Related papers: Detecting properties from descriptions of groups

We give an algorithm for computing the irreducible admissible representations of a real reductive group with regular integral infinitesimal character. This algorithm has been implemented on a computer, as part of the Atlas of Lie Groups and…

Shapley values has established itself as one of the most appropriate and theoretically sound frameworks for explaining predictions from complex machine learning models. The popularity of Shapley values in the explanation setting is probably…

The investigation of community structures in networks is an important issue in many domains and disciplines. This problem is relevant for social tasks (objective analysis of relationships on the web), biological inquiries (functional…

We consider object detection using a generic model for natural shapes. A common approach for object recognition involves matching object models directly to images. Another approach involves building intermediate representations via a…

In this paper we prove a new characterization of the distinguished unipotent orbits of a connected reductive group over an algebraically closed field of characteristic 0. For classical groups we prove the characterization by a combinatorial…

Community structure is largely regarded as an intrinsic property of complex real-world networks. However, recent studies reveal that networks comprise even more sophisticated modules than classical cohesive communities. More precisely,…

In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…

Computer based techniques for recognizing finitely presented groups are quite powerful. Tools available for this purpose are outlined. They are available both in stand-alone programs and in more comprehensive systems. A general…

Designing plausible network models typically requires scholars to form a priori intuitions on the key drivers of network formation. Oftentimes, these intuitions are supported by the statistical estimation of a selection of network evolution…

I postulate that human or other intelligent agents function or should function as follows. They store all sensory observations as they come - the data is holy. At any time, given some agent's current coding capabilities, part of the data is…

Recent research has shown that virtually all algorithms aimed at the identification of communities in networks are affected by the same main limitation: the impossibility to detect communities, even when these are well-defined, if the…

Humans possess an intricate and powerful visual system in order to perceive and understand the environing world. Human perception can effortlessly detect and correctly group features in visual data and can even interpret random-dot videos…

Selection functionality is as fundamental to vector graphics as it is for raster data. But vector selection is quite different: instead of pixel-level labeling, we make a binary decision to include or exclude each vector primitive. In the…

The framework of algorithmic knowledge assumes that agents use deterministic knowledge algorithms to compute the facts they explicitly know. We extend the framework to allow for randomized knowledge algorithms. We then characterize the…

In this paper we explore how machine learning techniques can be applied to the discovery of efficient mathematical identities. We introduce an attribute grammar framework for representing symbolic expressions. Given a set of grammar rules…

Considering a group of users, each specifying individual preferences over categorical attributes, the problem of determining a set of objects that are objectively preferable by all users is challenging on two levels. First, we need to…

The identification of dynamics from time series data is a problem of general interest. It is well established that dynamics on the level of invariant sets, the primary objects of interest in the classical theory of dynamical systems, is not…

This article studies two notions of generalized matroid representations motivated by algorithmic information theory and cryptographic secret sharing. The first (entropic representability) involves discrete random variables, while the second…

While Kolmogorov complexity is the accepted absolute measure of information content of an individual finite object, a similarly absolute notion is needed for the relation between an individual data sample and an individual model summarizing…

We construct efficient or query efficient quantum property testers for two existential group properties which have exponential query complexity both for their decision problem in the quantum and for their testing problem in the classical…