#### Filter Results:

#### Publication Year

2005

2016

#### Publication Type

#### Co-author

#### Key Phrase

#### Publication Venue

Learn More

In this article, we formulate for the first time the notion of a quantum evolutionary algorithm. In fact we define a quantum analogue for any elitist (1+1) randomized search heuristic. The quantum evolutionary algorithm, which we call <i>(1+1) quantum evolutionary algorithm</i> (QEA), is the quantum version of the classical (1+1) evolutionary algorithm… (More)

Black-box complexity is a complexity theoretic measure for how difficult a problem is to be optimized by a general purpose optimization algorithm. It is thus one of the few means trying to understand which problems are tractable for genetic algorithms and other randomized search heuristics. Most previous work on black-box complexity is on artificial test… (More)

For the theoretical study of real-world networks, we propose a model of scale-free random graphs with underlying geometry that we call geometric inhomogeneous random graphs (GIRGs). GIRGs generalize hyperbolic random graphs, which are a popular model to test algorithms for social and technological networks. Our generalization overcomes some limitations of… (More)

Black-box complexity theory provides lower bounds for the runtime %classes of black-box optimizers like evolutionary algorithms and serves as an inspiration for the design of new genetic algorithms. Several black-box models covering different classes of algorithms exist, each highlighting a different aspect of the algorithms under considerations. In this… (More)

As in classical runtime analysis the OneMax problem is the most prominent test problem also in black-box complexity theory. It is known that the unrestricted, the memory-restricted, and the ranking-based black-box complexities of this problem are all of order n/log n, where n denotes the length of the bit strings. The combined memory-restricted… (More)

- Johannes Lengler, Tobias Bittner, Doris Münster, Alaa El-Din A Gawad, Jochen Graw
- Ophthalmic research
- 2005

Sox2 transcription factor is expressed in neural tissues and sensory epithelia from the early stages of development. Particularly, it is known to activate crystallin gene expression and to be involved in differentiation of lens and neural tissues. However, its place in the signaling cascade is not well understood. Here, we report about the response of its… (More)

a r t i c l e i n f o a b s t r a c t In number theory, great efforts have been undertaken to study the Cohen–Lenstra probability measure on the set of all finite abelian p-groups. On the other hand, group theorists have studied a probability measure on the set of all partitions induced by the probability that a randomly chosen n × n-matrix over F p is… (More)

- Johannes Lengler
- 2007

In this paper, I will introduce a link between the volume of a finite abelian p-group in the Cohen-Lenstra measure and partitions of a certain type. These partitions will be classified by the output of an algorithm. Furthermore, I will derive a formula (7.2) for the probability of a p-group to have a specific exponent.

In this work we study a diffusion process in a network that consists of two types of vertices: inhibitory vertices (those obstructing the diffusion) and excitatory vertices (those facilitating the diffusion). We consider a continuous time model in which every edge of the network draws its transmission time randomly. For such an asynchronous diffusion… (More)

We present a high-capacity model for one-shot association learning (hetero-associative memory) in sparse networks. We assume that basic patterns are pre-learned in networks and associations between two patterns are presented only once and have to be learned immediately. The model is a combination of an Amit-Fusi like network sparsely connected to a Willshaw… (More)