In this paper, we discuss multivariately factorized probability distributions for permutation random variables and a greedy approach to estimating these probability distributions from data. We use the representation known as random keys for permutations. The major benefit of using random keys is that no infeasible solution can be generated if crossover is applied in an evolutionary algorithm (E...

We study de Rahm cohomology for various differential calculi on finite groups G up to order 8. These include the permutation group S3, the dihedral group D4 and the quaternion group Q. Poincaré duality holds in every case, and under some assumptions (essentially the existence of a top form) we find that it must hold in general. A short review of the bicovariant (noncommutative) differential cal...

Brain electrical activity as reflected in Electroencephalography (EEG) have been analyzed and diagnosed using various techniques. Among them complexity measure, nonlinearity, disorder and unpredictability play vital role due to nonlinear interconnection between functional and anatomical subsystem emerged in brain in healthy state and during various diseases. There are many social and economical...

Local search algorithms, such as simulated annealing, tabu search, and local hill climbers attempt to optimize a solution to a problem by making locally improving modifications to a candidate solution. They rely on a neighborhood operator to restrict the search to a typically small set of possible successor states. The genetic algorithm mutation operator, likewise, enables the exploration of th...

Abstract Quantum permutations arise in many aspects of modern “quantum mathematics”. However, the aim this article is to detach these objects from their context and give a friendly introduction purely within operator theory. We define quantum permutation matrices as whose entries are operators on Hilbert spaces; they obey certain assumptions generalizing classical matrices. number examples we l...

this paper presents a new audio encryption algorithm based on permutation and residue number system. in the current approach, signal samples are combined with residue number system through permutation; therefore, a specific noise is generated. then, the audio signal is combined with the noise, generated by the algorithm, to produce a silence signal. for this purpose, the algorithm uses a predef...

We designed a single-chain variant of the Arc repressor homodimer in which the beta strands that contact operator DNA are connected by a hairpin turn and the alpha helices that form the tetrahelical scaffold of the dimer are attached by a short linker. The designed protein represents a noncyclic permutation of secondary structural elements in another single-chain Arc molecule (Arc-L1-Arc), in w...

Multiple instance learning (MIL) is a variation of supervised learning where a single class label is assigned to a bag of instances. In this paper, we state the MIL problem as learning the Bernoulli distribution of the bag label where the bag label probability is fully parameterized by neural networks. Furthermore, we propose a neural network-based permutation-invariant aggregation operator tha...

Residuals have been studied for various forms of rewriting and residual systems have been defined to capture residuals in an abstract setting. In this article we study residuals in orthogonal Pattern Rewriting Systems (PRSs). First, the rewrite relation is defined by means of a higher-order rewriting logic, and proof terms are defined that witness reductions. Then, we have the formal machinery ...

A permutation class is splittable if it is contained in the merge of two of its proper subclasses. We characterise the unsplittable subclasses of the class of separable permutations both structurally and in terms of their bases.