Cosmological impact of redshift drift measurements

ABSTRACT The redshift drift is a model-independent probe of fundamental cosmology, but choosing a fiducial model one can also use it to constrain the model parameters. We compare the constraining power of redshift drift measurements by the Extremely Large Telescope (ELT), as studied by Liske et al., with that of two recently proposed alternatives: the cosmic accelerometer of Eikenberry et al., and the differential redshift drift of Cooke. We find that the cosmic accelerometer with a 6-yr baseline leads to weaker constraints than those of the ELT (by 60 per cent); however, with identical time baselines it outperforms the ELT by up to a factor of 6. The differential redshift drift always performs worse than the standard approach if the goal is to constrain the matter density; however, it can perform significantly better than it if the goal is to constrain the dark energy equation of state. Our results show that accurately measuring the redshift drift and using these measurements to constrain cosmological parameters are different merit functions: an experiment optimized for one of them will not be optimal for the other. These non-trivial trade-offs must be kept in mind as next-generation instruments enter their final design and construction phases.

Improved Analytical Theory of Ophthalmic Lens Design

A revisited form of the classic third-order ophthalmic lens design theory that provides a more precise and meaningful use of aspheric surfaces and a generalization of the standard oblique errors is presented. The classical third-order theory follows from the application of the Coddington equations to a ray trace through the lens and the expansion of the incidence angles and the surface sagittas appearing on them up to order two of the radial coordinate. In this work we show that the approximations for surface sagittas and angles can be decoupled, and the lens oblique powers predicted by the proposed theory provides a better fit to the numerical results obtained by exact raytracing and multi-parametric optimization than the classical third-order theory does. Modern ophthalmic lens design uses numerical optimization and exact ray tracing, but the methods presented in this paper provide a deeper understanding of the problem and its limitations. This knowledge and the more general merit functions that are also presented may help guide the numerical approaches.

Merit functions for absolute value variational inequalities

<abstract><p>This article deals with a class of variational inequalities known as absolute value variational inequalities. Some new merit functions for the absolute value variational inequalities are established. Using these merit functions, we derive the error bounds for absolute value variational inequalities. Since absolute value variational inequalities contain variational inequalities, absolute value complementarity problem and system of absolute value equations as special cases, the findings presented here recapture various known results in the related domains. The conclusions of this paper are more comprehensive and may provoke futuristic research.</p></abstract>

Depth extraction in computational integral imaging based on bilinear interpolation

We proposed a method using a merit function to determine the depth of objects in computational integral imaging by analyzing the existing methods for depth extraction of target objects. To improve the resolution of reconstructed slice images, we use a digital camera moving in horizontal and vertical direction with the set interval to get elemental images with high resolution and bilinear interpolation algorithm to increase the number of pixels in slice image which improves the resolution obviously. To show the feasibility of the proposed method, we carried out our experiment and presented the results. We also compared it with other merit functions. The results show that merit function SMD2 to determine the depth of objects is more accurate and suitable for real-time application.

Neural Network for Solving SOCQP and SOCCVI Based on Two Discrete-Type Classes of SOC Complementarity Functions

This paper focuses on solving the quadratic programming problems with second-order cone constraints (SOCQP) and the second-order cone constrained variational inequality (SOCCVI) by using the neural network. More specifically, a neural network model based on two discrete-type families of SOC complementarity functions associated with second-order cone is proposed to deal with the Karush-Kuhn-Tucker (KKT) conditions of SOCQP and SOCCVI. The two discrete-type SOC complementarity functions are newly explored. The neural network uses the two discrete-type families of SOC complementarity functions to achieve two unconstrained minimizations which are the merit functions of the Karuch-Kuhn-Tucker equations for SOCQP and SOCCVI. We show that the merit functions for SOCQP and SOCCVI are Lyapunov functions and this neural network is asymptotically stable. The main contribution of this paper lies on its simulation part because we observe a different numerical performance from the existing one. In other words, for our two target problems, more effective SOC complementarity functions, which work well along with the proposed neural network, are discovered.

Toward a signal-processing foundation for computational sensing and imaging: electro-optical basis and merit functions

We highlight the need for – and describe initial strategies to find – new digital-optical basis functions and performance merit functions to serve as a foundation for designing, analyzing, characterizing, testing, and comparing a range of computational imaging systems. Such functions will provide a firm theoretical foundation for computational sensing and imaging and enhanced design software, thereby broadly speeding the development of computational imaging systems.