Short-time asymptotic expansions of semilinear evolution equations

We develop an algebraic approach to constructing short-time asymptotic expansions of solutions of a class of abstract semilinear evolution equations. The expansions are typically valid for both the solution of the equation and its gradient. We apply a perturbation approach based on the symbolic calculus of pseudo-differential operators and heat kernel methods. The construction is explicit and can be done to arbitrary order. All results are rigorously formulated in terms of Banach algebras. As an application we obtain a novel approach to finding approximate solutions of Markovian backward stochastic differential equations. © 2016 Royal Society of Edinburgh

Comparing Techniques for Mobile Interaction with Objects from the Real World.

Mobile interaction with objects from the real world is gaining in popularity and importance as different mobile technologies increasingly provide the basis for the extraction and usage of information from physical objects. So far, Physical Mobile Interaction is used in rather simple ways. This paper presents a comparison and evaluation of more complex and sophisticated techniques for Physical Mobile Interaction. The results indicate the importance of usability guidelines that pay attention to these new interaction techniques

Chiral magnetoacoustics

Nonreciprocal microwave devices are key components of communication platforms. Nonreciprocity can arise in chiral systems, where chirality refers to a fixed handedness that is preserved under time reversal. Chiral excitations (quasiparticles) provide opportunities for the realization of miniaturized microwave components with directional properties. In particular, surface acoustic waves that propagate in magnetic media are chiral and can display pronounced nonreciprocal character. Because surface acoustic waves are an established technological platform, hybrid surface acoustic wave/spin wave devices have great application potential. In this mini-review, we introduce the general concept of chiral and nonreciprocal magnetoacoustic waves. We discuss a widely employed phenomenological model based on magnetoelastic coupling and magneto-rotation that quantitatively accounts for many experimental findings and give a brief overview over selected experiments and advances in this emerging research field

Pricing of Cyber Insurance Contracts in a Network Model

We develop a novel approach for pricing cyber insurance contracts. The considered cyber threats, such as viruses and worms, diffuse in a structured data network. The spread of the cyber infection is modeled by an interacting Markov chain. Conditional on the underlying infection, the occurrence and size of claims are described by a marked point process. We introduce and analyze a new polynomial approximation of claims together with a mean-field approach that allows to compute aggregate expected losses and prices of cyber insurance. Numerical case studies demonstrate the impact of the network topology and indicate that higher order approximations are indispensable for the analysis of non-linear claims. © 2018 by Astin Bulletin. All rights reserved