In this paper, we address the decision-making problem of a virtual power plant (VPP) involving self-scheduling and market involvement under uncertainty in wind speed electricity prices. The is modeled using risk-neutral two risk-averse two-stage stochastic programming formulations, where conditional value at risk used to represent risk. A sample average approximation methodology integrated with...

In this paper, we enumerate the number of oriented rational knots and links with any given crossing minimum genus. This allows us to obtain a precise formula for average minimal genus number.

Theta graphs are important geometric graphs that have many applications, including wireless networking, motion planning, real-time animation, and minimumspanning tree construction. We give closed form expressions for the average degree of theta graphs of a homogeneous Poisson point process over the plane. We then show that essentially the same bounds—with vanishing error terms—hold for theta gr...

This work has been inspired by problems addressed in the field of computer security, where the attacking of, e.g., password systems is an important issue. In [2] Lundin et al. discuss measures related to the number of guesses or attemts a supposed attacker needs for revealing information. Similar problems are considered in [1], [3] and [4]. In this presentation numerical approaches are discusse...

We are given a stack of pancakes of different sizes and the only allowed operation is to take several pancakes from top and flip them. The unburnt version requires the pancakes to be sorted by their sizes at the end, while in the burnt version they additionally need to be oriented burnt-side down. We present an algorithm with the average number of flips, needed to sort a stack of n burnt pancak...

The partial derivative automaton (Apd) is usually smaller than other non-deterministic finite automata constructed from a regular expression, and it can be seen as a quotient of the Glushkov automaton (Apos). By estimating the number of regular expressions that have ε as a partial derivative, we compute a lower bound of the average number of mergings of states in Apos and describe its asymptoti...