Related papers: Information Measures in Detecting and Recognizing …
Identifying symmetries in data sets is generally difficult, but knowledge about them is crucial for efficient data handling. Here we present a method how neural networks can be used to identify symmetries. We make extensive use of the…
We address the problem of finding optimal strategies for computing Boolean symmetric functions. We consider a collocated network, where each node's transmissions can be heard by every other node. Each node has a Boolean measurement and we…
In this paper we observe that information theoretical concepts are valuable tools for extracting information from images and, in particular, information on image symmetries. It is shown that the problem of detecting reflectional and…
What are the symmetries of a dataset? Whereas the symmetries of an individual data element can be characterized by its invariance under various transformations, the symmetries of an ensemble of data elements are ambiguous due to Jacobian…
A broad class of informationally complete symmetric measurements is introduced. It can be understood as a common generalization of symmetric, informationally complete POVMs and mutually unbiased bases. Additionally, it provides a natural…
Symmetries are a key concept to connect mathematical elegance with physical insight. We consider measurement assemblages in quantum mechanics and show how their symmetry can be described by means of the so-called discrete bundles. It turns…
Symmetry is a key feature observed in nature (from flowers and leaves, to butterflies and birds) and in human-made objects (from paintings and sculptures, to manufactured objects and architectural design). Rotational, translational, and…
A Boolean function is symmetric if it is invariant under all permutations of its arguments; it is quasi-symmetric if it is symmetric with respect to the arguments on which it actually depends. We present a test that accepts every…
Boolean matching is significant to digital integrated circuits design. An exhaustive method for Boolean matching is computationally expensive even for functions with only a few variables, because the time complexity of such an algorithm for…
Symmetry is one of the significant visual properties inside an image plane, to identify the geometrically balanced structures through real-world objects. Existing symmetry detection methods rely on descriptors of the local image features…
Automated symmetry detection is still a difficult task in 2021. However, it has applications in computer vision, and it also plays an important part in understanding art. This paper focuses on aiding the latter by comparing different…
The presence of symmetries imposes a stringent set of constraints on a system. This constrained structure allows intelligent agents interacting with such a system to drastically improve the efficiency of learning and generalization, through…
Symmetries are ubiquitous across all kinds of objects, whether in nature or in man-made creations. While these symmetries may seem intuitive to the human eye, detecting them with a machine is nontrivial due to the vast search space.…
In the past few years, the number of fine-art collections that are digitized and publicly available has been growing rapidly. With the availability of such large collections of digitized artworks comes the need to develop multimedia systems…
Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries…
The information processing abilities of a multilayer neural network with a number of hidden units scaling as the input dimension are studied using statistical mechanics methods. The mapping from the input layer to the hidden units is…
Measuring inter-dataset similarity is an important task in machine learning and data mining with various use cases and applications. Existing methods for measuring inter-dataset similarity are computationally expensive, limited, or…
Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…
Symmetry is an important composition feature by investigating similar sides inside an image plane. It has a crucial effect to recognize man-made or nature objects within the universe. Recent symmetry detection approaches used a smoothing…
We discuss the use of symmetries for analysing the structural identifiability and observability of control systems. Special emphasis is put on the role of discrete symmetries, in contrast to the more commonly studied continuous or Lie…