@article{301, abstract = {A representation formula for solutions of stochastic partial differential equations with Dirichlet boundary conditions is proved. The scope of our setting is wide enough to cover the general situation when the backward characteristics that appear in the usual formulation are not even defined in the Itô sense.}, author = {Gerencser, Mate and Gyöngy, István}, journal = {Stochastic Processes and their Applications}, number = {3}, pages = {995--1012}, publisher = {Elsevier}, title = {{A Feynman–Kac formula for stochastic Dirichlet problems}}, doi = {10.1016/j.spa.2018.04.003}, volume = {129}, year = {2019}, } @article{80, abstract = {We consider an interacting, dilute Bose gas trapped in a harmonic potential at a positive temperature. The system is analyzed in a combination of a thermodynamic and a Gross–Pitaevskii (GP) limit where the trap frequency ω, the temperature T, and the particle number N are related by N∼ (T/ ω) 3→ ∞ while the scattering length is so small that the interaction energy per particle around the center of the trap is of the same order of magnitude as the spectral gap in the trap. We prove that the difference between the canonical free energy of the interacting gas and the one of the noninteracting system can be obtained by minimizing the GP energy functional. We also prove Bose–Einstein condensation in the following sense: The one-particle density matrix of any approximate minimizer of the canonical free energy functional is to leading order given by that of the noninteracting gas but with the free condensate wavefunction replaced by the GP minimizer.}, author = {Deuchert, Andreas and Seiringer, Robert and Yngvason, Jakob}, journal = {Communications in Mathematical Physics}, number = {2}, pages = {723--776}, publisher = {Springer}, title = {{Bose–Einstein condensation in a dilute, trapped gas at positive temperature}}, doi = {10.1007/s00220-018-3239-0}, volume = {368}, year = {2019}, } @article{5911, abstract = {Empirical data suggest that inversions in many species contain genes important for intraspecific divergence and speciation, yet mechanisms of evolution remain unclear. While genes inside an inversion are tightly linked, inversions are not static but evolve separately from the rest of the genome by new mutations, recombination within arrangements, and gene flux between arrangements. Inversion polymorphisms are maintained by different processes, for example, divergent or balancing selection, or a mix of multiple processes. Moreover, the relative roles of selection, drift, mutation, and recombination will change over the lifetime of an inversion and within its area of distribution. We believe inversions are central to the evolution of many species, but we need many more data and new models to understand the complex mechanisms involved.}, author = {Faria, Rui and Johannesson, Kerstin and Butlin, Roger K. and Westram, Anja M}, issn = {01695347}, journal = {Trends in Ecology and Evolution}, number = {3}, pages = {239--248}, publisher = {Elsevier}, title = {{Evolving inversions}}, doi = {10.1016/j.tree.2018.12.005}, volume = {34}, year = {2019}, } @article{439, abstract = {We count points over a finite field on wild character varieties,of Riemann surfaces for singularities with regular semisimple leading term. The new feature in our counting formulas is the appearance of characters of Yokonuma–Hecke algebras. Our result leads to the conjecture that the mixed Hodge polynomials of these character varieties agree with previously conjectured perverse Hodge polynomials of certain twisted parabolic Higgs moduli spaces, indicating the possibility of a P = W conjecture for a suitable wild Hitchin system.}, author = {Hausel, Tamas and Mereb, Martin and Wong, Michael}, issn = {1435-9855}, journal = {Journal of the European Mathematical Society}, number = {10}, pages = {2995--3052}, publisher = {European Mathematical Society}, title = {{Arithmetic and representation theory of wild character varieties}}, doi = {10.4171/JEMS/896}, volume = {21}, year = {2019}, } @article{105, abstract = {Clinical Utility Gene Card. 1. Name of Disease (Synonyms): Pontocerebellar hypoplasia type 9 (PCH9) and spastic paraplegia-63 (SPG63). 2. OMIM# of the Disease: 615809 and 615686. 3. Name of the Analysed Genes or DNA/Chromosome Segments: AMPD2 at 1p13.3. 4. OMIM# of the Gene(s): 102771.}, author = {Marsh, Ashley and Novarino, Gaia and Lockhart, Paul and Leventer, Richard}, journal = {European Journal of Human Genetics}, pages = {161--166}, publisher = {Springer Nature}, title = {{CUGC for pontocerebellar hypoplasia type 9 and spastic paraplegia-63}}, doi = {10.1038/s41431-018-0231-2}, volume = {27}, year = {2019}, }