analytically proved here. We conjecture that Bessel filters also enjoy this scale invariance property for other kinds of features. The experimental results presente

Contour evolution scheme for variational image segmentation and smoothing

An algorithm, based on the Mumford–Shah (M–S) functional, for image contour segmentation and object smoothing in the presence of noise is proposed. However, in the proposed algorithm, contour length minimisation is not required and it is demonstrated that the M–S functional without contour length minimisation becomes an edge detector. Optimisation of this nonlinear functional is based on the method of calculus of variations, which is implemented by using the level set method. Fourier and Legendre’s series are also employed to improve the segmentation performance of the proposed algorithm. The segmentation results clearly demonstrate the effectiveness of the proposed approach for images with low signal-to-noise ratios

Nonlinear optimisation method for image segmentation and noise reduction using geometrical intrinsic properties

This paper considers the optimisation of a nonlinear functional for image segmentation and noise reduction. Equations optimising this functional are derived and employed to detect edges using geometrical intrinsic properties such as metric and Riemann curvature tensor of a smooth differentiable surface approximating the original image. Images are then smoothed using a Helmholtz type partial differential equation. The proposed approach is shown to be very efficient and robust in the presence of noise, and the reported results demonstrate better performance than the conventional derivative based edge detectors

Signal segmentation and denoising algorithm based on energy optimisation

A nonlinear functional is considered in this short communication for time interval segmentation and noise reduction of signals. An efficient algorithm that exploits the signal geometrical properties is proposed to optimise the nonlinear functional for signal smoothing. Discontinuities separating consecutive time intervals of the original signal are initially detected by measuring the curvature and arc length of the smoothed signal. The nonlinear functional is then optimised for each time interval to achieve noise reduction of the original noisy signal. This algorithm exhibits robustness for signals characterised by very low signal to noise ratios