A new species of Lepanthes from southwestern Colombia is presented here. farallonensis belongs to the informal group “manabina”, which comprises with concave and commonly pubescent leaves, flowers resting at adaxial side synsepal short long tails. similar L. smaragdina in broadly ovate dorsal sepal but differs conspicuously twisted upper lobes petals, outwardly bent a depression center laminae ...

The purpose of this note is to present several aspects of concentration phenomena in high dimensional geometry. At the heart of the study is a geometric analysis point of view coming from the theory of high dimensional convex bodies. The topic has a broad audience going from algorithmic convex geometry to random matrices. We have tried to emphasize different problems relating these areas of res...

A classification of SL(n) and translation covariant Minkowski valuations on log-concave functions is established. The moment vector and the recently introduced level set body of log-concave functions are characterized. Furthermore, analogs of the Euler characteristic and volume are characterized as SL(n) and translation invariant valuations on log-concave functions. 2000 AMS subject classificat...

The challenge 1 of the BIOVIS 2015 design contest consists in designing an intuitive visual depiction of base pairs binding probabilities for secondary structure of ncRNA. Our representation depicts the potential nucleotide pairs binding using nested concave hulls over the computed MFE ncRNA secondary structure. Thus, it allows to identify regions with a high level of uncertainty in the MFE com...

We generalize a well-known result of L. Caffarelli on Lipschitz estimates for optimal transportation T between uniformly log-concave probability measures. Let T : R → R be an optimal transportation pushing forward μ = e dx to ν = e dx. Assume that 1) the second differential quotient of V can be estimated from above by a power function, 2) modulus of convexity of W can be estimated from below by...

Graphical models are frequently used to explore networks, such as genetic networks, among a set of variables. This is usually carried out via exploring the sparsity of the precision matrix of the variables under consideration. Penalized likelihood methods are often used in such explorations. Yet, positive-definiteness constraints of precision matrices make the optimization problem challenging. ...

We study the relation x ≺L y on [0,∞)n defined by x ≺L y ⇔ ∑n i=1 ψ(xi) ≤ ∑n i=1 ψ(yi) for all ψ : [0,∞) → [0,∞) of the form ψ(s) = ∫ s 0 φ(t) dt t where φ is concave nondecreasing. (We also briefly explain how this arises in the context of some Lp inequalities between complex exponential sums conjectured by Hardy and Littlewood, and why the more familiar relation obtained by allowing any conca...

The eigenspace structure for a given n × n concave Monge matrix in a max-plus algebra is described. Based on the description, an O(n) algorithm for computing the eigenspace dimension is formulated, which is faster than the previously known algorithms. Analogous results for convex Monge matrices have been published in [M. Gavalec, J. Plavka, Structure of the eigenspace of a Monge matrix in max-p...