TY - GEN
AB - Soon, the genetic basis of most human Mendelian diseases will be solved. The next challenge will be to leverage this information to uncover basic mechanisms of disease and develop new therapies. To understand how this transformation is already beginning to unfold, we focus on the ciliopathies, a class of multi-organ diseases caused by disruption of the primary cilium. Through a convergence of data involving mutant gene discovery, proteomics, and cell biology, more than a dozen phenotypically distinguishable conditions are now united as ciliopathies. Sitting at the interface between simple and complex genetic conditions, these diseases provide clues to the future direction of human genetics.
AU - Gaia Novarino
AU - Akizu, Naiara
AU - Gleeson, Joseph G
ID - 2312
IS - 1
T2 - Cell
TI - Modeling human disease in humans: The ciliopathies
VL - 147
ER -
TY - CONF
AB - The binding of polarons, or its absence, is an old and subtle topic. After defining the model we state some recent theorems of ours. First, the transition from many-body collapse to the existence of a thermodynamic limit for N polarons occurs precisely at U = 2α, where U is the electronic Coulomb repulsion and α is the polaron coupling constant. Second, if U is large enough, there is no multi-polaron binding of any kind. We also discuss the Pekar-Tomasevich approximation to the ground state energy, which is valid for large α. Finally, we derive exact results, not reported before, about the one-dimensional toy model introduced by E. P. Gross.
AU - Frank, Rupert L
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Thomas, Lawrence E
ID - 2320
TI - Binding, stability, and non-binding of multi-polaron systems
ER -
TY - CONF
AB - We derive a sharp bound on the location of non-positive eigenvalues of Schrödinger operators on the half-line with complex-valued potentials.
AU - Frank, Rupert L
AU - Laptev, Ari
AU - Robert Seiringer
ID - 2321
TI - A sharp bound on eigenvalues of Schrödinger operators on the halfline with complex-valued potentials
VL - 214
ER -
TY - JOUR
AB - For an irreducible polynomial in at most two variables the problem of representing power-free integers is investigated.
AU - Timothy Browning
ID - 233
IS - 2
JF - Archiv der Mathematik
TI - Power-free values of polynomials
VL - 96
ER -
TY - JOUR
AB - We investigate the average order of the divisor function at values of binary cubic forms that are reducible over Q and discuss some applications.
AU - Timothy Browning
ID - 234
IS - 3
JF - Journal de Theorie des Nombres de Bordeaux
TI - The divisor problem for binary cubic forms
VL - 23
ER -