Related papers: Hard Core entropy: lower bounds
We suggest a robust nearest-neighbor approach to classifying high-dimensional data. The method enhances sensitivity by employing a threshold and truncates to a sequence of zeros and ones in order to reduce the deleterious impact of…
Nonequilibrium processes break time-reversal symmetry and generate entropy. Living systems are driven out-of-equilibrium at the microscopic level of molecular motors that exploit chemical potential gradients to transduce free energy to…
We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of…
The entropy of a hierarchical network topology in an ensemble of sparse random networks with "hidden variables" associated to its nodes, is the log-likelihood that a given network topology is present in the chosen ensemble.We obtain a…
High-order accurate, $\textit{entropy stable}$ numerical methods for hyperbolic conservation laws have attracted much interest over the last decade, but only a few rigorous convergence results are available, particularly in multiple space…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…
This paper deals with the construction of the multiparticle correlation expansion of relative entropy for lattice systems. Thanks to this analysis we are able to express the statistical distance between two systems as a series built over…
We consider critical models in one dimension. We study the ground state in thermodynamic limit [infinite lattice]. Following Bennett, Bernstein, Popescu, and Schumacher, we use the entropy of a sub-system as a measure of entanglement. We…
Designing the sensing architecture for large-scale spatio-temporal systems is hard when accuracy requirements are specified but sensor models are uncertain or unavailable. Classical design treats sensor placement and estimation…
Grid entropy is a deterministic quantity inherent to lattice models which captures the entropy of empirical measures along paths that converge weakly to a given target measure. In this paper, we study the limiting behaviour of empirical…
We use rigorous non-equilibrium thermodynamic arguments to prove (i) the residual entropy of any system is bounded below by the experimentally (calorimetrically) determined absolute temperature entropy, which itself is bounded below by the…
We consider the problem of succinctly encoding a static map to support approximate queries. We derive upper and lower bounds on the space requirements in terms of the error rate and the entropy of the distribution of values over keys: our…
The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…
We discuss the high density behavior of a system of hard spheres of diameter d on the hypercubic lattice of dimension n, in the limit n -> oo, d -> oo, d/n=delta. The problem is relevant for coding theory. We find a solution to the…
Behavior of the entropy numbers of classes of multivariate functions with mixed smoothness is studied here. This problem has a long history and some fundamental problems in the area are still open. The main goal of this paper is to develop…
A moment body is a linear projection of the spectraplex, the convex set of trace-one positive semidefinite matrices. Determining whether a given point lies within a given moment body is a problem with numerous applications in quantum state…
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…
Analyzing and controlling system entropy is a powerful tool for regulating predictability of control systems. Applications benefiting from such approaches range from reinforcement learning and data security to human-robot collaboration. In…
We formulate the entropy of a quantized artificial neural network as a differentiable function that can be plugged as a regularization term into the cost function minimized by gradient descent. Our formulation scales efficiently beyond the…
Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…