The sparsity and compressibility of finite-dimensional signals are of great interest in fields such as compressed sensing. The notion of compressibility is also extended to infinite sequences of i.i.d. or ergodic random variables based on the observed error in their nonlinear k-term approximation. In this work, we use the entropy measure to study the compressibility of continuous-domain innovat...

We introduce a structural quantity to probe the glass transition. This quantity is a linear generalized compressibility which depends solely on the positions of the particles. We have performed a molecular dynamics simulation on a glass-forming liquid consisting of a two-component mixture of soft spheres in three dimensions. As the temperature is lowered (or as the density is increased), the ge...

Strongly interacting atoms trapped in optical lattices can be used to explore phase diagrams of Hubbard models. Spatial inhomogeneity due to trapping typically obscures distinguishing observables. We propose that measures using boson double occupancy avoid trapping effects to reveal two key correlation functions. We define a boson core compressibility and core superfluid stiffness in terms of d...

We consider several examples of probabilistic existence proofs using compressibility arguments, including some results that involve Lovász local lemma. 1 Probabilistic proofs: a toy example There are many well known probabilistic proofs that objects with some properties exist. Such a proof estimates the probability for a random object to violate the requirements and shows that it is small (or a...

We continue the investigation of the path-connected geometry on the Cantor space and the related notions of dilution and compressibility described in [1]. These ideas are closely related to the notions of effective Hausdorff and packing dimensions of reals, and we argue that this geometry provides the natural context in which to study them. In particular we show that every regular real can be m...

.z I < p(e), E < p(E) < Po, and p(c) depends not only on e but also on w(z). The function p(E) clearly decreases monotonically with e; it also approaches zero with e, for the transformation z(w), although multiple-valued, is continuous. If now E(e) lies in Jz < E, E < Eo, then the convex hull of w(E(e)) contains the point w+, and the m antecedents z+ of w+ in jz < Po defined by equation (5) lie...

Compressed Sensing (CS) is a novel sampling paradigm that tries to take data-compression concepts down to the sampling layer of a sensory system. It states that discrete compressible signals are recoverable from sub-sampled data, when the data vector is acquired by a special linear transform of the original discrete signal vector. Distributed sampling problems especially in Wireless Sensor Netw...

The effects of solvent compressibility on the sedimentation behavior of macromolecules as observed in analytical ultracentrifugation are examined. Expressions for the density and pressure distributions in the solution column are derived and combined with the finite element solution of the Lamm equation in inhomogeneous media to predict the macromolecular concentration distributions under differ...