Electrochemical current-sensing atomic force microscopy in conductive solutions

Insulated atomic force microscopy probes carrying gold conductive tips were fabricated and employed as bifunctional force and current sensors in electrolyte solutions under electrochemical potential control. The application of the probes for current-sensing imaging, force and current–distance spectroscopy as well as scanning electrochemical microscopy experiments was demonstrated.

Two-dimensional assembly and local redox-activity of molecular hybrid structures in an electrochemical environment

The self-assembly and redox-properties of two viologen derivatives, N-hexyl-N-(6-thiohexyl)-4,4-bipyridinium bromide (HS-6V6-H) and N,N-bis(6-thiohexyl)-4,4-bipyridinium bromide (HS-6V6-SH), immobilized on Au(111)-(1x1) macro-electrodes were investigated by cyclic voltammetry, surface enhanced infrared spectroscopy (SEIRAS) and in situ scanning tunneling microscopy (STM). Depending on the assembly conditions one could distinguish three different types of adlayers for both viologens: a low coverage disordered and an ordered striped phase of flat oriented molecules as well as a high coverage monolayer composed of tilted viologen moieties. Both molecules, HS-6V6-H and HS-6V6-SH, were successfully immobilized on Au(poly) nano-electrodes, which gave a well-defined redox-response in the lower pA–current range. An in situ STM configuration was employed to explore electron transport properties of single molecule junctions Au(T)|HS-6V6-SH(HS-6V6-H)|Au(S). The observed sigmoidal potential dependence, measured at variable substrate potential ES and at constant bias voltage (ET–ES), was attributed to electronic structure changes of the viologen moiety during the one-electron reduction/re-oxidation process V2+ V+. Tunneling experiments in asymmetric, STM-based junctions Au(T)-S-6V6-H|Au(S) revealed current (iT)–voltage (ET) curves with a maximum located at the equilibrium potential of the redox-process V2+ V+. The experimental iT–ET characteristics of the HS-6V6-H–modified tunneling junction were tentatively attributed to a sequential two-step electron transfer mechanism.

Choosing a random distribution with prescribed risks

We describe several simulation algorithms that yield random probability distributions with given values of risk measures. In case of vanilla risk measures, the algorithms involve combining and transforming random cumulative distribution functions or random Lorenz curves obtained by simulating rather general random probability distributions on the unit interval. A new algorithm based on the simulation of a weighted barycentres array is suggested to generate random probability distributions with a given value of the spectral risk measure.

Estimating and quantifying uncertainties on level sets using the Vorob'ev expectation and deviation with Gaussian process models

Several methods based on Kriging have recently been proposed for calculating a probability of failure involving costly-to-evaluate functions. A closely related problem is to estimate the set of inputs leading to a response exceeding a given threshold. Now, estimating such a level set—and not solely its volume—and quantifying uncertainties on it are not straightforward. Here we use notions from random set theory to obtain an estimate of the level set, together with a quantification of estimation uncertainty. We give explicit formulae in the Gaussian process set-up and provide a consistency result. We then illustrate how space-filling versus adaptive design strategies may sequentially reduce level set estimation uncertainty.

Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

Stationarity of multivariate particle systems

A particle system is a family of i.i.d. stochastic processes with values translated by Poisson points. We obtain conditions that ensure the stationarity in time of the particle system in RdRd and in some cases provide a full characterisation of the stationarity property. In particular, a full characterisation of stationary multivariate Brown–Resnick processes is given.

Large deviations for heavy-tailed random elements in convex cones

We prove large deviation results for sums of heavy-tailed random elements in rather general convex cones being semigroups equipped with a rescaling operation by positive real numbers. In difference to previous results for the cone of convex sets, our technique does not use the embedding of cones in linear spaces. Examples include the cone of convex sets with the Minkowski addition, positive half-line with maximum operation and the family of square integrable functions with arithmetic addition and argument rescaling.

Multiasset Derivatives and Joint Distributions of Asset Prices

Several of multiasset derivatives like basket options or options on the weighted maximum of assets exhibit the property that their prices determine uniquely the underlying asset distribution. Related to that the question how to retrieve this distributions from the corresponding derivatives quotes will be discussed. On the contrary, the prices of exchange options do not uniquely determine the underlying distributions of asset prices and the extent of this non-uniqueness can be characterised. The discussion is related to a geometric interpretation of multiasset derivatives as support functions of convex sets. Following this, various symmetry properties for basket, maximum and exchange options are discussed alongside with their geometric interpretations and some decomposition results for more general payoff functions.

Applications of random set theory in econometrics

In recent years, the econometrics literature has shown a growing interest in the study of partially identified models, in which the object of economic and statistical interest is a set rather than a point. The characterization of this set and the development of consistent estimators and inference procedures for it with desirable properties are the main goals of partial identification analysis. This review introduces the fundamental tools of the theory of random sets, which brings together elements of topology, convex geometry, and probability theory to develop a coherent mathematical framework to analyze random elements whose realizations are sets. It then elucidates how these tools have been fruitfully applied in econometrics to reach the goals of partial identification analysis.

Whole genome RNAi screens reveal a critical role of REV3 in coping with replication stress

REV3, the catalytic subunit of translesion polymerase zeta (polζ), is commonly associated with DNA damage bypass and repair. Despite sharing accessory subunits with replicative polymerase δ, very little is known about the role of polζ in DNA replication. We previously demonstrated that inhibition of REV3 expression induces persistent DNA damage and growth arrest in cancer cells. To reveal determinants of this sensitivity and obtain insights into the cellular function of REV3, we performed whole human genome RNAi library screens aimed at identification of synthetic lethal interactions with REV3 in A549 lung cancer cells. The top confirmed hit was RRM1, the large subunit of ribonucleotide reductase (RNR), a critical enzyme of de novo nucleotide synthesis. Treatment with the RNR-inhibitor hydroxyurea (HU) synergistically increased the fraction of REV3-deficient cells containing single stranded DNA (ssDNA) as indicated by an increase in replication protein A (RPA). However, this increase was not accompanied by accumulation of the DNA damage marker γH2AX suggesting a role of REV3 in counteracting HU-induced replication stress (RS). Consistent with a role of REV3 in DNA replication, increased RPA staining was confined to HU-treated S-phase cells. Additionally, we found genes related to RS to be significantly enriched among the top hits of the synthetic sickness/lethality (SSL) screen further corroborating the importance of REV3 for DNA replication under conditions of RS.

Reconstruction and electrochemical oxidation of Au(110) surface in 0.1 M H2SO4

Variations of the surface structure and composition of the Au(110) electrode during the formation/lifting of the surface reconstruction and during the surface oxidation/reduction in 0.1 M aqueous sulfuric acid were studied by cyclic voltammetry, scanning tunneling microscopy and shell-isolated nanoparticle enhanced Raman spectroscopy. Annealing of the Au(110) electrode leads to a thermally-induced reconstruction formed by intermixed (1×3) and (1×2) phases. In a 0.1 M H2SO4 solution, the decrease of the potential of the atomically smooth Au(110)-(1×1) surface leads to the formation of a range of structures with increasing surface corrugation. The electrochemical oxidation of the Au(110) surface starts by the formation of anisotropic atomic rows of gold oxide. At higher potentials we observed a disordered structure of the surface gold oxide, similar to the one found for the Au(111) surface.