Stochastic relaxed inertial forward-backward-forward splitting for monotone inclusions in Hilbert spaces

Computational Optimization and Applications - We develop a globalized Proximal Newton method for composite and possibly non-convex minimization problems in Hilbert spaces. Additionally, we impose...     

Substituted cyclononatetraenes and nonafulvenes

Reaction of $\text{cis}$,$\text{cis}$,$\text{cis}$,$\text{cis}$-[9]annulene anion ($\text{1}$) with electrophiles ($\text{2a}$-$\text{d}$) leads to substituted $\text{cis}$,$\text{cis}$,$\text{cis}$,$\text{cis}$-1,3,5,7-cyclononatetraenes ($\text{3a}$-$\text{d}$) which are precursors for the preparation of 10- and 10,10′-donor-substituted nonafulvenes (e.g. $\text{7b′}$$\text{e′}$). The influence of solvent and temperature on the ¹H-nmr spectra of the nonafulvenes $\text{7b′}$-$\text{h′}$ has been investigated.     

Stochastic Mirror Descent Dynamics and Their Convergence in Monotone Variational Inequalities

We examine a class of stochastic mirror descent dynamics in the context of monotone variational inequalities (including Nash equilibrium and saddle-point problems). The dynamics under study are formulated as a stochastic differential equation, driven by a (single-valued) monotone operator and perturbed by a Brownian motion. The system’s controllable parameters are two variable weight sequences, that, respectively, pre- and post-multiply the driver of the process. By carefully tuning these parameters, we obtain global convergence in the ergodic sense, and we estimate the average rate of convergence of the process. We also establish a large deviations principle, showing that individual trajectories exhibit exponential concentration around this average.     

Czochralski's creative mistake: a milestone on the way to the Gigabit Era

Much of the rapid change in industry, science, and society is brought about by the meteoric development of the microelectronics industry. Daily life is affected by this development; one has only to think of mobile telephones and the chips on modern credit cards. The raw material for microelectronics is the single crystal of silicon, with very high purity and almost perfect crystal structure. About 95% of the world's current production of silicon single crystals is achieved using the process that Jan Czochralski discovered in 1916. Today, single crystals of silicon can be grown that are up to 2 m long, 300 mm in diameter, and weigh up to 265 kg. The use of magnetic fields has led to significant advances in crystal-drawing technology. Intensive research and development reveals that in addition to the technology, which provides crystals of ever-increasing diameter, defect engineering, and the control of the numerous temperature-dependent reactions of crystal defects, are of paramount importance.     

100 Jahre Einkristallzucht aus der Schmelze

Cars, television, mobile phones, digital cameras, cash machines: Daily life is strongly affected by microchips produced from high purity silicon single crystals via thin wafers. Most of these single crystals are prepared by a process invented by the German‐Polish scientist Jan Czochralski in 1916 in the “Kabelwerk Oberspree (KWO)” of the “Allgemeine Elektricitätsgesellschaft (AEG)” in Berlin‐Oberschöneweide. Czochralski discovered the famous method to pull single crystals by accident: Deep in thought, he dipped his pen not into an ink pot but into a crucible with liquid tin, both standing next to one another on his desk. Quickly he pulled his pen out and observed a thin thread of tin emerging from the tip. After etching, the thread was identified as a single crystal of tin. This observation is probably one of the most important technical inventions of the first half of the 20^th century. In 1917, he left the AEG in Berlin and worked in the metal research laboratory, later belonging to the “Metallgesellschaft”, in Frankfurt/Main. Until today, wafers of high‐purity silicon are prepared by the Czochralski method. Silicon wafers with 200 mm diameter were produced in 1990, 300 mm wafers in 2001. The production of wafers with 450 mm diameter was expected for 2016. Siltronic produced in 2009 the first dislocation‐free silicon single crystal with 450 mm diameter, and other companies followed. However, until now, the 450 mm technology is not standard. This is due to a combination of very high investment costs needed to establish the 450 mm technology and very low prices of microchips.     

Co-evolutionary dynamics and Bayesian interaction games

Recently there has been a growing interest in evolutionary models of play with endogenous interaction structure. We call such processes co-evolutionary dynamics of networks and play. We study a co-evolutionary process of networks and play in settings where players have diverse preferences. In the class of potential games we provide a closed-form solution for the unique invariant distribution of this process. Based on this result we derive various asymptotic statistics generated by the co-evolutionary process. We give a complete characterization of the random graph model, and stochastically stable states in the small noise limit. Thereby we can select among action profiles and networks which appear jointly with non-vanishing frequency in the limit of small noise in the population. We further study stochastic stability in the limit of large player populations.     

Evolution of social networks

Modeling the evolution of networks is central to our understanding of large communication systems, and more general, modern economic and social systems. The research on social and economic networks is truly interdisciplinary and the number of proposed models is huge. In this survey we discuss a small selection of modeling approaches, covering classical random graph models, and game-theoretic models to analyze the evolution of social networks. Based on these two basic modeling paradigms, we introduce co-evolutionary models of networks and play as a potential synthesis.