Genetic Algorithms to Maximize the Relevant Mutual Information in Communication Receivers

The preservation of relevant mutual information under compression is the fundamental challenge of the information bottleneck method. It has many applications in machine learning and in communications. The recent literature describes successful applications of this concept in quantized detection and channel decoding schemes. The focal idea is to build receiver algorithms intended to preserve the maximum possible amount of relevant information, despite very coarse quantization. The existent literature shows that the resulting quantized receiver algorithms can achieve performance very close to that of conventional high-precision systems. Moreover, all demanding signal processing operations get replaced with lookup operations in the considered system design. In this paper, we develop the idea of maximizing the preserved relevant information in communication receivers further by considering parametrized systems. Such systems can help overcome the need of lookup tables in cases where their huge sizes make them impractical. We propose to apply genetic algorithms which are inspired from the natural evolution of the species for the problem of parameter optimization. We exemplarily investigate receiver-sided channel output quantization and demodulation to illustrate the notable performance and the flexibility of the proposed concept.

MCMT in the Land of Parametrized Timed Automata

Timed networks are parametrized systems of timed au\-to\-ma\-ta. Solving reachability problems (e.g., whether a set of unsafe states can ever be reached from the set of initial states) for this class of systems allows one to prove safety properties regardless of the number of processes in the network. The difficulty in solving this kind of verification problems is two-fold. First, each process has (at least one) clock variable ranging over an infinite set, such as the reals or the integers. Second, every system is parameterized with respect to the number of processes and to the topology of the network. Reachability problem for some restricted classes of parameterized timed networks is decidable under suitable assumptions by a backward reachability procedure. Despite these theoretical results, there are few systems capable of automatically solving such problems. Instead, the number $n$ of processes in the network is fixed and a tool for timed automata (like Uppaal) is used to check the desired property for the given $n$.In this paper, we explain how to attack fully parameteric and timed reachability problems by translation to the declarative input language of \textsc{mcmt}, a model checker for infinite state systems based on Satisfiability Modulo Theories techniques. We show the success of our approach on a number of standard algorithms, such as the Fischer protocol. Preliminary experiments show that fully parametric problems can be more easily solved by \textsc{mcmt} than their instances for a fixed (and large) number of processes by other systems.

Frame-like Lagrangians and presymplectic AKSZ-type sigma models

We study supergeometric structures underlying frame-like Lagrangians. We show that for the theory in n space–time dimensions both the frame-like Lagrangian and its gauge symmetries are encoded in the target supermanifold equipped with the odd vector field, the closed two-form of ghost degree n-1, and the scalar potential of ghost degree n. These structures satisfy a set of compatibility conditions ensuring the gauge invariance of the theory. The Lagrangian and the gauge symmetries have the same structures as those of AKSZ sigma model so that frame-like formulation can be seen as its presymplectic generalization. In contrast to the conventional AKSZ model, the generalization allows to describe systems with local degrees of freedom in terms of finite-dimensional target space. We argue that the proposed frame-like approach is directly related de Donder–Weyl polymomentum Hamiltonian formalism. Along with the standard field-theoretical examples like Einstein–Yang–Mills theory, we consider free higher spin fields, multi-frame gravity and parametrized systems. In particular, we propose the frame-like action for free totally symmetric massless fields that involves all higher spin connections on an equal footing.