Publications

Annotation of nonmodel organisms is an open problem, especially the detection of untranslated regions (UTRs). Correct annotation of UTRs is crucial in transcriptomic analysis to accurately capture the expression of each gene yet is mostly overlooked in annotation pipelines. Here we present peaks2utr, an easy-to-use Python command line tool that uses the UTR enrichment of single-cell technologies, such as 10× Chromium, to accurately annotate 3′ UTRs for a given canonical annotation.

We study Lamé operators of the form L=−d2dx2+m(m+1)ω2℘(ωx+z0), with m∈N and ω a half-period of ℘(z). For rectangular period lattices, we can choose ω and z0 such that the potential is real, periodic and regular. It is known after Ince that the spectrum of the corresponding Lamé operator has a band structure with not more than m gaps. In the first part of the paper, we prove that the opened gaps are precisely the first m ones. In the second part, we study the Lamé spectrum for a generic period lattice when the potential is complex-valued. We concentrate on the m=1 case, when the spectrum consists of two regular analytic arcs, one of which extends to infinity, and briefly discuss the m=2 case, paying particular attention to the rhombic lattices.

Consider the Wronskians of the classical Hermite polynomials Hλ,l(x):=Wr(Hl(x), Hk1 (x), … , Hkn (x)), l ∈Z≥0{k1,…, kn}, where ki = λi + n − i, i = 1,…, n and λ = (λ1,…,λn) is a partition. Gomez-Ullate et al. showed that for a special class of partitions the corresponding polynomials are orthogonal and dense among all polynomials with respect to a certain inner product, but in contrast to the usual case have some degrees missing (so-called exceptional orthogonal polynomials). We generalise their results to all partitions by considering complex contours of integration and non-positive Hermitian products. The corresponding polynomials are orthogonal and dense in a finite-codimensional subspace of C[x] satisfying certain quasi-invariance conditions. A Laurent version of exceptional orthogonal polynomials, related to monodromy-free trigonometric Schrödinger operators, is also presented.