73 citations · 160 across the 24 of their papers we have counts for
6 papers · 1 filter
Strongly Convex Divergences
James Melbourne
We consider a sub-class of the -divergences satisfying a stronger convexity property, which we refer to as strongly convex, or -convex divergences. We derive new and old rela…
Convex Decreasing Algorithms: Distributed Synthesis and Finite-time Termination in Higher Dimension
James Melbourne, Govind Saraswat, Vivek Khatana +2
We introduce a general mathematical framework for distributed algorithms, and a monotonicity property frequently satisfied in application. These properties are leveraged to provide…
Concentration functions and entropy bounds for discrete log-concave distributions
Sergey G. Bobkov, Arnaud Marsiglietti, James Melbourne
Two-sided bounds are explored for concentration functions and Rényi entropies in the class of discrete log-concave probability distributions. They are used to derive certain varian…
Hindering loads prompt clustered configurations that enhance stability during cargo transport by multiple Kinesin-1
Shreyas Bhaban, Rachit Srivastava, James Melbourne +2
Transport of intracellular cargo is often mediated by teams of molecular motors that function in a chaotic environment under varying conditions. We show that the motors have unique…
Reversals of Rényi Entropy Inequalities under Log-Concavity
James Melbourne, Tomasz Tkocz
We establish a discrete analog of the Rényi entropy comparison due to Bobkov and Madiman. For log-concave variables on the integers, the min entropy is within log e of the usual Sh…
Geometric and Functional Inequalities for Log-concave Probability Sequences
Arnaud Marsiglietti, James Melbourne
We investigate geometric and functional inequalities for the class of log-concave probability sequences. We prove dilation inequalities for log-concave probability measures on the…