On stochastic auctions in risk-averse electricity markets with uncertain supply

This paper studies risk in a stochastic auction which facilitates the integration of renewable generation in electricity markets. We model market participants who are risk averse and reflect their risk aversion through coherent risk measures. We uncover a closed form characterization of a risk-averse generator’s optimal pre-commitment behaviour for a given real-time policy, both with and without risk trading.     

On uniform propagation of chaos

In this paper we obtain a time-uniform propagation estimate for a system of interacting diffusion processes. Using a well defined metric function h , our result guarantees a time-uniform estimate for the convergence of a class of interacting stochastic differential equations towards their mean field limit, under conditions that ensure that the decay associated to the internal dynamics term dominates the interaction and noise terms. Our result should have diverse applications, particularly in neuroscience, and allows for models more elaborate than the one of Wilson and Cowan. In particular, the internal dynamics need not be that of linear decay.     

An approach to find redundant objective function(s) and redundant constraint(s) in multi-objective nonlinear stochastic fractional programming problems

Structural redundancies in mathematical programming models are nothing uncommon and nonlinear programming problems are no exception. Over the past few decades numerous papers have been written on redundancy. Redundancy in constraints and variables are usually studied in a class of mathematical programming problems. However, main emphasis has so far been given only to linear programming problems. In this paper, an algorithm that identifies redundant objective function(s) and redundant constraint(s) simultaneously in multi-objective nonlinear stochastic fractional programming problems is provided. A solution procedure is also illustrated with numerical examples. The proposed algorithm reduces the number of nonlinear fractional objective functions and constraints in cases where redundancy exists.     

Joint distribution of direction and length of typical I-segment in a homogeneous random planar tessellation stable under iteration

The paper deals with homogeneous random planar tessellations stable under iteration (random STIT tessellations). The length distribution of the typical I-segment is already known in the isotropic case [8]. In the present paper, the anisotropic case is treated. Then also the direction of the typical I-segment is of interest. The joint distribution of direction and length of the typical I-segment is evaluated. As a first step, the corresponding joint distribution for the so-called typical remaining I-segment is derived. Dedicated to the 80th birthday of Klaus Krickeberg     

Blood Proteins Strongly Reduce the Mobility of Artificial Self‐Propelled Micromotors

Autonomous self‐propelled catalytic microjets are envisaged as an important technology in biomedical applications, including drug delivery, micro/nanosurgery, and active dynamic bioassays. The direct in vivo application of these microjets, specifically in blood, is however impeded by insufficient knowledge on the in vivo viability of the technique. This study highlights the effect of blood proteins on the viability of the microjets. The presence of blood proteins, including serum albumin and γ‐globulins at physiological concentrations, has been found to dramatically reduce the viability of the microjets. The reduction of viability has been measured in terms of a lower number of active microjets and a decrease in the velocity of propulsion. It is clear from this study that in order for microjets to function in biomedical applications, different modes of propulsion besides platinum‐catalyzed oxygen bubble ejection must be employed. These findings have serious implications for the biomedical applications of catalytic microjets.