Purpose. To define a three-dimensional (3D) vector method to describe the axial globe position in thyroid eye disease (TED). Methods. CT data from 59 patients with TED were collected and 3D images were reconstructed. A reference coordinate system was established, and the coordinates of the corneal apex and the eyeball center were calculated to obtain the globe vector [Formula: see text]. The me...

Obsessive Compulsive Disorder (OCD) affects 0.5-2% of young people many of whom are resistant to conventional treatments. This case study describes an 18-year-old male with OCD who first underwent cognitive behavioral therapy (CBT) for a 1-year period with a modest response (his OCD had shifted from severe to moderate). Within a year, his anxiety had deteriorated back to the severe range and he...

Shifted combinatorial optimization is a new nonlinear optimization framework which is a broad extension of standard combinatorial optimization, involving the choice of several feasible solutions at a time. This framework captures well studied and diverse problems ranging from so-called vulnerability problems to sharing and partitioning problems. In particular, every standard combinatorial optim...

In this article, we prove an asymptotic formula for mean values of long Dirichlet polynomials with higher order shifted divisor functions, assuming a smoothed additive conjecture functions. As consequence work, special cases conjectures Conrey-Keating [8] on functions as coefficients.

We use intermediate symplectic characters to give a proof and variations of Hopkins' conjecture, now proved by Hopkins Lai, on the number shifted plane partitions double staircase shape with bounded entries. In fact, we prove some character identities involving characters, find generating functions for such partitions. The key ingredients are bialternant formula which interpolates between those...

Let K be a totally real number field, π an irreducible cuspidal representation of GL2(K)\GL2(AK) with unitary central character, and χ a Hecke character of conductor q. Then L(1/2, π ⊗ χ) ≪ (Nq) 1 2 − 1 8 , where 0 6 θ 6 1/2 is any exponent towards the Ramanujan– Petersson conjecture (θ = 1/9 is admissible). The proof is based on a spectral decomposition of shifted convolution sums and a genera...

We suggest a new strategy for proving large N duality by interpreting GromovWitten, Donaldson-Thomas and Chern-Simons invariants of a Calabi-Yau threefold as different characterizations of the same holomorphic function. For the resolved conifold this function turns out to be the quantum Barnes function, a natural qdeformation of the classical one that in its turn generalizes Euler’s gamma funct...

A determinantal expansion due to Okada is used to derive both a deformation of Weyl’s denominator formula for the Lie algebra sp(2n) of the symplectic group and a further generalisation involving a product of the deformed denominator with a deformation of flagged characters of sp(2n). In each case the relevant expansion is expressed in terms of certain shifted sp(2n)-standard tableaux. It is th...

We give a product formula for the number of shifted plane partitions double staircase shape with bounded entries. This is first new example family shapes partition in many years. The proof based on theory lozenge tilings; specifically, we apply “free boundary” Kuo condensation due to Ciucu.