Related papers: Entropy-Bounded Computational Geometry Made Easier…
In many problems in data mining and machine learning, data items that need to be clustered or classified are not points in a high-dimensional space, but are distributions (points on a high dimensional simplex). For distributions, natural…
Gaussian distributions are plentiful in applications dealing in uncertainty quantification and diffusivity. They furthermore stand as important special cases for frameworks providing geometries for probability measures, as the resulting…
Conditional differential entropy provides an intuitive measure for relatively ranking time-series complexity by quantifying uncertainty in future observations given past context. However, its direct computation for high-dimensional…
We study the computational problem of rigorously describing the asymptotic behaviour of topological dynamical systems up to a finite but arbitrarily small pre-specified error. More precisely, we consider the limit set of a typical orbit,…
We introduce a new formalism and a number of new results in the context of geometric computational vision. The classical scope of the research in geometric computer vision is essentially limited to static configurations of points and lines…
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…
There are interesting extensions of the problem of determining a joint probability with known marginals. On the one hand, one may impose size constraints on the joint probabilities. On the other, one may impose additional constraints like…
We show that a geometrical notion of entropy, definable in flat space, governs the first quantum correction to the Bekenstein-Hawking black hole entropy. We describe two methods for calculating this entropy -- a straightforward Hamiltonian…
Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated…
We comment on some conceptual and and technical problems related to computational mechanics, point out some errors in several papers, and straighten out some wrong priority claims. We present explicitly the correct algorithm for…
We study the difficulty of computing topological entropy of subshifts subjected to mixing restrictions. This problem is well-studied for multidimensional subshifts of finite type : there exists a threshold in the irreducibility rate where…
We initiate a systematic study of the computational complexity of property testing, focusing on the relationship between query and time complexity. While traditional work in property testing has emphasized query complexity, relatively…
We present an amelioration of current known algorithms for optimal spectral partitioning problems. The idea is to use the advantage of a representation using density functions while decreasing the computational time. This is done by…
In this paper we explore how non trivial boundary conditions could influence the entanglement entropy in a topological order in 2+1 dimensions. Specifically we consider the special class of topological orders describable by the quantum…
Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be…
The geometric Brownian motion (GBM) is widely employed for modeling stochastic processes, yet its solutions are characterized by the log-normal distribution. This comprises predictive capabilities of GBM mainly in terms of forecasting…
For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information transmission above which a given compact subset of the state…
In this paper, we present a contraction-guided adaptive partitioning algorithm for improving interval-valued robust reachable set estimates in a nonlinear feedback loop with a neural network controller and disturbances. Based on an estimate…
We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…
Relative entropy coding (REC) algorithms encode a random sample following a target distribution $Q$, using a coding distribution $P$ shared between the sender and receiver. Sadly, general REC algorithms suffer from prohibitive encoding…