Proximal Algorithms for Discrete-Level Phase-Shifting Mask Design with Application to Optogenetics

This work studies the problem of designing computer-generated holograms using phase-shifting masks limited to represent only a small number of discrete phase levels. This problem has various applications, notably in the emerging field of optogenetics and lithography. A novel regularized cost function is proposed for the problem at hand that penalizes the unfeasible phase levels. Since the proposed cost function is non-smooth, we derive proper proximal gradient algorithms for its minimization. Simulation results, considering an optogenetics application, demonstrate that the proposed proximal gradient algorithm yields better performance as compared to other algorithms proposed in the literature.

Nucleation and Growth of Lattice Crystals

A variational lattice model is proposed to define an evolution of sets from a single point (nucleation) following a criterion of “maximization” of the perimeter. At a discrete level, the evolution has a “checkerboard” structure and its shape is affected by the choice of the norm defining the dissipation term. For every choice of the scales, the convergence of the discrete scheme to a family of expanding sets with constant velocity is proved.

The Three Levels of Law’s Goodness and then One More: Exploring John Finnis’s Account of Good Juridical Reasons for Action

The article revisits, in the first section, the core arguments of John Finnis’s account of law’s «goodness». Having established that the premises of these arguments are situated in Finnis’s theses on what constitutes good juridical reasons for action, and on law’s «double life», the three levels of law’s goodness are explored in detail. In the second section, the author argues that Aquinas’s juridical philosophy contains another discrete level of juridical goodness relevant to law. This level is then presented along with a critical assessment of its harmony with Finnis’s theory.

Energy Levels in Nanowires and Nanorods with a Finite Potential Well

The energy of electrons and holes in cylindrical quantum wires with a finite potential well was calculated by two methods. An analytical expression is approximately determined that allows one to calculate the energy of electrons and holes at the first discrete level in a cylindrical quantum wire. The electron energy was calculated by two methods for cylindrical layers of different radius. In the calculations, the nonparabolicity of the electron energy spectrum is taken into account. The dependence of the effective masses of electrons and holes on the radius of a quantum wires is determined. An analysis is made of the dependence of the energy of electrons and holes on the internal and external radii, and it is determined that the energy of electrons and holes in cylindrical layers with a constant thickness weakly depends on the internal radius. The results were obtained for the InP/InAs heterostructures.

Quasi-overlapping Semi-discrete Schwarz Waveform Relaxation Algorithms: The Hyperbolic Problem

The Schwarz waveform relaxation (SWR) algorithms have many favorable properties and are extensively studied and investigated for solving time dependent problems mainly at a continuous level. In this paper, we consider a semi-discrete level analysis and we investigate the convergence behavior of what so-called semi-discrete SWR algorithms combined with discrete transmission conditions instead of the continuous ones. We shall target here the hyperbolic problems but not the parabolic problems that are usually considered by most of the researchers in general when investigating the properties of the SWR methods. We first present the classical overlapping semi-discrete SWR algorithms with different partitioning choices and show that they converge very slow. We then introduce optimal, optimized, and quasi optimized overlapping semi-discrete SWR algorithms using new transmission conditions also with different partitioning choices. We show that the new algorithms lead to a much better convergence through using discrete transmission conditions associated with the optimized SWR algorithms at the semi-discrete level. In the performed semi-discrete level analysis, we also demonstrate the fact that as the ratio between the overlap size and the spatial discretization size gets bigger, the convergence factor gets smaller which results in a better convergence. Numerical results and experiments are presented in order to confirm the theoretical aspects of the proposed algorithms and providing an evidence of their usefulness and their accuracy.

An adaptive Cahn-Hilliard equation for enhanced edges in binary image inpainting

We consider the Cahn-Hilliard equation for solving the binary image inpainting problem with emphasis on the recovery of low-order sets (edges, corners) and enhanced edges. The model consists in solving a modified Cahn-Hilliard equation by weighting the diffusion operator with a function which will be selected locally and adaptively. The diffusivity selection is dynamically adopted at the discrete level using the residual error indicator. We combine the adaptive approach with a standard mesh adaptation technique in order to well approximate and recover the singular set of the solution. We give some numerical examples and comparisons with the classical Cahn-Hillard equation for different scenarios. The numerical results illustrate the effectiveness of the proposed model.

Meanings in the Digital Age. Homo Singularity

The paper approaches the techno-humanitarian balance of physical (accelerating) and humanitarian (controlling) technologies. It demonstrates that the absence of the human in this ba­lance makes the idea about ensuring the socio-system’s sustainable development through the establishment of techno-humanitarian balance erroneous. The required adequate proportion of “powers” between the technologies in the techno-humanitarian balance necessitates the civilization to attempt to “harness” not only the technological singularity but the humanitarian singularity, too. It is shown that the techno-humanitarian balance in the singularity mode destroys the human physical and mental nature. The human is introduced into the binary technological balance through transforming it into a triple balance and adding the semantic technologies inherent to human beings. The triple balance is characterized by the oppositions between intelligence and thinking, information and meanings. The paper explores the triple balance and its edges in the context of the ultimate singularity. It is shown that the human being, through thinking and meanings, can correlate themselves with the semantic singularity (the infinity of the semantic field) — thus becoming Homo Singularity. These conclusions are substantiated through the V.V. Nalimov’s probabilistic model of consciousess, which also mathe­matically formalizes the process of semantic decapsulation of the personality and the personal interaction with the semantic vacuum (infinity).The paper introduces the concept of finite dilatation of the cultural semantic field and the big semantic transition as the era of formation of Homo Singula­rity and beginning of their practical work with semantic infinity. The paper provides examples of such practical work in the fields of art and science. Homo Singularity not only prevents their physical and mental nature from destruction but also keeps the po­werful artificial intelligence under control by counte­ring big data with their ability to integrate the multiple into the single (whole) and make a transition from the discrete level of information to a continuous (infinite) level of meanings.